# Stored data for newform 126.4.a.h, downloaded from the LMFDB on 04 September 2025.
{"Nk2": 2016, "analytic_conductor": 7.434240660723318, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [3, -1], [7, 1]], "atkin_lehner_string": "--+", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [126, 1, [29, 73], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 1, "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": 1, "has_non_self_twist": 0, "hecke_cutters": [[5, [-14, 1]]], "hecke_orbit": 8, "hecke_orbit_code": 31525197458702462, "hecke_ring_generator_nbound": 1, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": true, "is_maximal": true, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "126.4.a.h", "level": 126, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 3, 7], "level_radical": 42, "minimal_twist": "14.4.a.a", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+2q^{2}+4q^{4}+14q^{5}-7q^{7}+8q^{8}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "126.4.a", "trace_display": [2, 0, 14, -7], "trace_hash": 1636107641857170350, "trace_moments": [{"__RealLiteral__": 0, "data": "0.021", "prec": 17}, {"__RealLiteral__": 0, "data": "0.992", "prec": 17}, {"__RealLiteral__": 0, "data": "0.067", "prec": 17}, {"__RealLiteral__": 0, "data": "1.974", "prec": 17}, {"__RealLiteral__": 0, "data": "0.223", "prec": 17}, {"__RealLiteral__": 0, "data": "4.977", "prec": 17}], "trace_zratio": 0, "traces": [0, 1, 2, 0, 4, 14, 0, -7, 8, 0, 28, 28, 0, 18, -14, 0, 16, -74, 0, 80, 56, 0, 56, 112, 0, 71, 36, 0, -28, -190, 0, 72, 32, 0, -148, -98, 0, -346, 160, 0, 112, -162, 0, -412, 112, 0, 224, -24, 0, 49, 142, 0, 72, -318, 0, 392, -56, 0, -380, 200, 0, -198, 144, 0, 64, 252, 0, -716, -296, 0, -196, -392, 0, 538, -692, 0, 320, -196, 0, 240, 224, 0, -324, 1072, 0, -1036, -824, 0, 224, -810, 0, -126, 448, 0, -48, 1120, 0, 1354, 98, 0, 284, 1358, 0, -832, 144, 0, -636, -444, 0, 1870, 784, 0, -112, -1378, 0, 1568, -760, 0, 400, 518, 0, -547, -396, 0, 288, -756, 0, 1944, 128, 0, 504, 848, 0, -560, -1432, 0, -592, 2966, 0, 2800, -392, 0, -784, 504, 0, -2660, 1076, 0, -1384, -510, 0, 592, 640, 0, -392, 1008, 0, -2686, 480, 0, 448, -784, 0, -1012, -648, 0, 2144, -544, 0, -1873, -2072, 0, -1648, -1858, 0, -497, 448, 0, -1620, 300, 0, -2358, -252, 0, 896, -4844, 0, -2072, -96, 0, 2240, -1392, 0, 1778, 2708, 0, 196, -1214, 0, 1040, 568, 0, 2716, 1330, 0, -2268, -1664, 0, 288, 2240, 0, -3868, -1272, 0, -888, -5768, 0, -504, 3740, 0, 1568, -1332, 0, 3968, -224, 0, -2756, 3936, 0, 4810, 3136, 0, -1520, 2182, 0, -336, 800, 0, 1036, 3000, 0, 2042, -1094, 0, -792, 686, 0, 1440, 576, 0, -1512, 528, 0, 3136, 3888, 0, 256, -5634, 0, 2422, 1008, 0, 1696, -168, 0, -4452, -1120, 0, -2864, 1310, 0, -2208, -1184, 0, 5932, 1988, 0, 5294, 5600, 0, -784, -3242, 0, -1592, -1568, 0, 1008, 1134, 0, 563, -5320, 0, 2152, 5022, 0, 2800, -2768, 0, -1020, 2016, 0, 2884, 1184, 0, 1280, -2772, 0, -9536, -784, 0, 2016, 968, 0, 3058, -5372, 0, 960, 4986, 0, -5320, 896, 0, -1568, -5920, 0, 1278, -2024, 0, -1296, 168, 0, 