{
  "level": 163,
  "full_hecke_discriminant": 1598161946303102976,
  "full_hecke_discriminant_factorization": "2^15 * 3^2 * 65657 * 82536739",
  "full_hecke_discriminant_v3": 2,
  "T2_charpoly": "x^13+2*x^12-17*x^11-30*x^10+109*x^9+160*x^8-325*x^7-362*x^6+444*x^5+326*x^4-223*x^3-84*x^2+18*x",
  "T2_minpoly": "x^13+2*x^12-17*x^11-30*x^10+109*x^9+160*x^8-325*x^7-362*x^6+444*x^5+326*x^4-223*x^3-84*x^2+18*x",
  "T2_is_primitive_over_Q": true,
  "Q_adic_factor_degrees_at_3": [
    1,
    1,
    1,
    4,
    6
  ],
  "Q_adic_linear_factor_count": 3,
  "Z_T2_order_discriminant": 163036280407189371350898287149056,
  "Z_T2_order_discriminant_factorization": "2^15 * 3^8 * 65657 * 374083^2 * 82536739",
  "Z_T2_index_in_full_order": 10100241,
  "Z_T2_index_factorization": "3^3 * 374083",
  "Z_T2_index_v3": 3,
  "T2_monogenic_order_has_same_3local_fiber_as_full_order": false,
  "singular_factor_basis": {
    "basis": [
      "1",
      "T3",
      "T11"
    ],
    "basis_det_v3": 1,
    "all_T1_to_T13_have_integral_coordinates_in_this_basis": true,
    "coordinate_valuations_T1_to_T13": {
      "1": [
        0,
        null,
        null
      ],
      "2": [
        1,
        1,
        0
      ],
      "3": [
        null,
        0,
        null
      ],
      "4": [
        0,
        2,
        1
      ],
      "5": [
        0,
        0,
        0
      ],
      "6": [
        4,
        1,
        3
      ],
      "7": [
        0,
        1,
        0
      ],
      "8": [
        1,
        1,
        0
      ],
      "9": [
        1,
        0,
        1
      ],
      "10": [
        1,
        2,
        0
      ],
      "11": [
        null,
        null,
        0
      ],
      "12": [
        5,
        0,
        4
      ],
      "13": [
        0,
        0,
        1
      ]
    }
  },
  "p_adic_shifted_local_relation": {
    "unit_u_in_y_squared_eq_9u": "1 + 3 + 2*3^2 + 3^3 + 2*3^4 + 3^7 + 3^8 + 3^9 + 3^10 + 2*3^11 + 2*3^12 + 2*3^13 + 2*3^16 + 3^17 + 3^18 + 3^19 + 3^21 + 2*3^24 + 3^25 + 3^26 + 2*3^27 + 3^30 + 3^31 + 2*3^32 + 3^34 + 3^35 + 2*3^37 + 2*3^38 + 2*3^39 + 3^40 + 2*3^43 + 2*3^44 + 2*3^48 + 2*3^51 + 3^52 + 2*3^54 + 2*3^55 + 3^56 + 3^58 + 2*3^60 + 2*3^61 + 2*3^62 + 3^63 + 2*3^65 + 2*3^66 + 2*3^67 + 3^69 + 3^70 + 3^73 + 2*3^75 + 3^77 + 3^78 + 3^79 + 3^80 + 2*3^81 + 3^82 + 2*3^83 + 3^84 + 3^85 + 3^86 + 3^87 + 3^88 + 2*3^91 + 2*3^92 + 3^93 + 2*3^95 + 3^97 + 2*3^98 + 3^99 + 2*3^100 + 3^101 + 3^103 + 3^105 + 2*3^106 + 2*3^107 + 2*3^108 + 2*3^109 + 3^110 + 2*3^111 + 2*3^112 + 2*3^113 + 2*3^114 + 2*3^116 + 3^117 + 2*3^118 + 3^119 + 2*3^120 + 3^122 + 3^123 + 3^124 + 2*3^125 + 2*3^127 + 2*3^128 + 3^129 + 2*3^130 + 2*3^131 + 2*3^132 + 3^133 + 3^134 + 3^137 + 3^138 + 3^139 + 2*3^143 + 2*3^144 + 3^145 + 2*3^146 + 2*3^147 + 2*3^148 + 3^149 + 3^151 + 3^152 + 2*3^156 + 3^157 + 2*3^161 + 3^162 + 2*3^164 + 2*3^165 + 2*3^166 + 3^167 + 3^168 + 2*3^169 + 3^171 + 2*3^172 + 3^173 + 2*3^175 + 3^176 + 2*3^177 + 2*3^178 + 3^179 + 3^180 + 2*3^181 + 3^182 + 3^183 + 3^184 + 3^185 + 3^187 + 3^188 + 3^190 + 2*3^191 + 3^192 + 3^194 + 3^195 + 2*3^196 + 3^199 + 2*3^202 + 3^203 + 3^204 + 3^207 + 2*3^209 + 3^210 + 3^211 + 3^212 + 3^213 + 3^214 + 2*3^216 + O(3^218)",
    "precision": 220
  },
  "mod_3k_local_factor_data": {
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      "lifted_idempotent_e_in_basis_1_T3_T11": [
        18,
        7,
        12
      ],
      "etale_idempotent_complement_u0_in_basis_1_T3_T11": [
        10,
        20,
        15
      ],
      "local_generator_n_in_basis_1_T3_T11": [
        0,
        24,
        19
      ],
      "local_relation_n_squared_eq_a_u0_plus_b_n": {
        "a": 9,
        "b": 0
      },
      "shift_to_remove_linear_term": 0,
      "shifted_relation_y_squared_eq_9u": {
        "constant": 9,
        "u_mod_3k": 1
      },
      "local_factor_operator_images_in_basis_u0_n": {
        "2": [
          6,
          19
        ],
        "3": [
          9,
          6
        ],
        "7": [
          8,
          19
        ],
        "11": [
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          1
        ],
        "19": [
          3,
          15
        ],
        "43": [
          19,
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        ],
        "67": [
          1,
          23
        ],
        "163": [
          26,
