# Stored data for newform 117.4.b.c, downloaded from the LMFDB on 30 January 2023. {"level_primes": [3, 13], "is_polredabs": true, "sato_tate_group": "3.2.1.d2", "rm_discs": [], "conrey_indexes": [64], "cm_discs": [-39], "trace_hash": 772154388136463795, "level_radical": 39, "hecke_ring_index_proved": true, "self_twist_type": 1, "related_objects": [], "prim_orbit_index": 2, "is_cm": true, "hecke_orbit": 3, "analytic_conductor": 6.9032234706716515, "inner_twist_count": 4, "field_disc_factorization": [[2, 4], [3, 1], [13, 2]], "is_rm": false, "char_order": 2, "level_is_square": false, "weight_parity": 1, "label": "117.4.b.c", "field_poly_is_real_cyclotomic": false, "is_self_twist": true, "is_twist_minimal": true, "minimal_twist": "117.4.b.c", "field_poly_is_cyclotomic": false, "dim": 4, "trace_zratio": {"__RealLiteral__": 0, "data": "0.886", "prec": 17}, "traces": [0, 4, 0, 0, -32, 0, 0, 0, 0, 0, 116, 0, 0, 0, 0, 0, -204, 0, 0, 0, 0, 0, 476, 0, 0, -500, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -884, 0, 0, 1808, 0, 0, 0, 0, 0, 1372, 0, 0, -676, 0, 0, -3232, 0, 0, 0, 0, 0, 0, 0, 0, 1632, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2924, 0, 0, 0, 0, 0, -2756, 0, 0, 0, 0, 0, -5140, 0, 0, 0, 0, 0, 6392, 0, 0, 3392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10252, 0, 0, -5324, 0, 0, 0, 0, 0, 0, 0, 0, 11492, 0, 0, 0, 0, 0, 0, 0, 0, -1360, 0, 0, 9476, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3736, 0, 0, -5916, 0, 0, 0, 0, 0, -12700, 0, 0, 8788, 0, 0, -14464, 0, 0, 0, 0, 0, 13148, 0, 0, 17720, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10976, 0, 0, 0, 0, 0, 0, 0, 0, -23464, 0, 0, 5408, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 34800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8848, 0, 0, 0, 0, 0, 0, 0, 0, 13624, 0, 0, 0, 0, 0, -40664, 0, 0, 0, 0, 0, 7076, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30844, 0, 0, 30536, 0, 0, 0, 0, 0, 0, 0, 0, 35828, 0, 0, -19652, 0, 0, 0, 0, 0, 17792, 0, 0, -6148, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6032, 0, 0, 0, 0, 0, 0, 0, 0, -31096, 0, 0, -20540, 0, 0, 0, 0, 0, 48716, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24276, 0, 0, 16784, 0, 0, 0, 0, 0, 27436, 0, 0, 0, 0, 0, -33184, 0, 0, 0, 0, 0, 0, 0, 0, -13988, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6020, 0, 0, 0, 0, 0, 6364, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27136, 0, 0, 63296, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 52432, 0, 0, 0, 0, 0, 0, 0, 0, -45280, 0, 0, 0, 0, 0, 24344, 0, 0, 0, 0, 0, -76240, 0, 0, -60436, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7540, 0, 0, 0, 0, 0, 5732, 0, 0, 0, 0, 0, 74936, 0, 0, 0, 0, 0, 39788, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35984, 0, 0, 0, 0, 0, 0, 0, 0, -16264, 0, 0, -19604, 0, 0, 64592, 0, 0, 0, 0, 0, -48668, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 95984, 0, 0, -186276, 0, 0, 0, 0, 0, 10880, 0, 0, 0, 0, 0, 98324, 0, 0, 0, 0, 0, 26260, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 57572, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -102016, 0, 0, -231608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47532, 0, 0, 29888, 0, 0, 0, 0, 0, 127700, 0, 0, 0, 0, 0, 101660, 0, 0, 0, 0, 0, 0, 0, 0, 73880, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50596, 0, 0, 0, 0, 0, 0, 0, 0, -102088, 0, 0, -70304, 0, 0, 0, 0, 0, 0, 0, 0, -11224, 0, 0, -92208, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 46268, 0, 0, 0, 0, 0, 37492, 0, 0, -116272, 0, 0, 147932, 0, 0, 0, 0, 0, -141760, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 154088, 0, 0, 0, 0, 0, 104480, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -159940, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31400, 