# Stored data for newform 126.4.a.d, downloaded from the LMFDB on 19 April 2024.
{"label": "126.4.a.d", "space_label": "126.4.a", "level": 126, "weight": 4, "hecke_orbit": 4, "hecke_orbit_code": 13510798949220478, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 2269224398846543891, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [-12, 1]]], "qexp_display": "q-2q^{2}+4q^{4}+12q^{5}+7q^{7}-8q^{8}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 2016, "fricke_eigenval": 1, "atkin_lehner_string": "+--", "analytic_conductor": 7.434240660723318, "hecke_ring_index": 1, "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": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": 0, "analytic_rank_proved": true, "char_values": [126, 1, [29, 73], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3, 7], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.014", "prec": 17}, {"__RealLiteral__": 0, "data": "0.976", "prec": 17}, {"__RealLiteral__": 0, "data": "0.025", "prec": 17}, {"__RealLiteral__": 0, "data": "1.927", "prec": 17}, {"__RealLiteral__": 0, "data": "0.066", "prec": 17}, {"__RealLiteral__": 0, "data": "4.769", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [3, -1], [7, -1]], "trace_display": [-2, 0, 12, 7], "traces": [0, 1, -2, 0, 4, 12, 0, 7, -8, 0, -24, -48, 0, 56, -14, 0, 16, 114, 0, 2, 48, 0, 96, 120, 0, 19, -112, 0, 28, 54, 0, 236, -32, 0, -228, 84, 0, 146, -4, 0, -96, -126, 0, -376, -192, 0, -240, 12, 0, 49, -38, 0, 224, -174, 0, -576, -56, 0, -108, -138, 0, 380, -472, 0, 64, 672, 0, -484, 456, 0, -168, -576, 0, -1150, -292, 0, 8, -336, 0, 776, 192, 0, 252, -378, 0, 1368, 752, 0, 384, 390, 0, 392, 480, 0, -24, 24, 0, -1330, -98, 0, 76, 1500, 0, 380, -448, 0, 348, -636, 0, 146, 1152, 0, 112, -198, 0, 1440, 216, 0, 276, 798, 0, 973, -760, 0, 944, -1272, 0, -376, -128, 0, -1344, -2130, 0, 14, 968, 0, -912, 78, 0, -2338, 336, 0, 1152, -2688, 0, 648, 2300, 0, 584, 1002, 0, -2752, -16, 0, 672, 2832, 0, -520, -1552, 0, -384, 840, 0, 1280, -504, 0, 756, -1764, 0, 939, -2736, 0, -1504, 768, 0, 133, -768, 0, -780, -1812, 0, -448, -784, 0, -960, 1752, 0, -5472, 48, 0, -48, 2136, 0, 4430, 2660, 0, 196, -198, 0, -2284, -152, 0, -3000, 378, 0, -1512, -760, 0, 896, -96, 0, 4412, -696, 0, 1272, -4512, 0, 1652, -292, 0, -2304, 6384, 0, 2072, -224, 0, 396, 366, 0, -376, -2880, 0, -432, 2262, 0, 144, -552, 0, -1596, -2592, 0, 110, -1946, 0, 1520, 588, 0, 112, -1888, 0, 2544, 1890, 0, -5760, 752, 0, 256, -2130, 0, 1022, 2688, 0, 4260, 4992, 0, -2088, -28, 0, -1936, -6816, 0, 8192, 1824, 0, -156, -912, 0, 2414, 4676, 0, -672, -1962, 0, 5402, -2304, 0, 5376, -882, 0, 8083, -1296, 0, -4600, 4788, 0, -1656, -1168, 0, -2004, 6720, 0, -2632, 5504, 0, 32, 4560, 0, -574, -1344, 0, -5664, 8808, 0, -2770, 1040, 0, 3104, -7566, 0, -2592, 768, 0, -1680, 228, 0, 1064, -2560, 0, 1008, 84, 0, -11320, -1512, 0, 3528, -5808, 0, -4786, -1878, 0, 5472, -11328, 0, 343, 3008, 0, -1536, -12648, 0, 9632, -266, 0, 1536, 3390, 0, -6912, 1560, 0, 3624, 10704, 0, -6855, 896, 0, 1568, -13800, 0, -8584, 1920, 0, -3504, -1218, 0, -2122, 10944, 0, -96, 3024, 0, -4912, 96, 0, -4272, -9060, 0, -4032, -8860, 0, -5320, -8994, 0, 13680, -392, 0, 396, 9312, 0, -12976, 4568, 0, 304, 3522, 0, 13216, 6000, 0, -756, -7008, 0, 12710, 3024, 0, 1520, -966, 0, -4536, -1792, 0, 192, -1638, 0, -12850, -8824, 0, 1392, 2166, 0, 2660, -2544, 0, 9024, 8016, 0, 2198, -3304, 0, 584, 240, 0, -376, 4608, 0, -12768, -7188, 0, 4680, -4144, 0, 448, 14670, 0, 6048, -792, 0, -732, 4704, 0, -5146, 752, 0, 5760, 1512, 0, 7184, 864, 0, -4524, 16518, 0, -3388, -288, 0, 1104, 18048, 0, 38, 3192, 0, 5184, -10092, 0, 8176, -220, 0, 3892, -15960, 0, 7832, -3040, 0, -1176, 