8612, 4288, 0, -1088, -10024, 0, -10206, -3746, 0, -4144, 2016, 0, -343, -3296, 0, -3716, -2004, 0, 1330, -994, 0, 896, -978, 0, -5488, -3240, 0, 600, 9680, 0, -459, -4716, 0, -504, 7532, 0, -8656, 1792, 0, -9688, 2226, 0, 5278, -4144, 0, -192, -3420, 0, 6340, 4480, 0, -2784, 6232, 0, -2744, 3556, 0, 5416, 14810, 0, -8288, 392, 0, -2428, 3360, 0, 5154, 2080, 0, 1136, -3282, 0, 1296, 5432, 0, 2660, -9688, 0, 5810, -4536, 0, -3328, -1400, 0, 15008, 576, 0, 4480, -13560, 0, -738, -7736, 0, -2544, -5254, 0, 1386, -1776, 0, -11536, -1272, 0, -5062, -1008, 0, 7480, 8960, 0, 5640, 3136, 0, -2664, -13388, 0, -11340, 7936, 0, -448, 3230, 0, -4536, -5512, 0, 7872, -1764, 0, -10646, 9620, 0, 6272, -7282, 0, 12688, -3040, 0, 4364, 2816, 0, 5012, -672, 0, 1600, -11536, 0, 5680, 2072, 0, 6000, 3160, 0, -6228, 4084, 0, -2188, 18956, 0, -14176, -1584, 0, 1372, 11268, 0, 14060, 2880, 0, 1152, 2744, 0, -4460, -3024, 0, 1056, 1512, 0, 19012, 6272, 0, 7776, 11790, 0, -3766, 512, 0, -11268, -11648, 0, -672, 4844, 0, 2016, -1362, 0, 6968, 3392, 0, -336, -5328, 0, 377, -8904, 0, -2240, -2916, 0, -6216, -5728, 0, 2620, 1372, 0, 7062, -4416, 0, -2368, 26180, 0, -8196, 11864, 0, 3976, -15200, 0, -1680, 10588, 0, 11200, 7466, 0, -7416, -1568, 0, -6484, -24968, 0, -19292, -3184, 0, -3136, -14250, 0, 6372, 2016, 0, 2268, 7952, 0, -8366, 1126, 0, -10640, -7504, 0, -8904, 4304, 0, 10044, -20384, 0, 5760, 5600, 0, -5536, -9378, 0, 7252, -2040, 0, 4032, 9000, 0, 7562, 5768, 0, 2368, -7658, 0, -2976, 2560, 0, -5544, -432, 0, 4278, -19072, 0, -1568, -18794, 0, 18040, 4032, 0, 1936, 5670, 0, -19459, 6116, 0, -10744, 25604, 0, -21688, 1920, 0, 9972, 27216, 0, 882, -10640, 0, 1792, 10558, 0, -26152, -3136, 0, -11840, -25584, 0, 5600, 2556, 0, -4048, -15198, 0, 11872, -2592, 0, 336, 6100, 0, -2318, 17224, 0, 8576, -7840, 0, -21280, -2176, 0, -20048, -5544, 0, -10222, -20412, 0, -7492, -25434, 0, -9478, -8288, 0, 4032, 8532, 0, 41524, -686, 0, -6592, -5724, 0, 20672, -7432, 0, -4008, 39200, 0, 11988, 2660, 0, -1988, 21458, 0, -27680, 1792, 0, -1956, -9506, 0, -9850, -10976, 0, -6480, 8064, 0, 7056, 1200, 0, 19360, 18840, 0, 5824, -918, 0, -9432, -13490, 0, 37504, -1008, 0, 15064, 30488, 0, 13338, -17312, 0, 3584, -20048, 0, 17100, -19376, 0, 4452, 19632, 0, -7140, 10556, 0, -8288, 3108, 0, 33912, -384, 0, -6840, 8288, 0, -31386, 12680, 0, 8960, 34558, 0, -13090, -5568, 0, 12464, 3600, 0, 39130, -5488, 0, 7112, 25982, 0, 5112, 10832, 0, 29620, -12960, 0, -10976, -16576, 0, 784, -37604, 0, 35424, -4856, 0, 6720, 9646, 0, -3564, 10308, 0, 4160, 30606, 0, 1776, 2272, 0, -6564, 15064, 0, -10976, 2592, 0, 10864, -16810, 0, -9368, 5320, 0, -19376, -14168, 0, -32960, 11620, 0, -9072, -34382, 0, -4472, -6656, 0, -2800, 1716, 0, -7910, 30016, 0, 1152, -3626, 0, -7616, 8960, 0, -27120, 19360, 0, 11711, -1476, 0, -15472, -26222, 0, 3829, -5088, 0, -10508, -38752, 0, 698, 2772, 0, -3552, 23406, 0, 7280, -23072, 0, -2544, -9808, 0, -26012, -10124, 0, -2016, 6720, 0, -12888, 14960, 0, 17920, 5292, 0, -8066, 11280, 0, 6272, -25842, 