# Stored data for newform 1050.4.g.a, downloaded from the LMFDB on 23 April 2024.
{"label": "1050.4.g.a", "space_label": "1050.4.g", "level": 1050, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 412383970330, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 767364766741799710, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[11, [72, 1]], [13, [1156, 0, 1]]], "qexp_display": "q-2iq^{2}-3iq^{3}-4q^{4}-6q^{6}-7iq^{7}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "g", "char_is_real": true, "Nk2": 16800, "analytic_conductor": 61.952005506027646, "hecke_ring_index": 1, "level_radical": 210, "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": "0.508", "prec": 17}, "analytic_rank_proved": true, "char_values": [1050, 2, [701, 127, 451], [2, 1, 2]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 3, 5, 7], "conrey_indexes": [799], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.034", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "16.445", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "166.180", "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, 0, 0], "traces": [0, 2, 0, 0, -8, 0, -12, 0, 0, -18, 0, -144, 0, 0, -28, 0, 32, 0, 0, -184, 0, -42, 0, 0, 48, 0, -136, 0, 0, 228, 0, 112, 0, 0, -24, 0, 72, 0, 0, -204, 0, 12, 0, 0, 576, 0, -720, 0, 0, -98, 0, -36, 0, 0, 108, 0, 112, 0, 0, 984, 0, -500, 0, 0, -128, 0, 864, 0, 0, -1080, 0, 72, 0, 0, 136, 0, 736, 0, 0, -112, 0, 162, 0, 0, 168, 0, 656, 0, 0, -780, 0, -476, 0, 0, -672, 0, -192, 0, 0, 1296, 0, -2700, 0, 0, 544, 0, 2616, 0, 0, 2228, 0, 204, 0, 0, 1104, 0, -912, 0, 0, -84, 0, 7706, 0, 0, -448, 0, 252, 0, 0, 984, 0, 360, 0, 0, 496, 0, 96, 0, 0, 2696, 0, -1008, 0, 0, -288, 0, 4040, 0, 0, -1116, 0, 3856, 0, 0, 2016, 0, 816, 0, 0, 3924, 0, -2520, 0, 0, -48, 0, 912, 0, 0, 2082, 0, 1656, 0, 0, -1368, 0, -2304, 0, 0, 5136, 0, -5396, 0, 0, 2880, 0, -672, 0, 0, 378, 0, -8232, 0, 0, 280, 0, 392, 0, 0, -5872, 0, 744, 0, 0, 144, 0, 8000, 0, 0, 13248, 0, -7016, 0, 0, -2784, 0, -432, 0, 0, 6060, 0, -408, 0, 0, -448, 0, -1848, 0, 0, -2668, 0, 3024, 0, 0, 1224, 0, -3936, 0, 0, 1176, 0, 11380, 0, 0, 2000, 0, -72, 0, 0, 1368, 0, 360, 0, 0, -4256, 0, 512, 0, 0, 476, 0, -2052, 0, 0, -3456, 0, 2576, 0, 0, 8268, 0, -5936, 0, 0, 10872, 0, 4320, 0, 0, -1008, 0, -8796, 0, 0, -288, 0, 9792, 