# Stored data for newform 225.4.b.h, downloaded from the LMFDB on 19 April 2024. {"label": "225.4.b.h", "space_label": "225.4.b", "level": 225, "weight": 4, "hecke_orbit": 8, "hecke_orbit_code": 31525266178179297, "dim": 4, "is_polredabs": true, "nf_label": "4.0.5776.1", "trace_hash": 1140544152894029649, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [324, 0, 40, 0, 1]], [7, [18225, 0, 946, 0, 1]], [11, [-108, 28, 1]]], "qexp_display": "q+(-\\beta _{1}+\\beta _{3})q^{2}+(-12+2\\beta _{2})q^{4}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "b", "char_is_real": true, "Nk2": 3600, "analytic_conductor": 13.275429751291638, "hecke_ring_index": 4, "level_radical": 15, "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": "0.508", "prec": 17}, "analytic_rank_proved": true, "char_values": [225, 2, [101, 127], [2, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [3, 5], "conrey_indexes": [199], "field_disc": 5776, "field_disc_factorization": [[2, 4], [19, 2]], "field_poly": [25, 0, -9, 0, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.054", "prec": 17}, {"__RealLiteral__": 0, "data": "3.836", "prec": 17}, {"__RealLiteral__": 0, "data": "1.746", "prec": 17}, {"__RealLiteral__": 0, "data": "77.388", "prec": 20}, {"__RealLiteral__": 0, "data": "71.317", "prec": 20}, {"__RealLiteral__": 0, "data": "2197.925", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "3.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, -48, 0, 0, 0, 0, 0, 0, -56, 0, 0, 252, 0, 240, 0, 0, -12, 0, 0, 0, 0, 0, 0, 1252, 0, 0, 184, 0, 244, 0, 0, 1384, 0, 0, 0, 0, 0, 0, -784, 0, 0, 64, 0, -1176, 0, 0, -520, 0, 0, 0, 0, 0, 0, 360, 0, 0, 248, 0, 1500, 0, 0, -2752, 0, 0, 0, 0, 0, 0, -1648, 0, 0, 2392, 0, 752, 0, 0, 1760, 0, 0, 0, 0, 0, 0, 1684, 0, 0, -1728, 0, -4396, 0, 0, 1192, 0, 0, 0, 0, 0, 0, -2016, 0, 0, -8808, 0, 3824, 0, 0, -4052, 0, 0, 0, 0, 0, 0, -6464, 0, 0, -7848, 0, -3324, 0, 0, 1328, 0, 0, 0, 0, 0, 0, 3840, 0, 0, 8316, 0, -3408, 0, 0, 4432, 0, 0, 0, 0, 0, 0, -824, 0, 0, 5896, 0, -1092, 0, 0, -6264, 0, 0, 0, 0, 0, 0, 216, 0, 0, 17312, 0, 14280, 0, 0, -10992, 0, 0, 0, 0, 0, 0, 6368, 0, 0, -6760, 0, -316, 0, 0, 16560, 0, 0, 0, 0, 0, 0, 1304, 0, 0, -2084, 0, -9568, 0, 0, 9204, 0, 0, 0, 0, 0, 0, 21584, 0, 0, -1048, 0, 6284, 0, 0, 6672, 0, 0, 0, 0, 0, 0, -23096, 0, 0, -3888, 0, -3760, 0, 0, -5188, 0, 0, 0, 0, 0, 0, 6752, 0, 0, -2848, 0, -924, 0, 0, -9488, 0, 0, 0, 0, 0, 0, 12912, 0, 0, -4864, 0, 13888, 0, 0, 88, 0, 0, 0, 0, 0, 0, 1980, 0, 0, 10472, 