# Stored data for newform 588.3.m.e, downloaded from the LMFDB on 18 April 2024.
{"label": "588.3.m.e", "space_label": "588.3.m", "level": 588, "weight": 3, "hecke_orbit": 5, "hecke_orbit_code": 18015223193535052, "dim": 8, "is_polredabs": true, "nf_label": "8.0.339738624.1", "trace_hash": 795347983855690982, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [196, -336, -256, 768, 1010, 0, -32, 0, 1]]], "qexp_display": "q+(-1+\\beta _{4})q^{3}+(-2\\beta _{2}-\\beta _{5}+\\beta _{6}+\\cdots)q^{5}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "m", "char_is_real": false, "Nk2": 5292, "analytic_conductor": 16.021839544385458, "hecke_ring_index": 49, "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": "0.170", "prec": 17}, "analytic_rank_proved": true, "char_values": [588, 6, [295, 197, 493], [6, 6, 5]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [313, 325], "field_disc": 339738624, "field_disc_factorization": [[2, 22], [3, 4]], "field_poly": [4, 0, -8, 0, 14, 0, -4, 0, 1], "hecke_ring_index_factorization": [[7, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.790", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "228.759", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "10537.151", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "2.2.3.c6", "trace_display": [0, -12, 0, 0], "traces": [0, 8, 0, -12, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, -48, 0, 96, 0, 0, 0, 8, 0, -36, 0, 0, 0, 80, 0, -48, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, -112, 0, 0, 0, 264, 0, 0, 0, 48, 0, 72, 0, 0, 0, -192, 0, -168, 0, 144, 0, 0, 0, -120, 0, 32, 0, 0, 0, 224, 0, -336, 0, 108, 0, 0, 0, 216, 0, -36, 0, 0, 0, -96, 0, -120, 0, -96, 0, 0, 0, 48, 0, 136, 0, 0, 0, 0, 0, -24, 0, 96, 0, 0, 0, -328, 0, -8, 0, 0, 0, 512, 0, 432, 0, 0, 0, 0, 0, 236, 0, -168, 0, 0, 0, -448, 0, 168, 0, -96, 0, 0, 0, 0, 0, -248, 0, 0, 0, -528, 0, 552, 0, -864, 0, 0, 0, -136, 0, -248, 0, 0, 0, 1040, 0, 96, 0, -216, 0, 0, 0, 48, 0, 0, 0, 0, 0, -72, 0, 288, 0, -192, 0, 0, 0, 168, 0, 560, 0, 0, 0, -288, 0, 120, 0, -144, 0, 0, 0, -224, 0, 136, 0, 0, 0, 256, 0, 384, 0, -96, 0, 0, 0, -72, 0, -24, 0, 0, 0, -256, 0, -336, 0, -816, 0, 0, 0, 336, 0, 216, 0, 0, 0, -216, 0, 72, 0, -480, 0, 0, 0, 88, 0, -216, 0, 0, 0, -464, 0, -96, 0, 108, 0, 0, 0, -88, 0, 192, 0, 0, 0, -528, 0, 144, 0, -984, 0, 0, 0, 120, 0, -128, 0, 0, 0, 192, 0, 360, 0, 1392, 0, 0, 0, -472, 0, 160, 0, 0, 0, 1200, 0, 528, 0, -408, 0, 0, 0, -388, 0, -336, 0, 0, 0, 16, 0, 0, 0, 1464, 0, 0, 0, 24, 0, 72, 0, 0, 0, -192, 0, 120, 0, -288, 0, 0, 0, 240, 0, -344, 0, 0, 0, -1008, 0, 816, 0, 24, 0, 0, 0, 64, 0, 192, 0, 0, 0, 224, 0, -768, 0, 480, 0, 0, 0, -432, 0, -184, 0, 0, 0, 0, 0, -2184, 0, 96, 0, 0, 0, 648, 0, -308, 0, 0, 0, 1360, 0, -2256, 0, 504, 0, 0, 0, 832, 0, -72, 0, 0, 0, 1472, 0, 672, 0, 1824, 0, 