0, 0, -69972, 0, 0, 0, 0, 0, 102544, 0, 0, -177112, 0, 0, -80912, 0, 0, 0, 0, 0, 65996, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 246264, 0, 0, 149408, 0, 0, 0, 0, 0, 0, 0, 0, 77740, 0, 0, -100144, 0, 0, 0, 0, 0, -97556, 0, 0, -82784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -156196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 93280, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -166132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 215288, 0, 0, 0, 0, 0, 0, 0, 0, -205804, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17952, 0, 0, 0, 0, 0, 215152, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 143252, 0, 0, 119164, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -108992, 0, 0, 46736, 0, 0, 0, 0, 0, -229672, 0, 0, 0, 0, 0, -93088, 0, 0, 0, 0, 0, -86536, 0, 0, 69368], "hecke_ring_index_factorization": [[2, 2], [3, 2]], "nf_label": "4.0.8112.1", "field_poly": [3, 0, 5, 0, 1], "has_non_self_twist": 1, "char_values": [117, 2, [92, 28], [2, 1]], "Nk2": 1872, "field_poly_root_of_unity": 0, "analytic_rank": 0, "char_orbit_label": "b", "weight": 4, "trace_display": [0, 0, 0, 0], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": false, "hecke_ring_index": 36, "level_is_prime": false, "char_is_minimal": true, "qexp_display": "q+\\beta _{1}q^{2}+(-8-\\beta _{2})q^{4}+(-2\\beta _{1}+\\beta _{3})q^{5}+\\cdots", "self_twist_discs": [-39], "char_is_real": true, "field_disc": 8112, "level_is_prime_power": false, "relative_dim": 4, "hecke_cutters": [[2, [243, 0, 32, 0, 1]]], "space_label": "117.4.b", "level": 117, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 39, 4, -1, 2, -39], [1, 1, 3, 2, -1, 2, 0], [1, 1, 13, 2, 1, 2, 0]], "char_degree": 1, "char_conductor": 13, "char_orbit_index": 2, "hecke_ring_generator_nbound": 2, "hecke_orbit_code": 9007268041326709, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.628", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "169.455", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "8842.114", "prec": 27}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "atkin_lehner_string": null, "atkin_lehner_eigenvals": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "fricke_eigenval": null, "artin_degree": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [-8, 0, -1, 0], [0, -2, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, -1, 0, 1], [0, 0, 0, 0], [29, 0, 17, 0], [0, -8, 0, 3], [0, 0, 0, 0], [0, 0, 13, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-51, 0, 8, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 30, 0, -9], [0, 0, 0, 0], [119, 0, 53, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-125, 0, -46, 0], [0, 13, 0, -13], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -51, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-221, 0, -29, 0], [0, -50, 0, 23], [0, 0, 0, 0], [452, 0, 0, 0], [0, 108, 0, -29], [0, 0, 0, 0], [0, 0, 0, 0], [0, 76, 0, 23], [0, 0, 0, 0], [343, 0, 0, 0], [0, -171, 0, 46], [0, 0, 0, 0], [-169, 0, -104, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-808, 0, -172, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 160, 0, 1], [0, 0, 0, 0], [0, 0, -262, 0], [0, 0, 0, 0], [0, 0, 0, 0], [408, 0, 115, 0], [0, -182, 0, 13], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -140, 0, -43], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 116, 0], [0, -10, 0, -43], [0, 0, 0, 0], [731, 0, 395, 0], [0, 208, 0, -51], [0, 0, 0, 0], [0, 0, 0, 0], [0, 452, 0, 0], [0, 0, 0, 0], [-689, 0, -119, 0], [0, -194, 0, -61], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-1285, 0, 269, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 343, 0, 0], [0, 0, 0, 0], [1598, 0, 493, 0]]}