0, 5856, 0, 0, 5880, 0, 0, 0, 0, 0, 0, -6312, 0, 0, 16736, 0, -9928, 0, 0, -15372, 0, 0, 0, 0, 0, 0, -34800, 0, 0, 16968, 0, 16724, 0, 0, -10448, 0, 0, 0, 0, 0, 0, 11784, 0, 0, -24140, 0, -45440, 0, 0, 5936, 0, 0, 0, 0, 0, 0, -27652, 0, 0, -25848, 0, 1168, 0, 0, -29232, 0, 0, 0, 0, 0, 0, -11928, 0, 0, -59784, 0, -13560, 0, 0, 9336, 0, 0, 0, 0, 0, 0, -1152, 0, 0, 24528, 0, -26184, 0, 0, 26608, 0, 0, 0, 0, 0, 0, 13536, 0, 0, -23632, 0, 37488, 0, 0, 12060, 0, 0, 0, 0, 0, 0, -29140, 0, 0, 4368, 0, 9264, 0, 0, 17976, 0, 0, 0, 0, 0, 0, 46080, 0, 0, 29664, 0, -7560, 0, 0, 48652, 0, 0, 0, 0, 0, 0, 65456, 0, 0, 43072, 0, -4968, 0, 0, -84000, 0, 0, 0, 0, 0, 0, 12696, 0, 0, 34524, 0, 52272, 0, 0, -2100, 0, 0, 0, 0, 0, 0, -53308, 0, 0, -56464, 0, -4832, 0, 0, -34432, 0, 0, 0, 0, 0, 0, -30528, 0, 0, 79136, 0, 78336, 0, 0, -21092, 0, 0, 0, 0, 0, 0, 33984, 0, 0, 45720, 0, -34296, 0, 0, 56912, 0, 0, 0, 0, 0, 0, 31520, 0, 0, -11356, 0, -53456, 0, 0, -10572, 0, 0, 0, 0, 0, 0, -7248, 0, 0, -29512, 0, -376, 0, 0, 50352, 0, 0, 0, 0, 0, 0, 50936, 0, 0, -88032, 0, -55328, 0, 0, 20300, 0, 0, 0, 0, 0, 0, -75672, 0, 0, 38896, 0, 54004, 0, 0, 21728, 0, 0, 0, 0, 0, 0, -9064, 0, 0, -3156, 0, -20352, 0, 0, -17284, 0, 0, 0, 0, 0, 0, 99372, 0, 0, -23448, 0, 89516, 0, 0, -13824, 0, 0, 0, 0, 0, 0, -62424, 0, 0, 12720, 0, -51288, 0, 0, 7780, 0, 0, 0, 0, 0, 0, 3424, 0, 0, 2896, 0, -85204, 0, 0, 70864, 0, 0, 0, 0, 0, 0, -27752, 0, 0, 16628, 0, -32400, 0, 0, -36668, 0, 0, 0, 0, 0, 0, 67148, 0, 0, -17168, 0, 24228, 0, 0, -93088, 0, 0, 0, 0, 0, 0, -28944, 0, 0, -19008, 0, 104, 0, 0, -22928, 0, 0, 0, 0, 0, 0, -173504, 0, 0, 36080, 0, 14088, 0, 0, -74448, 0, 0, 0, 0, 0, 0, -38024, 0, 0, -86596, 0, 175680, 0, 0, -27092, 0, 0, 0, 0, 0, 0, -17460, 0, 0, -49312, 0, -12864, 0, 0, 22504, 0, 0, 0, 0, 0, 0, -90280, 0, 0, 2048, 0, -92472, 0, 0, -73092, 0, 0, 0, 0, 0, 0, 160160, 0, 0, -11544, 0, -60496, 0, 0, -61872, 0, 0, 0, 0, 0, 0, 40840, 0, 0, 16164, 0, -127776, 0, 0, 93072, 0, 0, 0, 0, 0, 0, -27956, 0, 0, -83808, 0, 17376, 0, 0, 110792, 0, 0, 0, 0, 0, 0, -4272, 0, 0, 123584, 0, 171312, 0, 0, 74644, 0, 0, 0, 0, 0, 0, 87528, 0, 0, 18160, 0, 29152, 0, 0, 221728, 0, 0, 0, 0, 0, 0, 116496, 0, 0, 125828, 0, -84304, 0, 0, -90800, 0, 0, 0, 0, 0, 0, 23172, 0, 0, 5920, 0, -692, 0, 0, 16976, 0, 0, 0, 0, 0, 0, -67512, 0, 0, -184224, 0, 59400, 0, 0, -58600, 0, 0, 0, 0, 0, 0, 5888, 0, 0, -84200, 0, -29508, 0, 0, -131952, 0, 0, 0, 0, 0, 0, 59376, 0, 0, 132804, 0, 80928, 0, 0, 52800, 0, 0, 0, 0, 