0, 0, 9754, 0, 420, 0, 0, 588, 0, -544, 0, 0, -12240, 0, 2296, 0, 0, -2944, 0, 216, 0, 0, 12000, 0, -1056, 0, 0, 9640, 0, 448, 0, 0, -16416, 0, -4176, 0, 0, -648, 0, 2960, 0, 0, -2352, 0, -10040, 0, 0, -15936, 0, -672, 0, 0, -2772, 0, -8064, 0, 0, -2624, 0, -4152, 0, 0, -11884, 0, 1836, 0, 0, -5904, 0, 3120, 0, 0, -21192, 0, 3210, 0, 0, 1904, 0, 3000, 0, 0, -108, 0, 9156, 0, 0, 1728, 0, 2688, 0, 0, -9256, 0, -6384, 0, 0, 768, 0, -13240, 0, 0, -15948, 0, -2160, 0, 0, -5112, 0, -5184, 0, 0, 3864, 0, 19476, 0, 0, 10800, 0, -3192, 0, 0, 860, 0, 16308, 0, 0, 6480, 0, -2176, 0, 0, 3624, 0, -21380, 0, 0, -10464, 0, -432, 0, 0, 14688, 0, -8232, 0, 0, -1568, 0, -8912, 0, 0, -3568, 0, 882, 0, 0, -816, 0, -7552, 0, 0, -15300, 0, -864, 0, 0, -14256, 0, -4416, 0, 0, 324, 0, -6204, 0, 0, 3648, 0, 10632, 0, 0, 1736, 0, 14460, 0, 0, 672, 0, 336, 0, 0, 18576, 0, 2312, 0, 0, -30824, 0, -972, 0, 0, 4440, 0, -11904, 0, 0, 12512, 0, 1792, 0, 0, -21496, 0, -23904, 0, 0, -1008, 0, 51840, 0, 0, -28116, 0, 14140, 0, 0, -21240, 0, -3936, 0, 0, -6228, 0, -28932, 0, 0, -1440, 0, 3312, 0, 0, -40466, 0, -8856, 0, 0, 4680, 0, -1984, 0, 0, 7056, 0, 8716, 0, 0, -384, 0, 2856, 0, 0, 4500, 0, -20976, 0, 0, 19144, 0, -10784, 0, 0, 11152, 0, 2592, 0, 0, 4032, 0, 19088, 0, 0, -22404, 0, -21128, 0, 0, -168, 0, 1152, 0, 0, -19860, 0, 3192, 0, 0, -16160, 0, 26088, 0, 0, -10304, 0, -7668, 0, 0, -7776, 0, 4464, 0, 0, -21192, 0, 29236, 0, 0, -15424, 0, 16200, 0, 0, -4788, 0, -11424, 0, 0, 24976, 0, -8064, 0, 0, 36104, 0, 9720, 0, 0, -3264, 0, -23320, 0, 0, 408, 0, -12416, 0, 0, -20184, 0, -15696, 0, 0, -648, 0, -43020, 0, 0, 10080, 0, 2208, 0, 0, -70848, 0, -2352, 0, 0, -13368, 0, 192, 0, 0, 19488, 0, 5980, 0, 0, -3648, 0, -1224, 0, 0, -11328, 0, 36000, 0, 0, 29944, 0, -8328, 0, 0, 980, 0, -21384, 0, 0, -6624, 0, 1372, 0, 0, 44472, 0, -29048, 0, 0, 40128, 0, 5472, 0, 0, 15948, 0, 49500, 0, 0, 9216, 0, -360, 0, 0, 2084, 0, 1008, 0, 0, 504, 0, -20544, 0, 0, 73920, 0, 28000, 0, 0, 21584, 0, -46236, 0, 0, -1458, 0, 1968, 0, 0, -16064, 0, -11520, 0, 0, 73400, 0, 18768, 0, 0, 2688, 0, 13112, 0, 0, -9744, 0, -30272, 0, 0, -15504, 0, -1512, 0, 0, 77760, 0, 62892, 0, 0, 32928, 0, -11520, 0, 0, 37436, 0, -31860, 0, 0, -5904, 0, -1120, 0, 0, -1104, 0, -5184, 0, 0, -1568, 0, -2160, 0, 0, 4968, 0, -6468, 0, 0, 