# Stored data for newform 360.4.f.a, downloaded from the LMFDB on 30 April 2024. {"label": "360.4.f.a", "space_label": "360.4.f", "level": 360, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 343664492904, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 2295913385139444370, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [16, 0, 1]], [11, [-28, 1]]], "qexp_display": "q+(-5-5i)q^{5}+2iq^{7}+28q^{11}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "f", "char_is_real": true, "Nk2": 5760, "analytic_conductor": 21.24068760206662, "hecke_ring_index": 2, "level_radical": 30, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "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": [360, 2, [271, 181, 281, 217], [2, 2, 2, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [289], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.026", "prec": 17}, {"__RealLiteral__": 0, "data": "1.886", "prec": 17}, {"__RealLiteral__": 0, "data": "0.310", "prec": 17}, {"__RealLiteral__": 0, "data": "14.366", "prec": 20}, {"__RealLiteral__": 0, "data": "4.267", "prec": 17}, {"__RealLiteral__": 0, "data": "138.251", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c2", "trace_display": [0, 0, -10, 0], "traces": [0, 2, 0, 0, 0, -10, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, -150, 0, 0, 0, -476, 0, -360, 0, 0, 0, 80, 0, 0, 0, 0, 0, -844, 0, 0, 0, 0, 0, 0, 0, 654, 0, 0, 0, 0, 0, -280, 0, 0, 0, -1608, 0, -716, 0, 0, 0, 320, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 0, 0, 1864, 0, 0, 0, 0, 0, -2160, 0, 0, 0, -2292, 0, -128, 0, 0, 0, 320, 0, 0, 0, 0, 0, 2580, 0, 0, 0, 0, 0, 0, 0, -1932, 0, 0, 0, 0, 0, -560, 0, 0, 0, 864, 0, -1094, 0, 0, 0, 2750, 0, 0, 0, 0, 0, 1176, 0, 0, 0, 0, 0, 0, 0, 5728, 0, 0, 0, 0, 0, 2380, 0, 0, 0, 684, 0, 3272, 0, 0, 0, 1800, 0, 0, 0, 0, 0, 224, 0, 0, 0, 0, 0, 0, 0, 3882, 0, 0, 0, 0, 0, -800, 0, 0, 0, 6904, 0, 1052, 0, 0, 0, -800, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, -8696, 0, 0, 0, 0, 0, 4220, 0, 0, 0, -1792, 0, -832, 0, 0, 0, -5520, 0, 0, 0, 0, 0, 3456, 0, 0, 0, 0, 0, 0, 0, -6468, 0, 0, 0, 0, 0, -1200, 0, 0, 0, 9520, 0, 6460, 0, 0, 0, -3270, 0, 0, 0, 0, 0, -3416, 0, 0, 0, 0, 0, 0, 0, 320, 0, 0, 0, 0, 0, 4400, 0, 0, 0, -228, 0, -10472, 0, 0, 0, -4200, 0, 0, 0, 0, 0, -6444, 0, 0, 0, 0, 0, 0, 0, -13502, 0, 0, 0, 0, 0, 8040, 0, 0, 0, 896, 0, 2208, 0, 0, 0, 3580, 0, 0, 0, 0, 0, -19344, 0, 0, 0, 0, 0, 0, 0, -13328, 0, 0, 0, 0, 0, -3200, 0, 0, 0, 480, 0, 10832, 0, 0, 0, -17680, 0, 0, 0, 0, 0, -10080, 0, 0, 0, 0, 0, 0, 0, 4076, 0, 0, 0, 0, 0, -640, 0, 0, 0, -7792, 0, -11670, 0, 0, 0, 3040, 0, 0, 0, 0, 0, -1760, 0, 0, 0, 0, 0, 0, 0, 10832, 0, 0, 0, 0, 0, 2240, 0, 0, 0, -19284, 0, -6048, 0, 0, 0, -9320, 0, 0, 0, 0, 0, 26716, 0, 0, 0, 0, 0, 0, 0, -12820, 0, 0, 0, 0, 0, -25840, 0, 0, 0, 15288, 0, 29348, 0, 0, 0, 21600, 0, 0, 0, 0, 0, 19408, 0, 0, 0, 0, 0, 0, 0, 31368, 0, 0, 0, 0, 0, 11460, 0, 0, 0, -9564, 0, -23632, 0, 0, 0, 640, 0, 0, 0, 0, 0, 7524, 0, 0, 0, 0, 0, 0, 0, 7072, 0, 0, 0, 0, 0, 4800, 0, 0, 0, 32416, 0, 1280, 0, 0, 0, 16480, 0, 0, 0, 0, 0, -11272, 0, 0, 