# Stored data for newform 441.4.e.h, downloaded from the LMFDB on 25 April 2024. {"label": "441.4.e.h", "space_label": "441.4.e", "level": 441, "weight": 4, "hecke_orbit": 8, "hecke_orbit_code": 31525472336609721, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 917048228842615791, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [1, 1, 1]], [5, [256, -16, 1]], [13, [-28, 1]]], "qexp_display": "q-\\zeta_{6}q^{2}+(7-7\\zeta_{6})q^{4}+2^{4}\\zeta_{6}q^{5}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "e", "char_is_real": false, "Nk2": 7056, "analytic_conductor": 26.019842312531612, "hecke_ring_index": 1, "level_radical": 21, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [441, 3, [344, 199], [3, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [3, 7], "conrey_indexes": [226, 361], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.026", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "12.260", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "111.782", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c3", "trace_display": [-1, 0, 16, 0], "traces": [0, 2, -1, 0, 7, 16, 0, 0, -30, 0, 16, -8, 0, 56, 0, 0, -41, 54, 0, 110, 224, 0, 16, 48, 0, -131, -28, 0, 0, 220, 0, -12, -161, 0, -108, 0, 0, 246, 110, 0, -240, -364, 0, 256, 56, 0, 48, 324, 0, 0, 262, 0, 196, -162, 0, -256, 0, 0, -110, 810, 0, 488, 24, 0, -334, 448, 0, -244, -378, 0, 0, 1536, 0, 702, 246, 0, 1540, 0, 0, -440, 656, 0, 182, 2604, 0, 1728, -128, 0, 120, 730, 0, 0, 672, 0, 324, -1760, 0, 588, 0, 0, 917, -688, 0, -1388, -840, 0, 324, 244, 0, -90, 128, 0, 0, -2636, 0, -768, 770, 0, -1620, 0, 0, 1267, 488, 0, 84, -192, 0, -3552, 1455, 0, 448, -1118, 0, 0, 488, 0, -810, 2274, 0, -420, 0, 0, -768, -224, 0, 1760, -1404, 0, 3444, -2010, 0, -1112, -1650, 0, 0, -384, 0, -124, -440, 0, -5152, 0, 0, -2008, -1274, 0, -1302, -5768, 0, -2826, -864, 0, 896, 2228, 0, 0, 656, 0, 730, -820, 0, 7784, 0, 0, -720, -3936, 0, 432, 4536, 0, 3520, -5048, 0, 2962, -294, 0, 0, -6668, 0, -1860, 1965, 0, 1376, 0, 0, -2912, -1388, 0, -1148, -1760, 0, -8536, 1134, 0, 244, 2048, 0, 0, 180, 0, -896, 1512, 0, -10864, 0, 0, 1318, -2046, 0, 2980, 1536, 0, -3300, 4458, 0, -5184, -5670, 0, 0, -8880, 0, -3302, 1267, 0, 6832, 0, 0, 3080, 180, 0, 96, -3164, 0, -768, 1776, 0, 119, 2354, 0, 0, 6272, 0, -1118, -3872, 0, -5184, 0, 0, 1708, 180, 0, -2032, -4428, 0, -4548, -1048, 0, 5426, 210, 0, 0, -1684, 0, 3782, 5376, 0, 448, 0, 0, 1997, 1760, 0, -4914, 8624, 0, 25920, -3690, 0, -2010, 1344, 0, 0, 2224, 0, 4510, -7808, 0, 5348, 0, 0, 192, -3768, 0, -2438, 248, 0, -6160, -3186, 0, -880, -2672, 0, 0, 11880, 0, -3668, -2008, 0, 5460, 0, 0, -8672, 9114, 0, 2884, -7808, 0, 1628, 1413, 0, 6048, -96, 0, 0, -3840, 0, 2228, 9344, 0, -10360, 0, 0, -1288, 12178, 0, 12288, 10220, 0, 1640, 440, 0, -5241, -3892, 0, 0, 22464, 0, 9816, 1968, 0, 7872, 0, 0, 442, 432, 0, -4860, 6160, 0, -7920, 12320, 0, -5048, 6708, 0, 0, -5924, 0, 2058, -13350, 0, 5184, 0, 0, 3334, 7040, 0, 1356, 3720, 0, 10742, 6222, 0, -336, 4816, 0, 0, -3936, 0, -5150, -2912, 0, -19432, 0, 0, 20832, -4508, 0, 880, -4620, 0, 2524, 4268, 0, 2430, 7074, 0, 0, 3416, 0, 2048, -4488, 0, 34076, 0, 0, 630, -5280, 0, -16200, 3840, 0, -3024, -8772, 0, -11680, 5432, 0, 0, -4260, 0, 1456, -9226, 0, 4092, 0, 0, -10534, 2980, 0, 5376, 18536, 0, -18784, -4510, 0, 4458, -10806, 0, 0, 10368, 0, -12150, -1024, 0, -28820, 0, 0, 4440, 4940, 0, 6888, 6604, 0, 17738, 4704, 0, 5216, -7320, 0, 0, -8824, 0, 5940, 3080, 0, 984, 0, 0, -19060, -672, 0, 1582, -25536, 0, -22016, 384, 0, -12432, -5500, 0, 0, 23042, 0, 2354, 22208, 0, -5184, 0, 0, -6720, -7338, 0, 17582, -15652, 0, 7744, 648, 0, 9863, 2592, 0, 0, -10192, 