# Stored data for newform 504.6.a.i, downloaded from the LMFDB on 18 November 2025.
{"Nk2": 18144, "analytic_conductor": 80.83344518574224, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, 1], [3, -1], [7, 1]], "atkin_lehner_string": "+-+", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [504, 1, [127, 253, 281, 73], [1, 1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 345, "field_disc_factorization": [[3, 1], [5, 1], [23, 1]], "field_poly": [-86, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[5, [-1424, 82, 1]], [11, [16480, 340, 1]]], "hecke_orbit": 9, "hecke_orbit_code": 36028797119627768, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 6, "hecke_ring_index_factorization": [[2, 1], [3, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "504.6.a.i", "level": 504, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 3, 7], "level_radical": 42, "minimal_twist": "56.6.a.e", "nf_label": "2.2.345.1", "prim_orbit_index": 1, "qexp_display": "q+(-41-\\beta )q^{5}-7^{2}q^{7}+(-170-2\\beta )q^{11}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "5.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "504.6.a", "trace_display": [0, 0, -82, -98], "trace_hash": 818618709417656990, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.907", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.380", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "66.820", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.002", "prec": 17}, "traces": [0, 2, 0, 0, 0, -82, 0, -98, 0, 0, 0, -340, 0, 910, 0, 0, 0, -3216, 0, -674, 0, 0, 0, 1104, 0, 3322, 0, 0, 0, -8064, 0, -6212, 0, 0, 0, 4018, 0, -8512, 0, 0, 0, 1304, 0, -10004, 0, 0, 0, 12748, 0, 4802, 0, 0, 0, 11220, 0, 26360, 0, 0, 0, 12018, 0, 102738, 0, 0, 0, 43420, 0, 24136, 0, 0, 0, -89720, 0, -55588, 0, 0, 0, 16660, 0, 48824, 0, 0, 0, -35782, 0, 144276, 0, 0, 0, 18300, 0, -44590, 0, 0, 0, 120784, 0, -69984, 0, 0, 0, 237326, 0, 252196, 0, 0, 0, 300864, 0, 72760, 0, 0, 0, -65512, 0, 103776, 0, 0, 0, 157584, 0, -239462, 0, 0, 0, -389172, 0, 177896, 0, 0, 0, -298318, 0, 33026, 0, 0, 0, 335796, 0, 362546, 0, 0, 0, 6760, 0, 566604, 0, 0, 0, -521556, 0, -67128, 0, 0, 0, 689392, 0, 269310, 0, 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