# Stored data for newform 160.3.b.a, downloaded from the LMFDB on 24 April 2024. {"label": "160.3.b.a", "space_label": "160.3.b", "level": 160, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 68769808544, "dim": 4, "is_polredabs": true, "nf_label": "4.0.400.1", "trace_hash": 2081844097547266923, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [16, 0, 28, 0, 1]]], "qexp_display": "q-\\beta _{1}q^{3}-\\beta _{3}q^{5}+(-\\beta _{1}+4\\beta _{2})q^{7}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 4, "char_orbit_label": "b", "char_is_real": true, "Nk2": 1440, "analytic_conductor": 4.35968422976475, "hecke_ring_index": 16, "level_radical": 10, "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": "0.507", "prec": 17}, "analytic_rank_proved": true, "char_values": [160, 2, [31, 101, 97], [1, 2, 2]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 5], "conrey_indexes": [31], "field_disc": 400, "field_disc_factorization": [[2, 4], [5, 2]], "field_poly": [1, 0, 3, 0, 1], "hecke_ring_index_factorization": [[2, 4]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.777", "prec": 17}, {"__RealLiteral__": 0, "data": "0.325", "prec": 17}, {"__RealLiteral__": 0, "data": "73.297", "prec": 20}, {"__RealLiteral__": 0, "data": "30.086", "prec": 20}, {"__RealLiteral__": 0, "data": "1978.184", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "2.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 64, 0, 0, 0, -40, 0, 0, 0, -88, 0, 0, 0, 20, 0, 0, 0, -72, 0, 0, 0, 160, 0, 0, 0, 112, 0, 0, 0, 160, 0, 0, 0, -120, 0, 0, 0, -308, 0, 0, 0, 128, 0, 0, 0, -144, 0, 0, 0, 64, 0, 0, 0, -40, 0, 0, 0, -136, 0, 0, 0, -8, 0, 0, 0, 160, 0, 0, 0, 316, 0, 0, 0, -80, 0, 0, 0, -120, 0, 0, 0, 48, 0, 0, 0, 264, 0, 0, 0, 136, 0, 0, 0, -280, 0, 0, 0, -160, 0, 0, 0, -104, 0, 0, 0, -80, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 48, 0, 0, 0, 152, 0, 0, 0, 168, 0, 0, 0, 240, 0, 0, 0, -544, 0, 0, 0, 680, 0, 0, 0, -848, 0, 0, 0, -1128, 0, 0, 0, 320, 0, 0, 0, 428, 0, 0, 0, 48, 0, 0, 0, 176, 0, 0, 0, 520, 0, 0, 0, 40, 0, 0, 0, 1328, 0, 0, 0, -520, 0, 0, 0, 560, 0, 0, 0, -840, 0, 0, 0, 280, 0, 0, 0, 480, 0, 0, 0, -624, 0, 0, 0, -656, 0, 0, 0, -480, 0, 0, 0, -100, 0, 0, 0, -520, 0, 0, 0, -280, 0, 0, 0, -1056, 0, 0, 0, 576, 0, 0, 0, 200, 0, 0, 0, 936, 