{
  "level": 163,
  "cm_skeleton": {
    "pair_factor": "Z_3[eta]/(eta^2 - 3 eta)",
    "objects": [
      "B0",
      "R",
      "B3"
    ],
    "verified_branch_map_relations_mod_3^4": {
      "modulus": 81,
      "node_size": 2187,
      "verified": true,
      "failures": []
    },
    "exact_cross_branch_hom_argument": {
      "B0_to_B3": "An R-linear map is multiplication by lambda with 3*lambda = 0 in Z_3, hence lambda = 0.",
      "B3_to_B0": "An R-linear map is multiplication by lambda with 3*lambda = 0 in Z_3, hence lambda = 0."
    },
    "finite_truncation_ghost_maps": [
      {
        "modulus": 3,
        "solutions_to_3lambda_eq_0_mod_3k": [
          0,
          1,
          2
        ],
        "count": 3
      },
      {
        "modulus": 9,
        "solutions_to_3lambda_eq_0_mod_3k": [
          0,
          3,
          6
        ],
        "count": 3
      },
      {
        "modulus": 27,
        "solutions_to_3lambda_eq_0_mod_3k": [
          0,
          9,
          18
        ],
        "count": 3
      },
      {
        "modulus": 81,
        "solutions_to_3lambda_eq_0_mod_3k": [
          0,
          27,
          54
        ],
        "count": 3
      }
    ]
  },
  "residue_machine": {
    "cyclic_basis": [
      "w",
      "T3 w",
      "T11 w"
    ],
    "flag": [
      "0",
      "<T11 w>",
      "<T3 w, T11 w>",
      "<w, T3 w, T11 w>"
    ],
    "operator_flag_data_mod_3": {
      "3": {
        "preserves_socle_line": true,
        "preserves_middle_plane": true,
        "top_scalar": 0,
        "middle_scalar": 1,
        "bottom_scalar": 0,
        "matrix_mod_3": [
          [
            0,
            0,
            0
          ],
          [
            1,
            1,
            0
          ],
          [
            0,
            0,
            0
          ]
        ]
      },
      "7": {
        "preserves_socle_line": true,
        "preserves_middle_plane": true,
        "top_scalar": 2,
        "middle_scalar": 2,
        "bottom_scalar": 2,
        "matrix_mod_3": [
          [
            2,
            0,
            0
          ],
          [
            0,
            2,
            0
          ],
          [
            1,
            0,
            2
          ]
        ]
      },
      "11": {
        "preserves_socle_line": true,
        "preserves_middle_plane": true,
        "top_scalar": 0,
        "middle_scalar": 0,
        "bottom_scalar": 0,
        "matrix_mod_3": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            1,
            0,
            0
          ]
        ]
      },
      "19": {
        "preserves_socle_line": true,
        "preserves_middle_plane": true,
        "top_scalar": 0,
        "middle_scalar": 2,
        "bottom_scalar": 0,
        "matrix_mod_3": [
          [
            0,
            0,
            0
          ],
          [
            2,
            2,
            0
          ],
          [
            0,
            0,
            0
          ]
        ]
      },
      "43": {
        "preserves_socle_line": true,
        "preserves_middle_plane": true,
        "top_scalar": 1,
        "middle_scalar": 2,
        "bottom_scalar": 1,
        "matrix_mod_3": [
          [
            1,
            0,
            0
          ],
          [
            1,
            2,
            0
          ],
          [
            2,
            0,
            1
          ]
        ]
      },
      "67": {
        "preserves_socle_line": true,
        "preserves_middle_plane": true,
        "top_scalar": 1,
        "middle_scalar": 2,
        "bottom_scalar": 1,
        "matrix_mod_3": [
          [
            1,
            0,
            0
          ],
          [
            1,
            2,
            0
          ],
          [
            2,
            0,
            1
          ]
        ]
      },
      "163": {
        "preserves_socle_line": true,
        "preserves_middle_plane": true,
        "top_scalar": 2,
        "middle_scalar": 1,
        "bottom_scalar": 2,
        "matrix_mod_3": [
          [
            2,
            0,
            0
          ],
          [
            2,
            1,
            0
          ],
          [
            0,
            0,
            2
          ]
        ]
      }
    },
    "composition_factor_scalars": {
      "bottom": {
        "3": 0,
        "7": 2,
        "11": 0,
        "19": 0,
        "43": 1,
        "67": 1,
        "163": 2
      },
      "middle": {
        "3": 1,
        "7": 2,
        "11": 0,
        "19": 2,
        "43": 2,
        "67": 2,
        "163": 1
      },
      "top": {
        "3": 0,
        "7": 2,
        "11": 0,
        "19": 0,
        "43": 1,
        "67": 1,
        "163": 2
      }
    },
    "all_operators_preserve_flag": true
  },
  "projective_unit_group": {
    "all_classes": [
      [
        1,
        1,
        0
      ],
      [
        1,
        1,
        1
      ],
      [
        1,
        1,
        2
      ],
      [
        1,
        2,
        0
      ],
      [
        1,
        2,
