# Stored data for newform 378.3.b.c, downloaded from the LMFDB on 19 April 2024.
{"label": "378.3.b.c", "space_label": "378.3.b", "level": 378, "weight": 3, "hecke_orbit": 3, "hecke_orbit_code": 9007268024549754, "dim": 8, "is_polredabs": true, "nf_label": "8.0.157351936.1", "trace_hash": 1049776537257963150, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [3969, 0, 9828, 0, 2374, 0, 100, 0, 1]]], "qexp_display": "q-\\beta _{4}q^{2}-2q^{4}+(-\\beta _{1}+\\beta _{4}-\\beta _{6}+\\cdots)q^{5}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 3, "char_orbit_label": "b", "char_is_real": true, "Nk2": 3402, "analytic_conductor": 10.299753992819223, "hecke_ring_index": 5184, "level_radical": 42, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.510", "prec": 17}, "analytic_rank_proved": true, "char_values": [378, 2, [29, 325], [1, 2]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [323], "field_disc": 157351936, "field_disc_factorization": [[2, 16], [7, 4]], "field_poly": [16, 0, 0, 0, 1, 0, 0, 0, 1], "hecke_ring_index_factorization": [[2, 6], [3, 4]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.087", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "310.884", "prec": 24}, {"__RealLiteral__": 0, "data": "124.461", "prec": 24}, {"__RealLiteral__": 0, "data": "23184.949", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "2.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 8, 0, 0, -16, 0, 0, 0, 0, 0, 16, 0, 0, -40, 0, 0, 32, 0, 0, 40, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, -16, 0, 0, -8, 0, 0, -32, 0, 0, 40, 0, 0, -64, 0, 0, 56, 0, 0, 80, 0, 0, 56, 0, 0, 112, 0, 0, -88, 0, 0, -64, 0, 0, 240, 0, 0, -112, 0, 0, -288, 0, 0, -80, 0, 0, -424, 0, 0, 144, 0, 0, 200, 0, 0, 32, 0, 0, 56, 0, 0, 288, 0, 0, 600, 0, 0, 0, 0, 0, -320, 0, 0, -288, 0, 0, -216, 0, 0, 0, 0, 0, 128, 0, 0, -32, 0, 0, 264, 0, 0, 80, 0, 0, -136, 0, 0, -336, 0, 0, -168, 0, 0, 32, 0, 0, -744, 0, 0, -64, 0, 0, 664, 0, 0, 16, 0, 0, 648, 0, 0, 112, 0, 0, -536, 0, 0, 64, 0, 0, 712, 0, 0, 32, 0, 0, 56, 0, 0, -80, 0, 0, 224, 0, 0, 480, 0, 0, -496, 0, 0, 128, 0, 0, -1064, 0, 0, 272, 0, 0, -680, 0, 0, -112, 0, 0, 208, 0, 0, -512, 0, 0, -1080, 0, 0, -160, 0, 0, 784, 0, 0, 384, 0, 0, 56, 0, 0, -112, 0, 0, 1576, 0, 0, -80, 0, 0, 1392, 0, 0, -224, 0, 0, -552, 0, 0, 112, 0, 0, -152, 0, 0, 176, 0, 0, 784, 0, 0, -336, 0, 0, -560, 0, 0, 128, 0, 0, -336, 0, 0, -1664, 0, 0, -816, 0, 0, -480, 0, 0, -400, 0, 0, 400, 0, 0, 904, 0, 0, 224, 0, 0, 408, 0, 0, 1056, 0, 0, 96, 0, 0, 576, 0, 0, -1736, 0, 0, 1008, 0, 0, 0, 0, 0, 160, 0, 0, -1344, 0, 0, 240, 0, 0, -432, 0, 0, 848, 0, 0, -736, 0, 0, -224, 0, 0, 2528, 0, 0, -288, 0, 0, -1016, 0, 0, -608, 0, 0, 968, 0, 0, -400, 0, 0, 0, 0, 0, -512, 0, 0, 2880, 0, 0, -64, 0, 0, -256, 0, 0, -816, 0, 0, -1032, 