0, 0, 0, 160, 0, 0, 0, 1464, 0, 0, 0, -1080, 0, 0, 0, 280, 0, 0, 0, 640, 0, 0, 0, -848, 0, 0, 0, 672, 0, 0, 0, 512, 0, 0, 0, -240, 0, 0, 0, -436, 0, 0, 0, -1360, 0, 0, 0, -1280, 0, 0, 0, 744, 0, 0, 0, 440, 0, 0, 0, 2008, 0, 0, 0, -1240, 0, 0, 0, 112, 0, 0, 0, 696, 0, 0, 0, 320, 0, 0, 0, 1544, 0, 0, 0, -800, 0, 0, 0, -216, 0, 0, 0, -320, 0, 0, 0, -520, 0, 0, 0, -360, 0, 0, 0, -536, 0, 0, 0, 2000, 0, 0, 0, 868, 0, 0, 0, -1200, 0, 0, 0, -2480, 0, 0, 0, -544, 0, 0, 0, -1632, 0, 0, 0, -1080, 0, 0, 0, 960, 0, 0, 0, -1216, 0, 0, 0, 1824, 0, 0, 0, -64, 0, 0, 0, -984, 0, 0, 0, 120, 0, 0, 0, 1136, 0, 0, 0, 2928, 0, 0, 0, 1072, 0, 0, 0, 0, 0, 0, 0, -200, 0, 0, 0, 1920, 0, 0, 0, 936, 0, 0, 0, 336, 0, 0, 0, 340, 0, 0, 0, 0, 0, 0, 0, -1328, 0, 0, 0, 976, 0, 0, 0, -1560, 0, 0, 0, -536, 0, 0, 0, -80, 0, 0, 0, -3880, 0, 0, 0, 160, 0, 0, 0, -2320, 0, 0, 0, 1712, 0, 0, 0, 480, 0, 0, 0, -1176, 0, 0, 0, -240, 0, 0, 0, 2128, 0, 0, 0, -1112, 0, 0, 0, -640, 0, 0, 0, 568, 0, 0, 0, 864, 0, 0, 0, -160, 0, 0, 0, -216, 0, 0, 0, -440, 0, 0, 0, -500, 0, 0, 0, 2000, 0, 0, 0, 1488, 0, 0, 0, 2600, 0, 0, 0, -40, 0, 0, 0, -2960, 0, 0, 0, 1632, 0, 0, 0, -480, 0, 0, 0, -2880, 0, 0, 0, 400, 0, 0, 0, -336, 0, 0, 0, 720, 0, 0, 0, -1960, 0, 0, 0, 1288, 0, 0, 0, -1720, 0, 0, 0, 672, 0, 0, 0, -184, 0, 0, 0, 4256, 0, 0, 0, -32, 0, 0, 0, -800, 0, 0, 0, -1776, 0, 0, 0, 1296, 0, 0, 0, -728, 0, 0, 0, 2576, 0, 0, 0, 100, 0, 0, 0, -1280, 0, 0, 0, 3168, 0, 0, 0, -5328, 0, 0, 0, -992, 0, 0, 0, 200, 0, 0, 0, 160, 0, 0, 0, -2704, 0, 0, 0, 7240, 0, 0, 0, 3968, 0, 0, 0, -1200, 0, 0, 0, -360, 0, 0, 0, -3160, 0, 0, 0, 304, 0, 0, 0, 1560, 0, 0, 0, -560, 0, 0, 0, 1488, 0, 0, 0, -6560, 0, 0, 0, -2720, 0, 0, 0, -1920, 0, 0, 0, 680, 0, 0, 0, 344, 0, 0, 0, -1712, 0, 0, 0, -288, 0, 0, 0, 1144, 0, 0, 0, -360, 0, 0, 0, 2164, 0, 0, 0, 4016, 0, 0, 0, 1760, 0, 0, 0, -1824, 0, 0, 0, 600, 0, 0, 0, 728, 0, 0, 0, -992, 0, 0, 0, -512, 0, 0, 0, -1688, 0, 0, 0, 1600, 0, 0, 0, -2360, 0, 0, 0, 1744, 0, 0, 0, -3024, 0, 0, 0, 2560, 0, 0, 0, -600, 0, 0, 0, -1128, 0, 0, 0, 144, 0, 0, 0, 2512, 0, 0, 0, 600, 0, 0, 0, 920, 0, 0, 0, 4712, 0, 0, 0, 1680, 0, 0, 0, -528, 0, 0, 0, -2752, 0, 0, 0, 800, 0, 0, 0, 1728, 0, 0, 0, 2280, 0, 0, 0, 672, 0, 0, 0, 812, 0, 0, 0, -1280, 0, 0, 0, -2648, 0, 0, 0, -1840, 0, 0, 0, -904, 0, 