# Stored data for newform 128.3.c.a, downloaded from the LMFDB on 19 April 2024.
{"label": "128.3.c.a", "space_label": "128.3.c", "level": 128, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 137489285248, "dim": 4, "is_polredabs": true, "nf_label": "4.0.256.1", "trace_hash": 964130040057142736, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [-28, 4, 1]]], "qexp_display": "q+\\zeta_{8}q^{3}+(-2-\\zeta_{8}^{2})q^{5}+(-\\zeta_{8}-\\zeta_{8}^{3})q^{7}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 4, "char_orbit_label": "c", "char_is_real": true, "Nk2": 1152, "analytic_conductor": 3.4877473838118003, "hecke_ring_index": 128, "level_radical": 2, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 8, "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": "0.505", "prec": 17}, "analytic_rank_proved": true, "char_values": [128, 2, [127, 5], [1, 2]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2], "conrey_indexes": [127], "field_disc": 256, "field_disc_factorization": [[2, 8]], "field_poly": [1, 0, 0, 0, 1], "hecke_ring_index_factorization": [[2, 7]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.027", "prec": 17}, {"__RealLiteral__": 0, "data": "3.890", "prec": 17}, {"__RealLiteral__": 0, "data": "0.051", "prec": 17}, {"__RealLiteral__": 0, "data": "75.699", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2073.602", "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, -8, 0], "traces": [0, 4, 0, 0, 0, -8, 0, 0, 0, -12, 0, 0, 0, 24, 0, 0, 0, -8, 0, 0, 0, 32, 0, 0, 0, 44, 0, 0, 0, -136, 0, 0, 0, -16, 0, 0, 0, -40, 0, 0, 0, 8, 0, 0, 0, 280, 0, 0, 0, 4, 0, 0, 0, 88, 0, 0, 0, -176, 0, 0, 0, -296, 0, 0, 0, 80, 0, 0, 0, -288, 0, 0, 0, 88, 0, 0, 0, 352, 0, 0, 0, 116, 0, 0, 0, 272, 0, 0, 0, 216, 0, 0, 0, -512, 0, 0, 0, -328, 0, 0, 0, 24, 0, 0, 0, -64, 0, 0, 0, 440, 0, 0, 0, -312, 0, 0, 0, 184, 0, 0, 0, -204, 0, 0, 0, -400, 0, 0, 0, 560, 0, 0, 0, -224, 0, 0, 0, -56, 0, 0, 0, 320, 0, 0, 0, 400, 0, 0, 0, -264, 0, 0, 0, 536, 0, 0, 0, 24, 0, 0, 0, -320, 0, 0, 0, -224, 0, 0, 0, -404, 0, 0, 0, 88, 0, 0, 0, -528, 0, 0, 0, 184, 0, 0, 0, -816, 0, 0, 0, 192, 0, 0, 0, 312, 0, 0, 0, 568, 0, 0, 0, 528, 0, 0, 0, -528, 0, 0, 0, 624, 0, 0, 0, 416, 0, 0, 0, 1024, 0, 0, 0, 208, 0, 0, 0, -1156, 0, 0, 0, -328, 0, 0, 0, 344, 0, 0, 0, -1216, 0, 