        1
      ],
      [
        1,
        2,
        2
      ]
    ],
    "orders": {
      "[1, 1, 0]": 1,
      "[1, 1, 1]": 3,
      "[1, 1, 2]": 3,
      "[1, 2, 0]": 2,
      "[1, 2, 1]": 6,
      "[1, 2, 2]": 6
    },
    "named_heegner_classes": {
      "T7": {
        "raw_residue_coords_in_[e7,epair,n]": [
          2,
          2,
          2
        ],
        "projective_class_normalized_to_first_coordinate_1": [
          1,
          1,
          1
        ],
        "order": 3
      },
      "T43": {
        "raw_residue_coords_in_[e7,epair,n]": [
          2,
          1,
          1
        ],
        "projective_class_normalized_to_first_coordinate_1": [
          1,
          2,
          2
        ],
        "order": 6
      },
      "T67": {
        "raw_residue_coords_in_[e7,epair,n]": [
          2,
          1,
          1
        ],
        "projective_class_normalized_to_first_coordinate_1": [
          1,
          2,
          2
        ],
        "order": 6
      },
      "T163": {
        "raw_residue_coords_in_[e7,epair,n]": [
          1,
          2,
          0
        ],
        "projective_class_normalized_to_first_coordinate_1": [
          1,
          2,
          0
        ],
        "order": 2
      }
    },
    "generator": {
      "name": "T43",
      "class": [
        1,
        2,
        2
      ],
      "powers": [
        [
          1,
          1,
          0
        ],
        [
          1,
          2,
          2
        ],
        [
          1,
          1,
          2
        ],
        [
          1,
          2,
          0
        ],
        [
          1,
          1,
          1
        ],
        [
          1,
          2,
          1
        ]
      ],
      "generates_all_projective_classes": true
    }
  },
  "stable_interaction_quotient": {
    "verified_up_to_length": 8,
    "all_nonzero_words_reduce_to_four_normal_forms": true,
    "bad_words": [],
    "normal_forms": [
      "u^m e0",
      "u^m e3",
      "u^m x",
      "u^m y"
    ],
    "pair_transition_table": [
      {
        "left": "e0",
        "right": "e0",
        "result": {
          "u_power_added": 0,
          "symbol": "e0"
        }
      },
      {
        "left": "e0",
        "right": "e3",
        "result": "0"
      },
      {
        "left": "e0",
        "right": "x",
        "result": {
          "u_power_added": 0,
          "symbol": "x"
        }
      },
      {
        "left": "e0",
        "right": "y",
        "result": "0"
      },
      {
        "left": "e3",
        "right": "e0",
        "result": "0"
      },
      {
        "left": "e3",
        "right": "e3",
        "result": {
          "u_power_added": 0,
          "symbol": "e3"
        }
      },
      {
        "left": "e3",
        "right": "x",
        "result": "0"
      },
      {
        "left": "e3",
        "right": "y",
        "result": {
          "u_power_added": 0,
          "symbol": "y"
        }
      },
      {
        "left": "x",
        "right": "e0",
        "result": "0"
      },
      {
        "left": "x",
        "right": "e3",
        "result": {
          "u_power_added": 0,
          "symbol": "x"
        }
      },
      {
        "left": "x",
        "right": "x",
        "result": "0"
      },
      {
        "left": "x",
        "right": "y",
        "result": {
          "u_power_added": 1,
          "symbol": "e3"
        }
      },
      {
        "left": "y",
        "right": "e0",
        "result": {
          "u_power_added": 0,
          "symbol": "y"
        }
      },
      {
        "left": "y",
        "right": "e3",
        "result": "0"
      },
      {
        "left": "y",
        "right": "x",
        "result": {
          "u_power_added": 1,
          "symbol": "e0"
        }
      },
      {
        "left": "y",
        "right": "y",
        "result": "0"
      }
    ],
    "sample_reductions": {
      "e0": {
        "zero": false,
        "u_power": 0,
        "normal_form": "e0"
      },
      "e3": {
        "zero": false,
        "u_power": 0,
        "normal_form": "e3"
      },
      "x": {
        "zero": false,
        "u_power": 0,
        "normal_form": "x"
      },
      "y": {
        "zero": false,
        "u_power": 0,
        "normal_form": "y"
      },
      "e0 e0": {
        "zero": false,
        "u_power": 0,
        "normal_form": "e0"
      },
      "e0 x": {
        "zero": false,
        "u_power": 0,
        "normal_form": "x"
      },
      "e3 e3": {
        "zero": false,
        "u_power": 0,
        "normal_form": "e3"
      },
      "e3 y": {
        "zero": false,
        "u_power": 0,
        "normal_form": "y"
      },
      "x e3": {
        "zero": false,
        "u_power": 0,
        "normal_form": "x"
      },
      "x y": {
        "zero": false,
        "u_power": 1,
        "normal_form": "e3"
      },
      "y e0": {
        "zero": false,
        "u_power": 0,
        "normal_form": "y"
      },
      "y x": {
        "zero": false,
        "u_power": 1,
        "normal_form": "e0"
      }
    }
  }
}