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        ]
      },
      "T67_minus_T43_in_basis_u0_n": [
        9,
        3
      ],
      "maximal_ideal_generators_in_basis_u0_y": [
        [
          3,
          0
        ],
        [
          0,
          1
        ]
      ],
      "ideal_power_layers": [
        {
          "power": 1,
          "ideal_generators_in_basis_1_y": [
            [
              3,
              0
            ],
            [
              0,
              1
            ]
          ],
          "size": 243,
          "next_size": 27,
          "quotient_size": 9,
          "quotient_F3_dimension": 2
        },
        {
          "power": 2,
          "ideal_generators_in_basis_1_y": [
            [
              9,
              0
            ],
            [
              0,
              3
            ]
          ],
          "size": 27,
          "next_size": 3,
          "quotient_size": 9,
          "quotient_F3_dimension": 2
        },
        {
          "power": 3,
          "ideal_generators_in_basis_1_y": [
            [
              0,
              0
            ],
            [
              0,
              9
            ]
          ],
          "size": 3,
          "next_size": 1,
          "quotient_size": 3,
          "quotient_F3_dimension": 1
        }
      ]
    },
    "81": {
      "lifted_idempotent_e_in_basis_1_T3_T11": [
        72,
        61,
        12
      ],
      "etale_idempotent_complement_u0_in_basis_1_T3_T11": [
        10,
        20,
        69
      ],
      "local_generator_n_in_basis_1_T3_T11": [
        27,
        24,
        19
      ],
      "local_relation_n_squared_eq_a_u0_plus_b_n": {
        "a": 36,
        "b": 27
      },
      "shift_to_remove_linear_term": 54,
      "shifted_relation_y_squared_eq_9u": {
        "constant": 36,
        "u_mod_3k": 4
      },
      "local_factor_operator_images_in_basis_u0_n": {
        "2": [
          33,
          73
        ],
        "3": [
          36,
          33
        ],
        "7": [
          35,
          19
        ],
        "11": [
          0,
          1
        ],
        "19": [
          3,
          15
        ],
        "43": [
          46,
          20
        ],
        "67": [
          55,
          23
        ],
        "163": [
          80,
          0
        ]
      },
      "T67_minus_T43_in_basis_u0_n": [
        9,
        3
      ],
      "maximal_ideal_generators_in_basis_u0_y": [
        [
          3,
          0
        ],
        [
          27,
          1
        ]
      ],
      "ideal_power_layers": [
        {
          "power": 1,
          "ideal_generators_in_basis_1_y": [
            [
              3,
              0
            ],
            [
              0,
              1
            ]
          ],
          "size": 2187,
          "next_size": 243,
          "quotient_size": 9,
          "quotient_F3_dimension": 2
        },
        {
          "power": 2,
          "ideal_generators_in_basis_1_y": [
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              9,
              0
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            [
              0,
              3
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          ],
          "size": 243,
          "next_size": 27,
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          "quotient_F3_dimension": 2
        },
        {
          "power": 3,
          "ideal_generators_in_basis_1_y": [
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              27,
              0
            ],
            [
              0,
              9
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          ],
          "size": 27,
          "next_size": 3,
          "quotient_size": 9,
          "quotient_F3_dimension": 2
        },
        {
          "power": 4,
          "ideal_generators_in_basis_1_y": [
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              0,
              0
            ],
            [
              0,
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          ],
          "size": 3,
          "next_size": 1,
          "quotient_size": 3,
          "quotient_F3_dimension": 1
        }
      ]
    },
    "243": {
      "lifted_idempotent_e_in_basis_1_T3_T11": [
        72,
        61,
        12
      ],