0, 0, -392, 0, 0, 0, -1032, 0, 0, 0, -1264, 0, 0, 0, 928, 0, 0, 0, 1352, 0, 0, 0, 664, 0, 0, 0, -48, 0, 0, 0, -8, 0, 0, 0, 192, 0, 0, 0, -552, 0, 0, 0, 664, 0, 0, 0, 1632, 0, 0, 0, -628, 0, 0, 0, 952, 0, 0, 0, -608, 0, 0, 0, -1056, 0, 0, 0, -304, 0, 0, 0, 32, 0, 0, 0, -1400, 0, 0, 0, 504, 0, 0, 0, 752, 0, 0, 0, -248, 0, 0, 0, 128, 0, 0, 0, -1672, 0, 0, 0, 1032, 0, 0, 0, -1536, 0, 0, 0, 2624, 0, 0, 0, 1080, 0, 0, 0, -1592, 0, 0, 0, -64, 0, 0, 0, 116, 0, 0, 0, -944, 0, 0, 0, -1048, 0, 0, 0, 1048, 0, 0, 0, -688, 0, 0, 0, 896, 0, 0, 0, 1344, 0, 0, 0, 1880, 0, 0, 0, -112, 0, 0, 0, -968, 0, 0, 0, -392, 0, 0, 0, 536, 0, 0, 0, 520, 0, 0, 0, 352, 0, 0, 0, -336, 0, 0, 0, -8, 0, 0, 0, -1112, 0, 0, 0, -352, 0, 0, 0, -1032, 0, 0, 0, -2080, 0, 0, 0, -2060, 0, 0, 0, 848, 0, 0, 0, 696, 0, 0, 0, -2336, 0, 0, 0, 1160, 0, 0, 0, 760, 0, 0, 0, 3072, 0, 0, 0, 672, 0, 0, 0, 1552, 0, 0, 0, -8, 0, 0, 0, -1136, 0, 0, 0, 1936, 0, 0, 0, 720, 0, 0, 0, 528, 0, 0, 0, -448, 0, 0, 0, -352, 0, 0, 0, -944, 0, 0, 0, -1512, 0, 0, 0, 1504, 0, 0, 0, -576, 0, 0, 0, -184, 0, 0, 0, 352, 0, 0, 0, -1148, 0, 0, 0, -464, 0, 0, 0, -1008, 0, 0, 0, -1576, 0, 0, 0, -1776, 0, 0, 0, -904, 0, 0, 0, -896, 0, 0, 0, 2200, 0, 0, 0, -480, 0, 0, 0, 2672, 0, 0, 0, 200, 0, 0, 0, 128, 0, 0, 0, -504, 0, 0, 0, 2208, 0, 0, 0, 784, 0, 0, 0, -512, 0, 0, 0, 1928, 0, 0, 0, 2080, 0, 0, 0, 2392, 0, 0, 0, -3432, 0, 0, 0, -1088, 0, 0, 0, -3336, 0, 0, 0, 1688, 0, 0, 0, 2368, 0, 0, 0, -1068, 0, 0, 0, -1712, 0, 0, 0, -368, 0, 0, 0, -1000, 0, 0, 0, 2744, 0, 0, 0, -3424, 0, 0, 0, -176, 0, 0, 0, 2424, 0, 0, 0, -1800, 0, 0, 0, 440, 0, 0, 0, -1600, 0, 0, 0, -1536, 0, 0, 0, 3000, 0, 0, 0, 2136, 0, 0, 0, -3760, 0, 0, 0, 1648, 0, 0, 0, 656, 0, 0, 0, 3040, 0, 0, 0, -1040, 0, 0, 0, -2856, 0, 0, 0, -2688, 0, 0, 0, -1320, 0, 0, 0, -1024, 0, 0, 0, 3520, 0, 0, 0, 1856, 0, 0, 0, -2008, 0, 0, 0, 3204, 0, 0, 0, 632, 0, 0, 0, -1872, 0, 0, 0, 224, 0, 0, 0, 1680, 0, 0, 0, 1888, 0, 0, 0, 752, 0, 0, 0, 1400, 0, 0, 0, 1416, 0, 0, 0, -2352, 0, 0, 0, 440, 0, 0, 0, -424, 0, 0, 0, -320, 0, 0, 0, 480, 0, 0, 0, -2992, 0, 0, 0, 2464, 0, 0, 0, -2672, 0, 0, 0, -2536, 0, 0, 0, 1912, 0, 0, 0, -2432, 0, 0, 0, 1032, 0, 0, 0, -2368, 0, 0, 0, 688, 0, 0, 0, -4328, 0, 0, 0, 848, 0, 0, 0, -2280, 0, 0, 0, -2056, 0, 0, 0, 1024, 0, 0, 0, 1388, 0, 0, 0, 2344, 0, 