0, 0, -168, 0, -1208, 0, 0, 0, 192, 0, -576, 0, 912, 0, 0, 0, 312, 0, 984, 0, 0, 0, -2544, 0, -2352, 0, 744, 0, 0, 0, -16, 0, 192, 0, 0, 0, -544, 0, 792, 0, 360, 0, 0, 0, -552, 0, 1280, 0, 0, 0, 1728, 0, 864, 0, -432, 0, 0, 0, -352, 0, 1120, 0, 0, 0, -896, 0, -720, 0, 744, 0, 0, 0, -224, 0, -144, 0, 0, 0, 2400, 0, -1560, 0, -360, 0, 0, 0, -96, 0, -736, 0, 0, 0, 432, 0, 120, 0, 2160, 0, 0, 0, -88, 0, -1608, 0, 0, 0, -3120, 0, 1392, 0, 0, 0, 0, 0, 552, 0, 360, 0, 0, 0, -3536, 0, 108, 0, 312, 0, 0, 0, -288, 0, -344, 0, 0, 0, 384, 0, 72, 0, -1920, 0, 0, 0, 648, 0, 828, 0, 0, 0, -640, 0, 2064, 0, -1680, 0, 0, 0, -2120, 0, 288, 0, 0, 0, 2480, 0, 432, 0, -1152, 0, 0, 0, -120, 0, -1440, 0, 0, 0, 288, 0, -168, 0, 1776, 0, 0, 0, 1656, 0, 1192, 0, 0, 0, -768, 0, 672, 0, -408, 0, 0, 0, -1136, 0, 360, 0, 0, 0, 1856, 0, -384, 0, 288, 0, 0, 0, -384, 0, 1600, 0, 0, 0, 192, 0, 336, 0, -1872, 0, 0, 0, 1064, 0, -1032, 0, 0, 0, -1200, 0, 528, 0, 72, 0, 0, 0, 308, 0, -240, 0, 0, 0, 1696, 0, 384, 0, -2064, 0, 0, 0, 336, 0, -456, 0, 0, 0, 1632, 0, -1080, 0, -2016, 0, 0, 0, 2168, 0, -1280, 0, 0, 0, -960, 0, 1920, 0, -648, 0, 0, 0, -1384, 0, 816, 0, 0, 0, 1456, 0, 324, 0, -432, 0, 0, 0, -72, 0, -1296, 0, 0, 0, 960, 0, 528, 0, -96, 0, 0, 0, 192, 0, 984, 0, 0, 0, -624, 0, -2640, 0, 648, 0, 0, 0, 952, 0, -648, 0, 0, 0, -2512, 0, 696, 0, -4464, 0, 0, 0, 96, 0, -1168, 0, 0, 0, -216, 0, 4272, 0, -2208, 0, 0, 0, -1632, 0, -112, 0, 0, 0, -224, 0, 576, 0, -576, 0, 0, 0, 1376, 0, 792, 0, 0, 0, 272, 0, 792, 0, 1344, 0, 0, 0, -144, 0, 2584, 0, 0, 0, 1968, 0, 5280, 0, 2400, 0, 0, 0, -1832, 0, -296, 0, 0, 0, -576, 0, -48, 0, 384, 0, 0, 0, -2440, 0, -288, 0, 0, 0, -240, 0, -288, 0, -1704, 0, 0, 0, -360, 0, -1176, 0, 0, 0, -2784, 0, -1488, 0, -3648, 0, 0, 0, 16, 0, 840, 0, 0, 0, -3120, 0, 2688, 0, -480, 0, 0, 0, 1976, 0, -144, 0, 0, 0, 4168, 0, -1800, 0, 4392, 0, 0, 0, -528, 0, -1240, 0, 0, 0, 816, 0, -3456, 0, -48, 0, 0, 0, 664, 0, 896, 0, 0, 0, 2368, 0, 3600, 0, 1008, 0, 0, 0, 904, 0, -1080, 0, 0, 0, -3696, 0, -24, 0, 696, 0, 0, 0, 0, 0, 2176, 0, 0, 0, -2928, 0, -6288, 0, 2016, 0, 0, 0, 1200, 0, -72, 0, 0, 0, -1024, 0, -3072, 0, -216, 0, 0, 0, -2040, 0, -96, 0, 0, 0, -4368, 0, 288, 0, -3648, 0, 0, 0, -120, 0, 24, 0, 0, 0, 576, 0, -792, 0, 672, 0, 0, 0, -1064, 0, 2152, 0, 0, 0, 8272, 0, -2304, 0, 1032, 0, 0, 0, 2604, 0, 984, 0, 0, 0, 672, 0, 1512, 0, 8832, 0, 0, 0, -816, 0, 504, 0, 0, 0, -48, 0, 1104, 0, 5424, 0, 0, 0, -880, 0, -2568, 0, 0, 0, 1600, 0, -5280, 0, -576, 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, 7, 4, -1, 6, 0]], "char_orbit_index": 13, "prim_orbit_index": 4, "minimal_twist": "588.3.d.c", "char_is_minimal": false, "conrey_index": 313, "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, 0, 0, 0, 0], [-1, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, 0, 0, -1, 