49384, 0, 23488, 0, 0, -2016, 0, 7020, 0, 0, -2976, 0, -7616, 0, 0, -71508, 0, 67288, 0, 0, -9792, 0, -576, 0, 0, 4284, 0, 57468, 0, 0, -32000, 0, -13776, 0, 0, -35068, 0, 28716, 0, 0, -16176, 0, -52992, 0, 0, -81312, 0, -22786, 0, 0, 28064, 0, 6048, 0, 0, 28632, 0, 12240, 0, 0, 7000, 0, 11136, 0, 0, 90968, 0, -252, 0, 0, 1728, 0, 39752, 0, 0, 8064, 0, 8432, 0, 0, 66240, 0, -24240, 0, 0, 39132, 0, 13068, 0, 0, 1632, 0, -46848, 0, 0, -14896, 0, -11664, 0, 0, 6696, 0, 1792, 0, 0, 12768, 0, 7848, 0, 0, 7392, 0, -23136, 0, 0, 24300, 0, -47208, 0, 0, -14696, 0, 10672, 0, 0, -68368, 0, 37464, 0, 0, -12096, 0, 35936, 0, 0, 107844, 0, 9016, 0, 0, -14448, 0, -4896, 0, 0, -34980, 0, -7212, 0, 0, 15744, 0, -47232, 0, 0, 68680, 0, -30276, 0, 0, -23544, 0, -4704, 0, 0, 38052, 0, -53310, 0, 0, -45520, 0, 15120, 0, 0, 3312, 0, 111768, 0, 0, 23392, 0, -8000, 0, 0, 56160, 0, -20052, 0, 0, 288, 0, -2736, 0, 0, 59040, 0, 103360, 0, 0, -1008, 0, -5472, 0, 0, -1836, 0, 34272, 0, 0, -1440, 0, -65952, 0, 0, 28796, 0, 44916, 0, 0, -12492, 0, 17024, 0, 0, -57456, 0, 112684, 0, 0, -2048, 0, -9936, 0, 0, 2058, 0, -34200, 0, 0, 48384, 0, -1904, 0, 0, -14944, 0, 60192, 0, 0, 8208, 0, 74096, 0, 0, -98076, 0, -77576, 0, 0, -1344, 0, 13824, 0, 0, -540, 0, 35724, 0, 0, -10304, 0, -816, 0, 0, -108652, 0, 756, 0, 0, -30816, 0, -33072, 0, 0, 15504, 0, -60480, 0, 0, 23744, 0, 32376, 0, 0, -69354, 0, -120504, 0, 0, 8560, 0, -43488, 0, 0, 33740, 0, -24096, 0, 0, -17280, 0, 1568, 0, 0, -107028, 0, 194400, 0, 0, -8088, 0, 4032, 0, 0, 19668, 0, -90528, 0, 0, 35184, 0, 29424, 0, 0, 1868, 0, -23256, 0, 0, -2268, 0, 1152, 0, 0, 1488, 0, 10360, 0, 0, -39168, 0, 49392, 0, 0, -17280, 0, 89760, 0, 0, 74296, 0, -39016, 0, 0, 46000, 0, -8856, 0, 0, -1680, 0, -188352, 0, 0, -55776, 0, 41656, 0, 0, -52752, 0, -2352, 0, 0, -3240, 0, 72228, 0, 0, 2176, 0, -90024, 0, 0, 1368, 0, 74076, 0, 0, 35232, 0, 48960, 0, 0, -160416, 0, -51260, 0, 0, -9184, 0, -4464, 0, 0, -11424, 0, -14532, 0, 0, -20672, 0, 11776, 0, 0, 235440, 0, -14688, 0, 0, -864, 0, 22904, 0, 0, -51468, 0, 11776, 0, 0, 31224, 0, -48000, 0, 0, -20664, 0, 12120, 0, 0, 4224, 0, 10920, 0, 0, 33836, 0, -24264, 0, 0, -79488, 0, -38560, 0, 0, -69912, 0, 4760, 0, 0, -1792, 0, 42096, 0, 0, 9072, 0, 672, 0, 0, 6664, 0, 65664, 0, 0, 152672, 0, 10500, 0, 0, 