{
  "family": "E_k(1,χ₈) through k = 2 in the weight direction; a_n(X) = Σ_{d|n} χ₈(d)·d·⟨d⟩^X",
  "pseudocharacter": "𝒯_X(Frob_ℓ) = 1 + χ₈(ℓ)·ℓ^{1+X} for ℓ ≠ 11 — the sum of the two Jordan–Hölder characters 1 and χ₈·χ_cyc, deformed in the weight direction",
  "jordan_holder_characters": {
    "3": {
      "char_1": 1,
      "char_2": 8,
      "distinct_here": true
    },
    "5": {
      "char_1": 1,
      "char_2": 6,
      "distinct_here": true
    },
    "7": {
      "char_1": 1,
      "char_2": 7,
      "distinct_here": true
    },
    "13": {
      "char_1": 1,
      "char_2": 9,
      "distinct_here": true
    },
    "17": {
      "char_1": 1,
      "char_2": 6,
      "distinct_here": true
    },
    "19": {
      "char_1": 1,
      "char_2": 3,
      "distinct_here": true
    },
    "23": {
      "char_1": 1,
      "char_2": 1,
      "distinct_here": false
    },
    "29": {
      "char_1": 1,
      "char_2": 4,
      "distinct_here": true
    }
  },
  "characters_distinct": true,
  "distinctness_witness_prime": 3,
  "canonical_eisenstein_quotient": true,
  "why_it_matters": "PC-001 §4: a generic auxiliary Galois representation does not provide a one-dimensional Eisenstein quotient. Distinct Jordan–Hölder characters make the residual representation multiplicity-free, so the quotient exists and is canonical — it cannot be chosen per partner.",
  "trace_matches_q_expansion": true,
  "chi8_agrees_with_RUN077": {
    "1": true,
    "3": true,
    "5": true,
    "7": true
  },
  "refinement": {
    "a_11": -10,
    "hecke_polynomial": "U² + 10U − 11 = (U − 1)(U + 11)",
    "roots": [
      1,
      -11
    ],
    "slopes": {
      "1": 0,
      "-11": 1
    },
    "critical_slope_1_root": -11,
    "critical_branch_is_chi8_chi_cyc": true
  },
  "trace_jet_mod_X2": {
    "3": {
      "constant": 1329,
      "log_11": 847,
      "X_coefficient": 121,
      "constant_is_the_q_expansion": true
    },
    "5": {
      "constant": 1327,
      "log_11": 44,
      "X_coefficient": 1111,
      "constant_is_the_q_expansion": true
    },
    "7": {
      "constant": 8,
      "log_11": 220,
      "X_coefficient": 209,
      "constant_is_the_q_expansion": true
    },
    "13": {
      "constant": 1319,
      "log_11": 374,
      "X_coefficient": 462,
      "constant_is_the_q_expansion": true
    },
    "17": {
      "constant": 18,
      "log_11": 935,
      "X_coefficient": 1254,
      "constant_is_the_q_expansion": true
    },
    "19": {
      "constant": 1313,
      "log_11": 517,
      "X_coefficient": 825,
      "constant_is_the_q_expansion": true
    },
    "23": {
      "constant": 24,
      "log_11": 1111,
      "X_coefficient": 264,
      "constant_is_the_q_expansion": true
    },
    "29": {
      "constant": 1303,
      "log_11": 517,
      "X_coefficient": 979,
      "constant_is_the_q_expansion": true
    }
  },
  "jet_precision": "11^3",
  "jet_nontrivial": true,
  "log_lands_in_11Z_11": true,
  "log_is_additive": true,
  "label": "COMPUTED_HERE",
  "agrees": true
}