0, 0, 432, 0, 0, 0, 3160, 0, 0, 0, -824, 0, 0, 0, 64, 0, 0, 0, -48, 0, 0, 0, 3008, 0, 0, 0, 3544, 0, 0, 0, 1016, 0, 0, 0, 1032, 0, 0, 0, 3872, 0, 0, 0, 768, 0, 0, 0, 1856, 0, 0, 0, 320, 0, 0, 0, 80, 0, 0, 0, -3312, 0, 0, 0, -1864, 0, 0, 0, -3152, 0, 0, 0, -3680, 0, 0, 0, -4400, 0, 0, 0, 3144, 0, 0, 0, 2616, 0, 0, 0, -6176, 0, 0, 0, -4264, 0, 0, 0, 1848, 0, 0, 0, 1664, 0, 0, 0, -240, 0, 0, 0, 328, 0, 0, 0, 288, 0, 0, 0, -4348, 0, 0, 0, 2704, 0, 0, 0, 2912, 0, 0, 0, -1824, 0, 0, 0, 2936, 0, 0, 0, -3112, 0, 0, 0, 1040, 0, 0, 0, 1312, 0, 0, 0, 1136, 0, 0, 0, -1064, 0, 0, 0], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": true, "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": 3, "prim_orbit_index": 2, "minimal_twist": "128.3.c.a", "char_is_minimal": true, "conrey_index": 127, "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], [-2, 0, -1, 0], [0, 0, 0, 0], [0, -1, 0, -1], [0, 0, 0, 0], [-3, 0, -2, 0], [0, 0, 0, 0], [0, 1, 0, 2], [0, 0, 0, 0], [6, 0, -1, 0], [0, 0, 0, 0], [0, -7, 0, 1], [0, 0, 0, 0], [-2, 0, -2, 0], [0, 0, 0, 0], [0, 3, 0, -2], [0, 0, 0, 0], [8, 0, 0, 0], [0, 0, 0, 0], [0, 5, 0, -3], [0, 0, 0, 0], [11, 0, 4, 0], [0, 0, 0, 0], [0, -4, 0, 2], [0, 0, 0, 0], [-34, 0, -1, 0], [0, 0, 0, 0], [0, 12, 0, 4], [0, 0, 0, 0], [-4, 0, 2, 0], [0, 0, 0, 0], [0, 0, 0, -4], [0, 0, 0, 0], [-10, 0, 7, 0], [0, 0, 0, 0], [0, 1, 0, 1], [0, 0, 0, 0], [2, 0, 4, 0], [0, 0, 0, 0], [0, -13, 0, -4], [0, 0, 0, 0], [70, 0, 7, 0], [0, 0, 0, 0], [0, -6, 0, 2], [0, 0, 0, 0], [1, 0, 8, 0], [0, 0, 0, 0], [0, -12, 0, 2], [0, 0, 0, 0], [22, 0, -1, 0], [0, 0, 0, 0], [0, 7, 0, 7], [0, 0, 0, 0], [-44, 0, -10, 0], [0, 0, 0, 0], [0, 11, 0, 0], [0, 0, 0, 0], [-74, 0, 7, 0], [0, 0, 0, 0], [0, -1, 0, -9], [0, 0, 0, 0], [20, 0, -4, 0], [0, 0, 0, 0], [0, -9, 0, 6], [0, 0, 0, 0], [-72, 0, -16, 0], [0, 0, 0, 0], [0, -9, 0, -1], [0, 0, 0, 0], [22, 0, 6, 0], [0, 0, 0, 0], [0, 31, 0, -4], [0, 0, 0, 0], [88, 0, -16, 0], [0, 0, 0, 0], [0, 22, 0, -10], [0, 0, 0, 0], [29, 0, -6, 0], [0, 0, 0, 0], [0, 29, 0, 8], [0, 0, 0, 0], [68, 0, 6, 0], [0, 0, 0, 0], [0, -39, 0, 1], [0, 0, 0, 0], [54, 0, -10, 0], [0, 0, 0, 0], [0, -8, 0, -12], [0, 0, 0, 0], [-128, 0, -16, 0], [0, 0, 0, 0], [0, -35, 0, -3], [0, 0, 0, 0], [-82, 0, -10, 0], [0, 0, 0, 0], [0, 15, 0, 16], [0, 0, 0, 0]]}