0, -5692, -5328, 0, -26776, 13536, 0, -13608, -22680, 0, 15872, -1920, 0, 4200, -896, 0, 6460, -13680, 0, 23532, -9072, 0, -11024, -33012, 0, 17004, 15744, 0, -3528, 14568, 0, 30016, -21292, 0, 19240, -5936, 0, -1400, 12544, 0, -14564, -7056, 0, -24566, 25376, 0, -6080, 13830, 0, 3920, 8728, 0, 5632, -29008, 0, -24166, 10024, 0, -1344, 10838, 0, -18144, 3200, 0, -23072, 40916, 0, 9684, 11360, 0, 4144, -56618, 0, -19488, 12000, 0, 6320, -20762, 0, -24607, -12456, 0, 8168, 24892, 0, 17504, -4376, 0, 37912, -23112, 0, -19600, -28352, 0, -3168, -23874, 0, -22680, 2744, 0, 22536, 15312, 0, -16996, 28120, 0, 5760, -46144, 0, -16528, 2304, 0, 5488, 14560, 0, -28606, -8920, 0, -6048], "weight": 4, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0], 1, 2, 0, 4, 14, 0, -7, 8, 0, 28, 28, 0, 18, -14, 0, 16, -74, 0, 80, 56, 0, 56, 112, 0, 71, 36, 0, -28, -190, 0, 72, 32, 0, -148, -98, 0, -346, 160, 0, 112, -162, 0, -412, 112, 0, 224, -24, 0, 49, 142, 0, 72, -318, 0, 392, -56, 0, -380, 200, 0, -198, 144, 0, 64, 252, 0, -716, -296, 0, -196, -392, 0, 538, -692, 0, 320, -196, 0, 240, 224, 0, -324, 1072, 0, -1036, -824, 0, 224, -810, 0, -126, 448, 0, -48, 1120, 0, 1354, 98, 0, 284, 1358, 0, -832, 144, 0, -636, -444, 0, 1870, 784, 0, -112, -1378, 0, 1568, -760, 0, 400, 518, 0, -547, -396, 0, 288, -756, 0, 1944, 128, 0, 504, 848, 0, -560, -1432, 0, -592, 2966, 0, 2800, -392, 0, -784, 504, 0, -2660, 1076, 0, -1384, -510, 0, 592, 640, 0, -392, 1008, 0, -2686, 480, 0, 448, -784, 0, -1012, -648, 0, 2144, -544, 0, -1873, -2072, 0, -1648, -1858, 0, -497, 448, 0, -1620, 300, 0, -2358, -252, 0, 896, -4844, 0, -2072, -96, 0, 2240, -1392, 0, 1778, 2708, 0, 196, -1214, 0, 1040, 568, 0, 2716, 1330, 0, -2268, -1664, 0, 288, 2240, 0, -3868, -1272, 0, -888, -5768, 0, -504, 3740, 0, 1568, -1332, 0, 3968, -224, 0, -2756, 3936, 0, 4810, 3136, 0, -1520, 2182, 0, -336, 800, 0, 1036, 3000, 0, 2042, -1094, 0, -792, 686, 0, 1440, 576, 0, -1512, 528, 0, 3136, 3888, 0, 256, -5634, 0, 2422, 1008, 0, 1696, -168, 0, -4452, -1120, 0, -2864, 1310, 0, -2208, -1184, 0, 5932, 1988, 0, 5294, 5600, 0, -784, -3242, 0, -1592, -1568, 0, 1008, 1134, 0, 563, -5320, 0, 2152, 5022, 0, 2800, -2768, 0, -1020, 2016, 0, 2884, 1184, 0, 1280, -2772, 0, -9536, -784, 0, 2016, 968, 0, 3058, -5372, 0, 960, 4986, 0, -5320, 896, 0, -1568, -5920, 0, 1278, -2024, 0, -1296, 168, 0, 8612, 4288, 0, -1088, -10024, 0, -10206, -3746, 0, -4144, 2016, 0, -343, -3296, 0, -3716, -2004, 0, 1330, -994, 0, 896, -978, 0, -5488, -3240, 0, 600, 9680, 0, -459, -4716, 0, -504, 7532, 0, -8656, 1792, 0, -9688, 2226, 0, 5278, -4144, 0, -192, -3420, 0, 6340, 4480, 0, -2784, 6232, 0, -2744, 3556, 0, 5416, 14810, 0, -8288, 392, 0, -2428, 3360, 0, 5154, 2080, 0, 1136, -3282, 0, 1296, 5432, 0, 2660, -9688, 0, 5810, -4536, 0, -3328, -1400, 0, 15008, 576, 0, 4480, -13560, 0, -738, -7736, 0, -2544, -5254, 0, 1386, -1776, 0, -11536, -1272, 0, -5062, -1008, 0, 7480, 8960, 0, 5640, 3136, 0, -2664, -13388, 0, -11340, 7936, 0, -448, 3230, 0, -4536, -5512, 0, 7872, -1764, 0, -10646, 