6732, 0, 6156, -224, 0, 3776, -4032, 0, 18668, -5088, 0, -3780, 6048, 0, 18000, 11520, 0, -1504, -11328, 0, -8050, -512, 0, 4260, 4560, 0, -576, -2044, 0, -5376, 4146, 0, -1006, -8520, 0, -9984, 26904, 0, 2233, 4176, 0, 56, -7056, 0, -7632, 3872, 0, 13632, -2352, 0, -14722, -16384, 0, -3648, 1752, 0, -13480, 312, 0, 1824, 108, 0, 5432, -4828, 0, -9352, -6222, 0, -21056, 1344, 0, 3924, -4926, 0, -2376, -10804, 0, 4608, -22182, 0, 3296, -10752, 0, 1764, 2280, 0, -24334, -16166, 0, 2592, -2646, 0, 8352, 9200, 0, -9576, -1638, 0, 472, 3312, 0, 2336, 7446, 0, 9576, 4008, 0, -13440, 6504, 0, 16058, 5264, 0, -11008, 11676, 0, 10208, -64, 0, -9120, 672, 0, -14974, 1148, 0, 2688, -7254, 0, 12458, 11328, 0, -17616, 2730, 0, -17639, 5540, 0, -2080, 16644, 0, 28352, -6208, 0, 15132, -4512, 0, 2744, 5184, 0, -1536, -27390, 0, -21490, 3360, 0, -456, -17652, 0, 6624, -2128, 0, 5120, 4782, 0, -25560, -2016, 0, -168, 27144, 0, -11860, 22640, 0, 3024, 168, 0, 6480, -7056, 0, 11616, -18240, 0, 5546, 9572, 0, 3756, 14880, 0, -9310, -10944, 0, 22656, -20964, 0, 936, -686, 0, -6016, -9744, 0, 13106, 3072, 0, 25296, -28056, 0, -14364, -19264, 0, 532, 4590, 0, 292, -3072, 0, -6780, 10500, 0, -862, 13824, 0, -3120, 28320, 0, -32256, -7248, 0, -21408, 3540, 0, 2660, 13710, 0, -1792, 1026, 0, -4228, -3136, 0, 27600, -42864, 0, 5420, 17168, 0, -3840, 23232, 0, 1280, 7008, 0, 2436, 35712, 0, 12024, 4244, 0, -21888, -4452, 0, 24464, 192, 0, -6048, -33024, 0, 30242, 9824, 0, -192, 2154, 0, 1022, 8544, 0, 18120, -7728, 0, 10262, 8064, 0, 17720, -9084, 0, 4484, 10640, 0, 17988, -252, 0, 27648, -27360, 0, 784, -6240, 0, -19798, -792, 0, -18624, -1386, 0, 21280, 25952, 0, -9136, -30240, 0, 1368, -608, 0, -7044, 55200, 0, 10080, -26432, 0, -12000, 2346, 0, -29806, 1512, 0, 14016, 15360, 0, -752, -25420, 0, -6048, 1506, 0, -20392, -3040, 0, 1932, -36108, 0, -13876, 9072, 0, 3584, 5586, 0, -21168, -384, 0, 3276, -23436, 0, -21473, 25700, 0, 17648, 11268, 0, 6811, -2784, 0, -4332, 17520, 0, 8120, -5320, 0, 5088, 50010, 0, 34526, -18048, 0, -16032, 17256, 0, 9216, -4396, 0, 6608, -37248, 0, -27104, -1168, 0, -480, -8904, 0, 8714, 752, 0, -9216, 22806, 0, 40196, 25536, 0, 14376, -40812, 0, -2632, -9360, 0, 8288, 24, 0, -21744, -896, 0, -29340, 12744, 0, -19836, -12096, 0, 1584, -5376, 0, -13588, 1464, 0, -9408, 47304, 0, 18144, 10292, 0, -1504, -14910, 0, 1784, -11520, 0, -3024, -32256, 0, 2774, -14368, 0, -1728, 35922, 0, 98, 9048, 0, -33036, -65664, 0, -26782, 6776, 0, 576, -4044, 0, -15120, -2208, 0, -36096, 2136, 0, -64400, -76, 0, -6384, 15174, 0, 25632, -10368, 0, 20184, 546, 0, 25905, -16352, 0, 440, 53160, 0, 25832, -7784, 0, 31920, 37686, 0, -16366, -15664, 0, 6080, 54006, 0, -18720, 2352, 0, -13464, -33276, 0, -2376, -12312, 0, 448, -45120, 0, -3760, -7552, 0, 8064, -27408, 0, 36524, -37336, 0, 10176], "weight_parity": 1, "has_non_self_twist": 0, "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]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "14.4.a.b", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0], [1], [-2], [0], [4], [12], [0], [7], [-8], [0], [-24], [-48], [0], [56], [-14], [0], [16], [114], [0], [2], [48], [0], [96], [120], [0], [19], [-112], [0], [28], [54], [0], [236], [-32], [0], [-228], [84], [0], [146], [-4], [0], [-96], [-126], [0], [-376], [-192], [0], [-240], [12], [0], [49], [-38], [0], [224], [-174], [0], [-576], [-56], [0], [-108], [-138], [0], [380], [-472], [0], [64], [672], [0], [-484], [456], [0], [-168], [-576], [0], [-1150], [-292], [0], [8], [-336], [0], [776], [192], [0], [252], [-378], [0], [1368], [752], [0], [384], [390], [0], [392], [480], [0], [-24], [24], [0], [-1330], [-98], [0], [76]]}