      "etale_idempotent_complement_u0_in_basis_1_T3_T11": [
        172,
        182,
        231
      ],
      "local_generator_n_in_basis_1_T3_T11": [
        108,
        186,
        181
      ],
      "local_relation_n_squared_eq_a_u0_plus_b_n": {
        "a": 198,
        "b": 189
      },
      "shift_to_remove_linear_term": 216,
      "shifted_relation_y_squared_eq_9u": {
        "constant": 198,
        "u_mod_3k": 22
      },
      "local_factor_operator_images_in_basis_u0_n": {
        "2": [
          195,
          235
        ],
        "3": [
          198,
          195
        ],
        "7": [
          116,
          181
        ],
        "11": [
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        "19": [
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          15
        ],
        "43": [
          127,
          182
        ],
        "67": [
          136,
          185
        ],
        "163": [
          242,
          0
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      },
      "T67_minus_T43_in_basis_u0_n": [
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      ],
      "maximal_ideal_generators_in_basis_u0_y": [
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        ],
        [
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      ],
      "ideal_power_layers": [
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          "power": 1,
          "ideal_generators_in_basis_1_y": [
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          "size": 19683,
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        {
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          "size": 2187,
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          "quotient_F3_dimension": 2
        },
        {
          "power": 3,
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          "quotient_F3_dimension": 2
        },
        {
          "power": 4,
          "ideal_generators_in_basis_1_y": [
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          ],
          "size": 27,
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          "quotient_F3_dimension": 2
        },
        {
          "power": 5,
          "ideal_generators_in_basis_1_y": [
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              0
            ],
            [
              0,
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          ],
          "size": 3,
          "next_size": 1,
          "quotient_size": 3,
          "quotient_F3_dimension": 1
        }
      ]
    },
    "729": {
      "lifted_idempotent_e_in_basis_1_T3_T11": [
        72,
        547,
        255
      ],
      "etale_idempotent_complement_u0_in_basis_1_T3_T11": [
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        182,
        474
      ],
      "local_generator_n_in_basis_1_T3_T11": [
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        186,
        181
      ],
      "local_relation_n_squared_eq_a_u0_plus_b_n": {
        "a": 441,
        "b": 189
      },
      "shift_to_remove_linear_term": 459,
      "shifted_relation_y_squared_eq_9u": {
        "constant": 441,
        "u_mod_3k": 49
      },
      "local_factor_operator_images_in_basis_u0_n": {
        "2": [
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          721
        ],
        "3": [
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        ],
        "7": [
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        ],
        "11": [
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        "19": [
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        "67": [
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        "163": [
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      },
      "T67_minus_T43_in_basis_u0_n": [
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      "maximal_ideal_generators_in_basis_u0_y": [
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      "ideal_power_layers": [
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        {
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        {
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        },
        {
          "power": 6,
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              0,
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      ]
    }
  }
}