0, 0, -50132, 0, 0, 24000, 0, -128044, 0, 0, 27240, 0, 0, 0, 0, 0, 0, 25888, 0, 0, 221824, 0, -30432, 0, 0, -11552, 0, 0, 0, 0, 0, 0, -122400, 0, 0, -48360, 0, 15104, 0, 0, -192288, 0, 0, 0, 0, 0, 0, -76088, 0, 0, 213992, 0, 180208, 0, 0, 57060, 0, 0, 0, 0, 0, 0, 110784, 0, 0, 13192, 0, -30056, 0, 0, 107432, 0, 0, 0, 0, 0, 0, -47704, 0, 0, -140768, 0, 82520, 0, 0, 11672, 0, 0, 0, 0, 0, 0, 136928, 0, 0, 45432, 0, -44696, 0, 0, -64304, 0, 0, 0, 0, 0, 0, 37656, 0, 0, -127964, 0, -46192, 0, 0, 67968, 0, 0, 0, 0, 0, 0, 33872, 0, 0, 94728, 0, -81052, 0, 0, -117504, 0, 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": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "75.4.a.d", "char_is_minimal": false, "conrey_index": 199, "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, -1, 0, 1], [0, 0, 0, 0], [-12, 0, 2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -13, 0, -4], [0, 42, 0, -6], [0, 0, 0, 0], [0, 0, 0, 0], [-14, 0, -4, 0], [0, 0, 0, 0], [0, 9, 0, -16], [63, 0, 9, 0], [0, 0, 0, 0], [60, 0, -32, 0], [0, -34, 0, -20], [0, 0, 0, 0], [-3, 0, 4, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -62, 0, -10], [0, -66, 0, 12], [0, 0, 0, 0], [0, 0, 0, 0], [313, 0, -25, 0], [0, 0, 0, 0], [0, 4, 0, 22], [46, 0, -28, 0], [0, 0, 0, 0], [61, 0, 28, 0], [0, -332, 0, 44], [0, 0, 0, 0], [346, 0, 14, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 142, 0, -24], [0, 79, 0, -7], [0, 0, 0, 0], [0, 0, 0, 0], [-196, 0, 52, 0], [0, 0, 0, 0], [0, 345, 0, -4], [16, 0, 20, 0], [0, 0, 0, 0], [-294, 0, 78, 0], [0, -310, 0, -32], [0, 0, 0, 0], [-130, 0, -104, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -716, 0, 210], [0, 424, 0, -28], [0, 0, 0, 0], [0, 0, 0, 0], [90, 0, 90, 0], [0, 0, 0, 0], [0, -578, 0, 74], [62, 0, 64, 0], [0, 0, 0, 0], [375, 0, 56, 0], [0, 471, 0, 33], [0, 0, 0, 0], [-688, 0, 120, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 179, 0, -100], [0, -352, 0, 172], [0, 0, 0, 0], [0, 0, 0, 0], [-412, 0, -20, 0], [0, 0, 0, 0], [0, -54, 0, 8], [598, 0, -166, 0], [0, 0, 0, 0], [188, 0, -54, 0], [0, 486, 0, 108], [0, 0, 0, 0], [440, 0, -160, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 1184, 0, -248], [0, -78, 0, -192], [0, 0, 0, 0], [0, 0, 0, 0], [421, 0, -349, 0], [0, 0, 0, 0], [0, -132, 0, -84], [-432, 0, -144, 0], [0, 0, 0, 0], [-1099, 0, -172, 0], [0, 1248, 0, -276], [0, 0, 0, 0], [298, 0, 278, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -521, 0, 0], [0, -1846, 0, -26], [0, 0, 0, 0], [0, 0, 0, 0]]}