0, 0, -112, 0, 0, 688, 0, 0, 368, 0, 0, -120, 0, 0, -576, 0, 0, -552, 0, 0, -576, 0, 0, -728, 0, 0, -1200, 0, 0, -2144, 0, 0, -304, 0, 0, 1184, 0, 0, 0, 0, 0, 2848, 0, 0, 560, 0, 0, -1760, 0, 0, 640, 0, 0, 2936, 0, 0, 448, 0, 0, -1312, 0, 0, 576, 0, 0, 728, 0, 0, 1664, 0, 0, -2456, 0, 0, 432, 0, 0, -496, 0, 0, 2352, 0, 0, -2160, 0, 0, 0, 0, 0, 1224, 0, 0, -672, 0, 0, -1536, 0, 0, -256, 0, 0, 504, 0, 0, -880, 0, 0, -560, 0, 0, 64, 0, 0, 1632, 0, 0, -1776, 0, 0, 2008, 0, 0, -528, 0, 0, -1760, 0, 0, 112, 0, 0, -1672, 0, 0, -160, 0, 0, 1320, 0, 0, 480, 0, 0, 1744, 0, 0, 272, 0, 0, 784, 0, 0, -2976, 0, 0, 696, 0, 0, 672, 0, 0, -920, 0, 0, -528, 0, 0, 360, 0, 0, 336, 0, 0, -960, 0, 0, -272, 0, 0, -328, 0, 0, -64, 0, 0, -472, 0, 0, 2176, 0, 0, 560, 0, 0, 1488, 0, 0, -776, 0, 0, 1376, 0, 0, -968, 0, 0, 128, 0, 0, 2840, 0, 0, -1008, 0, 0, 1680, 0, 0, -1328, 0, 0, -2064, 0, 0, -144, 0, 0, 2224, 0, 0, -32, 0, 0, -1232, 0, 0, 2688, 0, 0, 2056, 0, 0, -1296, 0, 0, -2152, 0, 0, -3504, 0, 0, -1024, 0, 0, -224, 0, 0, -2568, 0, 0, 352, 0, 0, 504, 0, 0, 1072, 0, 0, -1496, 0, 0, -1824, 0, 0, -280, 0, 0, -128, 0, 0, 784, 0, 0, 1744, 0, 0, 440, 0, 0, -1424, 0, 0, -80, 0, 0, 672, 0, 0, -984, 0, 0, -64, 0, 0, -304, 0, 0, 448, 0, 0, 2704, 0, 0, -112, 0, 0, 1288, 0, 0, 3648, 0, 0, 280, 0, 0, 160, 0, 0, 424, 0, 0, 2640, 0, 0, 1080, 0, 0, -448, 0, 0, 3272, 0, 0, 48, 0, 0, -776, 0, 0, -960, 0, 0, -3024, 0, 0, -2624, 0, 0, -336, 0, 0, 992, 0, 0, 1848, 0, 0, -1568, 0, 0, -2704, 0, 0, -256, 0, 0, -1216, 0, 0, -672, 0, 0, -3288, 0, 0, 2128, 0, 0, -1840, 0, 0, 1440, 0, 0, -3640, 0, 0, -544, 0, 0, 784, 0, 0, -4672, 0, 0, -1584, 0, 0, 1360, 0, 0, 5408, 0, 0, -1616, 0, 0, 3424, 0, 0, 224, 0, 0, -1984, 0, 0, -3552, 0, 0, 4048, 0, 0, -416, 0, 0, 4584, 0, 0, 2304, 0, 0, -1232, 0, 0, 1024, 0, 0, -888, 0, 0, 1072, 0, 0, -376, 0, 0, 2160, 0, 0, 2424, 0, 0, -1120, 0, 0, 3144, 0, 0, 320, 0, 0, -1928, 0, 0, -1056, 0, 0, 1992, 0, 0, -1568, 0, 0, -784, 0, 0, 4768, 0, 0, -1712, 0, 0, -768, 0, 0, -560, 0, 0, -1728, 0, 0, -1808, 0, 0, -112, 0, 0, -4640, 0, 0, 2944, 0, 0, -3960, 0, 0, 224, 0, 0, -728, 0, 0, -2416, 0, 0, 3920, 0, 0, -3152, 0, 0, 1896, 0, 0, 2896, 0, 0, -3216, 0, 0, 160, 0, 0, -1768, 0, 0, 1680, 0, 0, -2936, 0, 0, -2784, 0, 0, 168, 0, 0, -1040, 0, 0, 3264, 0, 0, 448, 0, 0, 280, 0, 0, 3808, 0, 0, -3704, 0, 0, 1104, 0, 0, -1728, 0, 0, 2512, 0, 0, 3664, 0, 0, -224, 0, 0, 4272, 0, 0, 128, 0, 0, 2936, 0, 0, 304, 0, 0, 2752, 0, 0, 208, 0, 0, -728, 0, 0, -352, 0, 0, -2880, 0, 0, -2160, 0, 0, 4328, 0, 0, -1568, 0, 0, -4472, 0, 0, -896, 0, 0, -1496, 0, 0, 672], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "378.3.b.c", "char_is_minimal": true, "conrey_index": 323, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 1, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 