9620, 0, 6272, -7282, 0, 12688, -3040, 0, 4364, 2816, 0, 5012, -672, 0, 1600, -11536, 0, 5680, 2072, 0, 6000, 3160, 0, -6228, 4084, 0, -2188, 18956, 0, -14176, -1584, 0, 1372, 11268, 0, 14060, 2880, 0, 1152, 2744, 0, -4460, -3024, 0, 1056, 1512, 0, 19012, 6272, 0, 7776, 11790, 0, -3766, 512, 0, -11268, -11648, 0, -672, 4844, 0, 2016, -1362, 0, 6968, 3392, 0, -336, -5328, 0, 377, -8904, 0, -2240, -2916, 0, -6216, -5728, 0, 2620, 1372, 0, 7062, -4416, 0, -2368, 26180, 0, -8196, 11864, 0, 3976, -15200, 0, -1680, 10588, 0, 11200, 7466, 0, -7416, -1568, 0, -6484, -24968, 0, -19292, -3184, 0, -3136, -14250, 0, 6372, 2016, 0, 2268, 7952, 0, -8366, 1126, 0, -10640, -7504, 0, -8904, 4304, 0, 10044, -20384, 0, 5760, 5600, 0, -5536, -9378, 0, 7252, -2040, 0, 4032, 9000, 0, 7562, 5768, 0, 2368, -7658, 0, -2976, 2560, 0, -5544, -432, 0, 4278, -19072, 0, -1568, -18794, 0, 18040, 4032, 0, 1936, 5670, 0, -19459, 6116, 0, -10744, 25604, 0, -21688, 1920, 0, 9972, 27216, 0, 882, -10640, 0, 1792, 10558, 0, -26152, -3136, 0, -11840, -25584, 0, 5600, 2556, 0, -4048, -15198, 0, 11872, -2592, 0, 336, 6100, 0, -2318, 17224, 0, 8576, -7840, 0, -21280, -2176, 0, -20048, -5544, 0, -10222, -20412, 0, -7492, -25434, 0, -9478, -8288, 0, 4032, 8532, 0, 41524, -686, 0, -6592, -5724, 0, 20672, -7432, 0, -4008, 39200, 0, 11988, 2660, 0, -1988, 21458, 0, -27680, 1792, 0, -1956, -9506, 0, -9850, -10976, 0, -6480, 8064, 0, 7056, 1200, 0, 19360, 18840, 0, 5824, -918, 0, -9432, -13490, 0, 37504, -1008, 0, 15064, 30488, 0, 13338, -17312, 0, 3584, -20048, 0, 17100, -19376, 0, 4452, 19632, 0, -7140, 10556, 0, -8288, 3108, 0, 33912, -384, 0, -6840, 8288, 0, -31386, 12680, 0, 8960, 34558, 0, -13090, -5568, 0, 12464, 3600, 0, 39130, -5488, 0, 7112, 25982, 0, 5112, 10832, 0, 29620, -12960, 0, -10976, -16576, 0, 784, -37604, 0, 35424, -4856, 0, 6720, 9646, 0, -3564, 10308, 0, 4160, 30606, 0, 1776, 2272, 0, -6564, 15064, 0, -10976, 2592, 0, 10864, -16810, 0, -9368, 5320, 0, -19376, -14168, 0, -32960, 11620, 0, -9072, -34382, 0, -4472, -6656, 0, -2800, 1716, 0, -7910, 30016, 0, 1152, -3626, 0, -7616, 8960, 0, -27120, 19360, 0, 11711, -1476, 0, -15472, -26222, 0, 3829, -5088, 0, -10508, -38752, 0, 698, 2772, 0, -3552, 23406, 0, 7280, -23072, 0, -2544, -9808, 0, -26012, -10124, 0, -2016, 6720, 0, -12888, 14960, 0, 17920, 5292, 0, -8066, 11280, 0, 6272, -25842, 0, -5692, -5328, 0, -26776, 13536, 0, -13608, -22680, 0, 15872, -1920, 0, 4200, -896, 0, 6460, -13680, 0, 23532, -9072, 0, -11024, -33012, 0, 17004, 15744, 0, -3528, 14568, 0, 30016, -21292, 0, 19240, -5936, 0, -1400, 12544, 0, -14564, -7056, 0, -24566, 25376, 0, -6080, 13830, 0, 3920, 8728, 0, 5632, -29008, 0, -24166, 10024, 0, -1344, 10838, 0, -18144, 3200, 0, -23072, 40916, 0, 9684, 11360, 0, 4144, -56618, 0, -19488, 12000, 0, 6320, -20762, 0, -24607, -12456, 0, 8168, 24892, 0, 17504, -4376, 0, 37912, -23112, 0, -19600, -28352, 0, -3168, -23874, 0, -22680, 2744, 0, 22536, 15312, 0, -16996, 28120, 0, 5760, -46144, 0, -16528, 2304, 0, 5488, 14560, 0, -28606, -8920, 0, -6048]}