0, 0, 0, 0, 0, 11120, 0, 0, 0, 0, 0, -12900, 0, 0, 0, -34684, 0, -1216, 0, 0, 0, 32080, 0, 0, 0, 0, 0, 9772, 0, 0, 0, 0, 0, 0, 0, 22766, 0, 0, 0, 0, 0, -17840, 0, 0, 0, 18312, 0, -31540, 0, 0, 0, 9660, 0, 0, 0, 0, 0, 15232, 0, 0, 0, 0, 0, 0, 0, 8832, 0, 0, 0, 0, 0, 22480, 0, 0, 0, -33516, 0, 16112, 0, 0, 0, 5600, 0, 0, 0, 0, 0, 10336, 0, 0, 0, 0, 0, 0, 0, 11520, 0, 0, 0, 0, 0, -4320, 0, 0, 0, -18832, 0, 18540, 0, 0, 0, 5470, 0, 0, 0, 0, 0, 1920, 0, 0, 0, 0, 0, 0, 0, 52000, 0, 0, 0, 0, 0, -8750, 0, 0, 0, -8640, 0, 23320, 0, 0, 0, -37680, 0, 0, 0, 0, 0, 15204, 0, 0, 0, 0, 0, 0, 0, -45024, 0, 0, 0, 0, 0, -5880, 0, 0, 0, 27720, 0, -33116, 0, 0, 0, -2560, 0, 0, 0, 0, 0, -20048, 0, 0, 0, 0, 0, 0, 0, -6592, 0, 0, 0, 0, 0, -21200, 0, 0, 0, -7040, 0, 9216, 0, 0, 0, -28640, 0, 0, 0, 0, 0, 4636, 0, 0, 0, 0, 0, 0, 0, -33668, 0, 0, 0, 0, 0, 8960, 0, 0, 0, -14800, 0, -12832, 0, 0, 0, 35700, 0, 0, 0, 0, 0, -59616, 0, 0, 0, 0, 0, 0, 0, -52080, 0, 0, 0, 0, 0, -3420, 0, 0, 0, 7136, 0, -41384, 0, 0, 0, -16360, 0, 0, 0, 0, 0, -27956, 0, 0, 0, 0, 0, 0, 0, -5852, 0, 0, 0, 0, 0, 27000, 0, 0, 0, 27008, 0, 3584, 0, 0, 0, -41440, 0, 0, 0, 0, 0, -8992, 0, 0, 0, 0, 0, 0, 0, -12960, 0, 0, 0, 0, 0, -1120, 0, 0, 0, -21396, 0, -12816, 0, 0, 0, -15440, 0, 0, 0, 0, 0, -46260, 0, 0, 0, 0, 0, 0, 0, -73388, 0, 0, 0, 0, 0, 20880, 0, 0, 0, -3408, 0, 64510, 0, 0, 0, -19410, 0, 0, 0, 0, 0, -2240, 0, 0, 0, 0, 0, 0, 0, 12016, 0, 0, 0, 0, 0, 88080, 0, 0, 0, 52192, 0, 28288, 0, 0, 0, -2000, 0, 0, 0, 0, 0, -55676, 0, 0, 0, 0, 0, 0, 0, 15072, 0, 0, 0, 0, 0, -34520, 0, 0, 0, 85680, 0, 47520, 0, 0, 0, -5260, 0, 0, 0, 0, 0, 94944, 0, 0, 0, 0, 0, 0, 0, -23928, 0, 0, 0, 0, 0, 8000, 0, 0, 0, -30428, 0, -20928, 0, 0, 0, -60480, 0, 0, 0, 0, 0, 72068, 0, 0, 0, 0, 0, 0, 0, -4864, 0, 0, 0, 0, 0, 720, 0, 0, 0, 8480, 0, 5218, 0, 0, 0, -4160, 0, 0, 0, 0, 0, -48600, 0, 0, 0, 0, 0, 0, 0, -64176, 0, 0, 0, 0, 0, -7440, 0, 0, 0, -15456, 0, 23336, 0, 0, 0, 43480, 0, 0, 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, 5, 2, 1, 2, 0]], "char_orbit_index": 6, "prim_orbit_index": 2, "minimal_twist": "120.4.f.c", "char_is_minimal": true, "conrey_index": 289, "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], [1, 0], [0, 0], [0, 0], [0, 0], [-5, -5], [0, 0], [0, 2], [0, 0], [0, 0], [0, 0], [28, 0], [0, 0], [0, 8], [0, 0], [0, 0], [0, 0], [0, -54], [0, 0], [-32, 0], [0, 0], [0, 0], [0, 0], [0, -14], [0, 0], [-75, 50], [0, 0], [0, 0], [0, 0], [-238, 0], [0, 0], [-180, 0], [0, 0], [0, 0], [0, 0], [40, -10], [0, 0], [0, -20], [0, 0], [0, 0], [0, 0], [-422, 0], [0, 0], [0, -138], [0, 0], [0, 0], [0, 0], [0, -30], [0, 0], [327, 0], [0, 0], [0, 0], [0, 0], [0, 110], [0, 0], [-140, -140], [0, 0], [0, 0], [0, 0], [-804, 0], [0, 0], [-358, 0], [0, 0], [0, 0], [0, 0], [160, -40], [0, 0], [0, -442], [0, 0], [0, 0], [0, 0], [64, 0], [0, 0], [0, 76], [0, 0], [0, 0], [0, 0], [0, 56], [0, 0], [932, 0], [0, 0], [0, 0], [0, 0], [0, -646], [0, 0], [-1080, 270], [0, 0], [0, 0], [0, 0], [-1146, 0], [0, 0], [-64, 0], [0, 0], [0, 0], [0, 0], [160, 160], [0, 0], [0, 412], [0, 0], [0, 0], [0, 0]]}