16704, 0, -44560, 0, 0, 57900, 0, -69944, 0, 0, -37248, 0, 2592, 0, 0, 59628, 0, 35940, 0, 0, -11840, 0, 19512, 0, 0, 6048, 0, 99360, 0, 0, -36360, 0, 9408, 0, 0, 44832, 0, -11948, 0, 0, 40160, 0, 2448, 0, 0, -70272, 0, -363168, 0, 0, -82080, 0, 63744, 0, 0, 136000, 0, 10044, 0, 0, 2688, 0, 133064, 0, 0, -6624, 0, -46340, 0, 0, -21480, 0, 11088, 0, 0, -34704, 0, -108180, 0, 0, 32256, 0, 1536, 0, 0, 98994, 0, -22044, 0, 0, 16008, 0, 10496, 0, 0, -17892, 0, -102308, 0, 0, 16608, 0, -18144, 0, 0, 53904, 0, -47328, 0, 0, -144, 0, 47536, 0, 0, -155488, 0, -21672, 0, 0, -7344, 0, -12512, 0, 0, -120420, 0, 2736, 0, 0, 37800, 0, 23616, 0, 0, -70848, 0, -11172, 0, 0, -12480, 0, -40320, 0, 0, -208732, 0, -35316, 0, 0, -7056, 0, 84768, 0, 0, 105432, 0, -25920, 0, 0, -12840, 0, -68280, 0, 0, 22680, 0, 20064, 0, 0, 65152, 0, -7616, 0, 0, -96088, 0, 35088, 0, 0, -12000, 0, -31240, 0, 0, -31416, 0, -23936, 0, 0, -35712, 0, 432, 0, 0, -4104, 0, -100812, 0, 0, -36624, 0, 118032, 0, 0, -97492, 0, -1512, 0, 0, -8208, 0, -6912, 0, 0, -220512, 0, 10304, 0, 0, -10752, 0, -2160, 0, 0, -98928, 0, 40464, 0, 0, -13688, 0, 37024, 0, 0, -5488, 0, -18738, 0, 0, 25536, 0, -31192, 0, 0, -194112, 0, 112504, 0, 0, -66912, 0, -3072, 0, 0, -14904, 0, 44640, 0, 0, 52960, 0, -6744, 0, 0, -23980, 0, 72576, 0, 0, -2856, 0, 63792, 0, 0, -39072, 0, -26432, 0, 0, 8640, 0, 12312, 0, 0, 111144, 0, -100776, 0, 0, -21968, 0, 20448, 0, 0, 120488, 0, -2016, 0, 0, 20736, 0, 34000, 0, 0, -49896, 0, -11152, 0, 0, 69240, 0, -15456, 0, 0, -1224, 0, -41844, 0, 0, -77904, 0, -290880, 0, 0, -15268, 0, -46224, 0, 0, -49608, 0, -43200, 0, 0, 119424, 0, 51196, 0, 0, 12768, 0, 35616, 0, 0, 48564, 0, 37212, 0, 0, -60352, 0, -3440, 0, 0, 80352, 0, 12840, 0, 0, -65232, 0, -114688, 0, 0, 840, 0, -72352, 0, 0, 63648, 0, -25920, 0, 0, 2352, 0, -277632, 0, 0, 8704, 0, 1176, 0, 0, -102028, 0, -12132, 0, 0, 6048, 0, -14496, 0, 0, 363600, 0, -137770, 0, 0, 85520, 0, 52776, 0, 0, 44136, 0, 71760, 0, 0, -107884, 0, 41856, 0, 0, -24808, 0, -3402, 0, 0, 1728, 0, 95480, 0, 0, -165708, 0, 112176, 0, 0, 118440, 0, -58752, 0, 0, 74088, 0, 121596, 0, 0, 32928, 0, 184656, 0, 0, 43792, 0, 111444, 0, 0, -58524, 0, 6272, 0, 0, 11424, 0, 215212, 0, 0, 35648, 0, -2520, 0, 0, -282528, 0, 24000, 0, 0, 11944, 0, 14272, 0, 0, -10048, 0, -79128, 