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      "level": 163,
      "dim_S": 13,
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        "linear_factor_count": 3,
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      "three_linear_factor_coordinates": {
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      "level": 829,
      "dim_S": 68,
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      "t2_charpoly_degree": 68,
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*3^17+3^18+3^19+2*3^20+3^22+2*3^23+3^24+2*3^26+2*3^28+2*3^29+3^30+2*3^31+3^34+3^36+3^38+3^39+2*3^41+3^43+3^44+3^46+2*3^47+3^50+2*3^53+3^55+2*3^56+3^59+2*3^60+2*3^61+2*3^62+2*3^64+3^66+2*3^67+2*3^68+2*3^71+3^72+3^73+2*3^74+3^77+3^78+3^79+O(3^80))*x+1+3+2*3^2+2*3^3+2*3^5+3^6+2*3^8+3^9+2*3^10+3^11+3^12+2*3^13+3^14+2*3^15+2*3^16+2*3^19+2*3^20+3^21+3^24+2*3^25+3^27+3^28+3^29+2*3^31+3^32+2*3^34+2*3^36+3^37+3^39+3^40+2*3^42+2*3^45+2*3^47+3^48+3^49+3^52+2*3^53+2*3^54+3^55+2*3^56+2*3^57+3^58+2*3^60+3^61+3^62+2*3^63+3^65+3^66+2*3^68+3^69+3^71+3^72+3^73+2*3^75+3^76+2*3^77+2*3^78+3^79+O(3^80)"
          }
        ],
        "linear_factor_count": 3,
        "linear_root_residues": [
          {
            "3": 0,
            "9": 3,
            "27": 12,
            "81": 12
          },
          {
            "3": 0,
            "9": 0,
            "27": 0,
            "81": 27
          },
          {
            "3": 0,
            "9": 0,
            "27": 0,
            "81": 0
          }
        ],
        "factor_degree_multiset": [
          1,
          1,
          1,
          2,
          3,
          4,
          9,
          14,
          33
        ]
      },
      "three_linear_factor_coordinates": {
        "available": false,
        "reason": "T_2 is not primitive enough over Q to recover Hecke operators from its powers"
      }
    },
    {
      "level": 2053,
      "dim_S": 170,
      "qdim3_signature": {
        "dim_Q": 3,
        "status": "canonical",
        "independent_I_E_N": true,
        "E_minpoly": "x^2 + 2*x",
        "N_minpoly": "x^2",
        "E_idempotent": true,
        "N_nilpotent": true,
        "orthogonal": true
      },
      "t2_charpoly_degree": 170,
      "t2_root_counts_mod_3k": {
        "3": 1,
        "9": 3,
        "27": 9,
        "81": 9
      },
      "q3_factor_signature": {
        "precision": 80,
        "factor_rows": [
          {
            "degree": 1,
            "multiplicity": 1,
            "poly": "(1+O(3^80))*x+2*3+3^5+3^6+2*3^7+2*3^8+3^9+3^14+3^15+3^18+3^19+2*3^20+3^21+3^22+3^23+2*3^24+2*3^26+2*3^27+3^29+2*3^30+3^31+2*3^32+3^34+2*3^35+2*3^36+3^39+2*3^40+2*3^41+2*3^42+3^44+3^46+2*3^47+3^48+2*3^49+3^50+3^51+2*3^52+2*3^53+3^54+2*3^55+2*3^56+2*3^57+2*3^59+2*3^60+3^62+3^63+3^64+3^65+3^67+2*3^68+2*3^69+2*3^70+2*3^71+2*3^72+3^73+3^74+2*3^76+3^77+2*3^78+2*3^79+O(3^80)",
            "root_residues": {
              "3": 0,
              "9": 3,
              "27": 21,
              "81": 75
            }
          },
          {
            "degree": 2,