0, -3904, 3660, 0, -360, 0, 0, 1618, -2032, 0, 8694, -2880, 0, 32288, -15918, 0, -1048, 12100, 0, 0, -10852, 0, -1470, 4654, 0, 7168, 0, 0, 842, 10078, 0, -21088, -7564, 0, -23040, -5930, 0, 19048, 1568, 0, 0, -12576, 0, 14366, 1997, 0, 24640, 0, 0, -1296, -10530, 0, -4312, 7252, 0, -2640, -12960, 0, 10086, -1062, 0, 0, -28140, 0, 1344, -10200, 0, -50316, 0, 0, 7784, -20272, 0, -25664, -35420, 0, 15616, 9072, 0, -19018, -2674, 0, 0, -34668, 0, -18730, -1344, 0, 7536, 0, 0, 14839, -2438, 0, 868, 26568, 0, -13856, 6600, 0, -3186, -28416, 0, 0, 1760, 0, -23280, 16302, 0, 9436, 0, 0, -5940, -21436, 0, 6480, 7336, 0, -28112, 4458, 0, 17888, 7462, 0, 0, 53280, 0, -7432, -8672, 0, -39060, 0, 0, 5280, -20188, 0, 3904, -7808, 0, 116, -814, 0, -9891, -21516, 0, 0, -25920, 0, -96, 18108, 0, 72768, 0, 0, -5248, -4536, 0, 10078, 31192, 0, -18688, -3360, 0, -9828, 5180, 0, 0, -37524, 0, -27060, 1336, 0, -24356, 0, 0, -6810, 12288, 0, -10950, -1152, 0, -7168, 5740, 0, 440, 4860, 0, 0, 10482, 0, 27244, -14410, 0, -27272, 0, 0, -11232, 6912, 0, -2088, -19632, 0, -15456, -1952, 0, 5160, 27552, 0, 0, 56304, 0, 32160, 442, 0, 6048, 0, 0, 16808, 13284, 0, -3080, -35584, 0, 43348, 3960, 0, 26400, 7422, 0, 0, -70672, 0, 6708, 22680, 0, 27580, 0, 0, -20734, -6232, 0, -1572, -8820, 0, 26700, -20020, 0, -6144, -2592, 0, 0, -3968, 0, 1766, -23338, 0, -14080, 0, 0, 13664, 1356, 0, 13020, -2408, 0, 34992, -21091, 0, 6222, 5616, 0, 0, 672, 0, 10320, -7050, 0, 46564, 0, 0, 1968, 32128, 0, 14080, 10300, 0, -40768, 10142, 0, 9192, 20820, 0, 0, 93432, 0, -11240, 20832, 0, -9352, 0, 0, -46144, -6160, 0, 2310, -1400, 0, -24578, -1262, 0, -29876, -22608, 0, 0, 13284, 0, 7074, -11808, 0, -74984, 0, 0, -3660, 28894, 0, 2770, 28672, 0, 8976, 17688, 0, -35648, -17038, 0, 0, 7040, 0, -6832, 1350, 0, 10560, 0, 0, 33566, -16200, 0, 5248, 33516, 0, 22936, -10584, 0, -8772, -50356, 0, 0, 23360, 0, -38024, -35640, 0, -26240, 0, 0, 2130, -1320, 0, 8748, -2912, 0, 39540, 62272, 0, 8716, 14322, 0, 0, -15264, 0, -10416, -10534, 0, 41720, 0, 0, 23080, 11520, 0, -9268, 43008, 0, -64452, 9392, 0, -17710, 45110, 0, 0, 62412, 0, -10806, -6912, 0, 33348, 0, 0, 36288, 43832, 0, -8736, -66420, 0, 2048, -736, 0, 19656, 14410, 0, 0, -76276, 0, 80768, -31080, 0, -9880, 0, 0, 29647, 6888, 0, 23114, 94784, 0, 52448, -19005, 0, 4704, 18762, 0, 0, -10432, 0, 20008, 38394, 0, -11680, 0, 0, 4412, 5388, 0, -53344, -11880, 0, 43120, 6144, 0, -25472, -1932, 0, 0, -59520, 0, 17096, -19060, 0, 2880], "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, 7, 3, 1, 3, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "7.4.a.a", "char_is_minimal": false, "conrey_index": 226, "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, -1], [0, 0], [7, -7], [0, 16], [0, 0], [0, 0], [-15, 0], [0, 0], [16, -16], [-8, 8], [0, 0], [28, 0], [0, 0], [0, 0], [0, -41], [54, -54], [0, 0], [0, 110], [112, 0], [0, 0], [8, 0], [0, 48], [0, 0], [-131, 131], [0, -28], [0, 0], [0, 0], [110, 0], [0, 0], [-12, 12], [-161, 161], [0, 0], [-54, 0], [0, 0], [0, 0], [0, 246], [110, -110], [0, 0], [0, -240], [-182, 0], [0, 0], [128, 0], [0, 56], [0, 0], [48, -48], [0, 324], [0, 0], [0, 0], [131, 0], [0, 0], [196, -196], [-162, 162], [0, 0], [-128, 0], [0, 0], [0, 0], [0, -110], [810, -810], [0, 0], [0, 488], [12, 0], [0, 0], [-167, 0], [0, 448], [0, 0], [-244, 244], [0, -378], [0, 0], [0, 0], [768, 0], [0, 0], [702, -702], [246, -246], [0, 0], [770, 0], [0, 0], [0, 0], [0, -440], [656, -656], [0, 0], [0, 182], [1302, 0], [0, 0], [864, 0], [0, -128], [0, 0], [120, -120], [0, 730], [0, 0], [0, 0], [336, 0], [0, 0], [324, -324], [-1760, 1760], [0, 0], [294, 0], [0, 0], [0, 0], [0, 917]]}