0, 0, -7440, 0, 0, 0, 1320, 0, 0, 0, 3840, 0, 0, 0, -4200, 0, 0, 0, -2320, 0, 0, 0, -640, 0, 0, 0, 1040, 0, 0, 0, 1960, 0, 0, 0, -528, 0, 0, 0, -1136, 0, 0, 0, -2400, 0, 0, 0, 960, 0, 0, 0, 3160, 0, 0, 0, -2720, 0, 0, 0, 2592, 0, 0, 0, -3720, 0, 0, 0, 560, 0, 0, 0, -208, 0, 0, 0, -1104, 0, 0, 0, -376, 0, 0, 0, 2504, 0, 0, 0, 1520, 0, 0, 0, 2272, 0, 0, 0, 3016, 0, 0, 0, 960, 0, 0, 0, 2340, 0, 0, 0, 720, 0, 0, 0, 2400, 0, 0, 0, -3344, 0, 0, 0, -6008, 0, 0, 0, 1040, 0, 0, 0, 2120, 0, 0, 0, 1848, 0, 0, 0, -960, 0, 0, 0, 288, 0, 0, 0], "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, 4, 2, -1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "160.3.b.a", "char_is_minimal": true, "conrey_index": 31, "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], [1, 0, 0, 0], [0, 0, 0, 0], [0, -1, 0, 0], [0, 0, 0, 0], [0, 0, 0, -1], [0, 0, 0, 0], [0, -1, 4, 0], [0, 0, 0, 0], [-5, 0, 0, 6], [0, 0, 0, 0], [0, 3, 1, 0], [0, 0, 0, 0], [16, 0, 0, 2], [0, 0, 0, 0], [0, -2, 1, 0], [0, 0, 0, 0], [-10, 0, 0, 4], [0, 0, 0, 0], [0, -3, -3, 0], [0, 0, 0, 0], [-22, 0, 0, 14], [0, 0, 0, 0], [0, -1, 10, 0], [0, 0, 0, 0], [5, 0, 0, 0], [0, 0, 0, 0], [0, 8, -6, 0], [0, 0, 0, 0], [-18, 0, 0, -12], [0, 0, 0, 0], [0, 2, 8, 0], [0, 0, 0, 0], [40, 0, 0, -16], [0, 0, 0, 0], [0, -6, -7, 0], [0, 0, 0, 0], [28, 0, 0, -2], [0, 0, 0, 0], [0, -12, -2, 0], [0, 0, 0, 0], [40, 0, 0, -14], [0, 0, 0, 0], [0, -1, -8, 0], [0, 0, 0, 0], [-30, 0, 0, 5], [0, 0, 0, 0], [0, 1, -14, 0], [0, 0, 0, 0], [-77, 0, 0, -10], [0, 0, 0, 0], [0, 18, -4, 0], [0, 0, 0, 0], [32, 0, 0, -14], [0, 0, 0, 0], [0, 5, -5, 0], [0, 0, 0, 0], [-36, 0, 0, 12], [0, 0, 0, 0], [0, -1, -29, 0], [0, 0, 0, 0], [16, 0, 0, -22], [0, 0, 0, 0], [0, 41, 22, 0], [0, 0, 0, 0], [-10, 0, 0, -16], [0, 0, 0, 0], [0, -11, 28, 0], [0, 0, 0, 0], [-34, 0, 0, 26], [0, 0, 0, 0], [0, -16, -34, 0], [0, 0, 0, 0], [-2, 0, 0, 60], [0, 0, 0, 0], [0, -5, 0, 0], [0, 0, 0, 0], [40, 0, 0, -48], [0, 0, 0, 0], [0, -24, -36, 0], [0, 0, 0, 0], [79, 0, 0, -6], [0, 0, 0, 0], [0, 17, 2, 0], [0, 0, 0, 0], [-20, 0, 0, 10], [0, 0, 0, 0], [0, -6, 12, 0], [0, 0, 0, 0], [-30, 0, 0, 0], [0, 0, 0, 0], [0, -4, 78, 0], [0, 0, 0, 0], [12, 0, 0, 4], [0, 0, 0, 0], [0, -3, 9, 0], [0, 0, 0, 0], [66, 0, 0, -24], [0, 0, 0, 0], [0, -45, 25, 0], [0, 0, 0, 0]]}