            "multiplicity": 1,
            "poly": "(1+O(3^80))*x^2+(2+3+2*3^2+3^9+3^10+3^11+2*3^12+2*3^13+3^14+2*3^15+3^16+2*3^17+3^19+3^20+3^22+2*3^23+2*3^24+2*3^25+3^26+2*3^27+2*3^28+2*3^29+3^30+3^31+2*3^32+3^34+3^35+3^37+3^38+2*3^40+2*3^41+2*3^42+2*3^43+2*3^46+2*3^47+3^48+3^51+2*3^52+2*3^54+2*3^55+3^59+3^60+3^62+2*3^64+2*3^68+3^69+2*3^73+3^78+3^79+O(3^80))*x+2+2*3+2*3^5+2*3^6+2*3^8+2*3^9+3^10+3^13+3^14+2*3^15+3^16+2*3^17+2*3^18+3^19+3^20+2*3^21+3^23+2*3^24+2*3^27+3^28+3^29+2*3^32+2*3^35+3^41+2*3^43+3^46+3^47+2*3^48+2*3^50+3^51+2*3^52+2*3^53+2*3^54+2*3^55+2*3^59+2*3^60+2*3^62+2*3^63+2*3^64+3^65+3^66+2*3^67+3^68+2*3^69+3^71+3^72+2*3^73+2*3^74+3^76+3^78+2*3^79+O(3^80)"
          },
          {
            "degree": 2,
            "multiplicity": 1,
            "poly": "(1+O(3^80))*x^2+(1+2*3^2+3^3+2*3^5+3^6+2*3^7+2*3^8+2*3^9+2*3^10+3^11+3^12+3^13+2*3^14+3^15+3^16+2*3^17+2*3^20+3^21+2*3^23+2*3^24+2*3^25+2*3^28+2*3^29+2*3^31+2*3^34+3^36+3^38+3^39+3^40+2*3^41+3^43+3^45+3^46+2*3^47+3^48+3^49+2*3^50+2*3^51+3^52+2*3^54+2*3^55+3^56+2*3^59+2*3^61+3^63+2*3^66+2*3^67+2*3^68+2*3^69+2*3^70+2*3^71+2*3^72+3^73+3^74+2*3^79+O(3^80))*x+2+3+3^2+2*3^3+2*3^4+3^7+3^9+2*3^10+3^11+2*3^13+3^17+3^18+3^19+2*3^20+2*3^22+2*3^23+2*3^24+2*3^25+3^26+3^28+3^30+2*3^32+2*3^33+2*3^35+3^36+2*3^37+2*3^38+3^40+2*3^41+3^42+2*3^43+3^46+3^47+2*3^48+2*3^49+2*3^51+2*3^52+3^53+3^54+3^59+2*3^60+2*3^61+2*3^62+2*3^63+2*3^64+2*3^65+2*3^66+2*3^67+3^71+3^73+2*3^75+3^76+3^78+O(3^80)"
          },
          {
            "degree": 2,
            "multiplicity": 1,
            "poly": "(1+O(3^80))*x^2+(3+2*3^2+2*3^3+3^5+2*3^9+3^10+3^11+3^12+2*3^14+3^15+3^16+3^19+3^20+2*3^23+3^24+2*3^25+2*3^26+2*3^29+2*3^30+2*3^31+2*3^32+3^33+2*3^35+2*3^36+3^37+3^38+2*3^39+3^42+3^43+3^44+2*3^47+3^50+2*3^51+2*3^52+3^53+3^55+2*3^56+3^58+2*3^59+3^61+3^62+2*3^65+2*3^66+2*3^67+2*3^68+3^69+3^70+2*3^71+2*3^72+2*3^73+3^74+2*3^77+2*3^79+O(3^80))*x+3^2+3^3+2*3^5+2*3^6+3^7+2*3^8+3^9+2*3^10+2*3^11+2*3^12+3^13+2*3^14+3^15+2*3^17+3^18+3^21+3^22+3^23+3^25+2*3^26+3^27+3^28+2*3^29+2*3^30+3^31+2*3^33+2*3^35+2*3^36+3^37+2*3^38+2*3^39+2*3^40+2*3^43+3^44+3^46+3^47+3^48+3^51+3^53+2*3^55+3^56+3^57+3^60+3^61+2*3^62+2*3^64+2*3^65+2*3^67+2*3^68+2*3^69+2*3^72+2*3^74+2*3^75+2*3^77+2*3^79+O(3^80)"
          },
          {
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          {
            "degree": 80,
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          }
        ],
        "linear_factor_count": 1,
        "linear_root_residues": [
          {
            "3": 0,
            "9": 3,
            "27": 21,
            "81": 75
          }
        ],
        "factor_degree_multiset": [
          1,
          2,
          2,
          2,
          4,
          5,
          6,
          8,
          28,
          32,
          80
        ]
      },
      "three_linear_factor_coordinates": {
        "available": false,
        "reason": "level does not have exactly three linear Q_3 factors"
      }
    }
  ],
  "moduli": [
    3,
    9,
    27,
    81
  ],
  "precision": 80
}