2, 0, -1, 0, 0], [0, -1, 1, 0, -1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 0, -1, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 0, 0, 0, 0, 0, 0], [0, 1, 2, 0, -1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 3, 0, 1, 0, -1], [0, 2, 0, 0, -2, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, -2, 0, -1, 0, -1], [0, 4, 2, 0, -4, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -4, 0, 2, 0, -2], [0, -2, -2, 0, 5, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0], [0, 3, 1, 0, 7, 0, 5, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 0, -1, 0, -3, 0, -3], [0, 0, 0, 0, -4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, -2, 0, 1, 0, -2], [0, 0, 1, 0, -7, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 6, 0, 2, 0, -2], [0, -2, -2, 0, -5, 0, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, 0, -4, 0, 2, 0, 0], [0, 1, 0, 0, 9, 0, -9, 0], [0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, -11, 0, -1], [0, 2, -2, 0, 2, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-8, 0, 0, 4, 0, 4, 0, -2], [0, -13, -4, 0, 18, 0, 6, 0], [0, 0, 0, 0, 0, 0, 0, 0], [7, 0, 0, 0, 0, 0, 0, 0], [0, -4, -4, 0, 0, 0, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [10, 0, 0, 2, 0, -2, 0, 2], [0, -6, 4, 0, -18, 0, -6, 0], [0, 0, 0, 0, 0, 0, 0, 0], [7, 0, 0, 13, 0, -7, 0, 1], [0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [14, 0, 0, -10, 0, 3, 0, -1], [0, -9, 0, 0, -2, 0, -10, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-11, 0, 0, -13, 0, 13, 0, -1], [0, 6, -6, 0, 5, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-8, 0, 0, 0, 0, 0, 0, 0], [0, 21, 5, 0, -21, 0, 15, 0], [0, 0, 0, 0, 0, 0, 0, 0], [30, 0, 0, 10, 0, 8, 0, 4], [0, -2, -4, 0, 2, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-14, 0, 0, -2, 0, 0, 0, -1], [0, 8, -4, 0, -4, 0, -8, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-36, 0, 0, -14, 0, -4, 0, -2], [0, -4, -4, 0, 1, 0, 6, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-10, 0, 0, -6, 0, -2, 0, 2], [0, -7, 1, 0, 7, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-53, 0, 0, -10, 0, 11, 0, 1], [0, -4, 0, 0, 4, 0, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [18, 0, 0, 18, 0, 1, 0, 0], [0, 7, 2, 0, 2, 0, 22, 0], [0, 0, 0, 0, 0, 0, 0, 0], [25, 0, 0, 22, 0, -16, 0, 4], [0, 22, -2, 0, -5, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 0, 4, 0, 2, 0, 2], [0, -14, 6, 0, 30, 0, -6, 0], [0, 0, 0, 0, 0, 0, 0, 0], [7, 0, 0, 5, 0, -7, 0, 1], [0, -8, -4, 0, 8, 0, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [36, 0, 0, -12, 0, -13, 0, 4], [0, 11, 1, 0, 17, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [75, 0, 0, -23, 0, -11, 0, 5], [0, 0, 0, 0, -7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 0, -4, 0, 4]]}