1, 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, -3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 1, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, -4, 1, 0, -8, 1, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, -3, 3, 4, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [16, 0, -4, 0, 8, -2, 2, 1], [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, 2, 0, -4, -2, 9, -2, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-9, 2, -1, 0, -9, -1, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, 0, 6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [10, 1, 5, 6, 0, 0, -6, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-4, -3, -14, -4, 4, 14, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, 0, 0, -1, 0, -3], [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, 12, 0, -8, 16, -9, -4, 6], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 12, -1, 0, 12, -2, 4], [0, 0, 0, 0, 0, 0, 0, 0], [14, 5, -13, -7, 28, -26, -7, 5], [0, 0, 0, 0, 0, 0, 0, 0], [-14, 2, -8, 8, 0, 0, -8, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -3, -3, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [44, 0, -4, 0, 22, -2, -8, 7], [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, -6, -12, -9, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [18, 6, -26, -4, 18, -26, -8, 12], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -10, 6, 0, -20, 6, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-24, 1, 6, 2, 0, 0, -2, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-14, 5, -22, 12, 14, 22, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [24, 0, -28, 0, 12, -14, -5, -8], [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, 10, 0, -8, 30, 19, -4, 5], [0, 0, 0, 0, 0, 0, 0, 0], [8, 6, 12, 4, 8, 12, 8, 12], [0, 0, 0, 0, 0, 0, 0, 0], [2, -3, -9, 6, 4, -18, 6, -3], [0, 0, 0, 0, 0, 0, 0, 0], [28, -1, -43, 8, 0, 0, -8, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-28, 8, -6, -15, 28, 6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [18, 0, 2, 0, 9, 1, 0, -6], [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, -8, 0, 0, -54, -28, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0], [-9, 0, 0, 0, -9, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-16, 14, -6, -6, -32, -12, -6, 14], [0, 0, 0, 0, 0, 0, 0, 0], [-12, 0, 15, 4, 0, 0, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-10, -3, -5, -18, 10, 5, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-16, 0, -46, 0, -8, -23, 11, 16], [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, 6, 0, 8, -12, -42, 4, 3], [0, 0, 0, 0, 0, 0, 0, 0], [34, 4, -36, 10, 34, -36, 20, 8], [0, 0, 0, 0, 0, 0, 0, 0], [28, -4, -10, -3, 56, -20, -3, -4], [0, 0, 0, 0, 0, 0, 0, 0], [0, -3, 3, 0, 0, 0, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0]]}