0, 0, -3528, 0, 119024, 0, 0, -57000, 0, 181440, 0, 0, -119808, 0, 3264, 0, 0, -135036, 0, 184824, 0, 0, 30208, 0, 61824, 0, 0, 282740, 0, 52848, 0, 0, 73440, 0, 61200, 0, 0, -74340, 0, -232556, 0, 0, 3456, 0, -13776, 0, 0, -6696, 0, 23160, 0, 0, 145072, 0, 57024, 0, 0, -8352, 0, -31008, 0, 0, 17664, 0, -65664, 0, 0, 55104, 0, -298400, 0, 0, -5040, 0, -1296, 0, 0, 34356, 0, 11592, 0, 0, 24816, 0, -4896, 0, 0, 105222, 0, 46836, 0, 0, -72000, 0, -14592, 0, 0, -149904, 0, -255812, 0, 0, -42528, 0, 6336, 0, 0, 16380, 0, -237864, 0, 0, -162152, 0, -6944, 0, 0, -259168, 0, -119232, 0, 0, -57840, 0, -4320, 0, 0, -194940, 0, -28000, 0, 0, -56256, 0, -2688, 0, 0, 63144, 0, 221580, 0, 0, -1344, 0, 132264, 0, 0, 82080, 0, 9996, 0, 0, 98496, 0, -74304, 0, 0, 248400, 0, -5544, 0, 0, -9248, 0, 25056, 0, 0, -66840, 0, 52392, 0, 0, 105472, 0, 123296, 0, 0, 67004, 0, -55872, 0, 0, 3888, 0, -37744, 0, 0, 245244, 0, -248288, 0, 0, 204504, 0, -17760, 0, 0, 29268, 0, -44472, 0, 0, 47616, 0, -56736, 0, 0, -369792, 0, -54540, 0, 0, 14112, 0, -50048, 0, 0, -24072, 0, 66808, 0, 0, -7168, 0, 60240, 0, 0, 3672, 0, 388512, 0, 0, -208376, 0, 85984, 0, 0, 90320, 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": 7, "prim_orbit_index": 2, "minimal_twist": "42.4.a.a", "char_is_minimal": false, "conrey_index": 799, "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, -2], [0, -3], [-4, 0], [0, 0], [-6, 0], [0, -7], [0, 8], [-9, 0], [0, 0], [-72, 0], [0, 12], [0, -34], [-14, 0], [0, 0], [16, 0], [0, -6], [0, 18], [-92, 0], [0, 0], [-21, 0], [0, 144], [0, -180], [24, 0], [0, 0], [-68, 0], [0, 27], [0, 28], [114, 0], [0, 0], [56, 0], [0, -32], [0, 216], [-12, 0], [0, 0], [36, 0], [0, 34], [0, 184], [-102, 0], [0, 0], [6, 0], [0, 42], [0, 164], [288, 0], [0, 0], [-360, 0], [0, -168], [0, -48], [-49, 0], [0, 0], [-18, 0], [0, 136], [0, 654], [54, 0], [0, 0], [56, 0], [0, 276], [0, -228], [492, 0], [0, 0], [-250, 0], [0, -112], [0, 63], [-64, 0], [0, 0], [432, 0], [0, 124], [0, 24], [-540, 0], [0, 0], [36, 0], [0, -72], [0, 1010], [68, 0], [0, 0], [368, 0], [0, 504], [0, 204], [-56, 0], [0, 0], [81, 0], [0, -12], [0, 228], [84, 0], [0, 0], [328, 0], [0, -342], [0, -576], [-390, 0], [0, 0], [-238, 0], [0, 720], [0, -168], [-336, 0], [0, 0], [-96, 0], [0, 70], [0, 98], [648, 0], [0, 0]]}