# Stored data for newform 882.4.g.u, downloaded from the LMFDB on 19 April 2024.
{"label": "882.4.g.u", "space_label": "882.4.g", "level": 882, "weight": 4, "hecke_orbit": 21, "hecke_orbit_code": 90072404931380082, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 1489459971669392540, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [81, -9, 1]], [11, [3249, 57, 1]], [13, [-70, 1]]], "qexp_display": "q+2\\zeta_{6}q^{2}+(-4+4\\zeta_{6})q^{4}+9\\zeta_{6}q^{5}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "g", "char_is_real": false, "Nk2": 14112, "analytic_conductor": 52.039684625063224, "hecke_ring_index": 1, "level_radical": 42, "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": [882, 3, [785, 199], [3, 2]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [361, 667], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.011", "prec": 17}, {"__RealLiteral__": 0, "data": "1.942", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.311", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "102.630", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c3", "trace_display": [2, 0, 9, 0], "traces": [0, 2, 2, 0, -4, 9, 0, 0, -16, 0, -18, -57, 0, 140, 0, 0, -16, -51, 0, 5, -72, 0, -228, 69, 0, 44, 140, 0, 0, -228, 0, 23, 32, 0, -204, 0, 0, 253, -10, 0, -72, -84, 0, -248, -228, 0, -138, -201, 0, 0, 176, 0, -280, -393, 0, -1026, 0, 0, -228, -219, 0, -709, 92, 0, 128, 630, 0, -419, -204, 0, 0, 192, 0, -313, -506, 0, -40, 0, 0, -461, 144, 0, -84, -1176, 0, -918, -248, 0, 456, 1017, 0, 0, -552, 0, 402, -45, 0, 3668, 0, 0, 176, 285, 0, -499, -1120, 0, -1572, -1107, 0, -923, -1026, 0, 0, -3084, 0, -621, 456, 0, -876, 0, 0, -1918, 1418, 0, 92, 3042, 0, -4112, 128, 0, -1260, -2049, 0, 0, -1676, 0, 408, -141, 0, -2968, 0, 0, 192, -3990, 0, -1026, -1252, 0, -2024, -57, 0, -839, -40, 0, 0, 414, 0, -2833, 922, 0, 576, 0, 0, 2311, 168, 0, -1176, 2520, 0, 5406, -918, 0, 496, -3267, 0, 0, 1824, 0, -2034, 1287, 0, 5348, 0, 0, -552, -2277, 0, -2907, 1608, 0, -180, 4185, 0, 85, 3668, 0, 0, 780, 0, -2833, -352, 0, 1140, 0, 0, -378, 998, 0, -1120, -570, 0, -248, -1572, 0, 2214, -1116, 0, 0, -3692, 0, 2052, -3570, 0, -112, 0, 0, -3084, 3057, 0, -961, -2484, 0, 1824, -2829, 0, 1809, -876, 0, 0, 7080, 0, 5231, 3836, 0, 5672, 0, 0, 350, -184, 0, 3042, 10080, 0, -7866, -4112, 0, -256, 1437, 0, 0, -5040, 0, 4098, -2325, 0, -7074, 0, 0, -1676, 2385, 0, -331, 1632, 0, -564, 2508, 0, -4871, -2968, 0, 0, 14052, 0, -5353, -384, 0, -15960, 0, 0, 2312, 2052, 0, -1252, 8316, 0, -3942, -2024, 0, 114, 4830, 0, 0, -3356, 0, 80, 6381, 0, 19208, 0, 0, 414, -10131, 0, 10799, -11332, 0, 3688, 531, 0, 6498, 576, 0, 0, -510, 0, 3080, -4622, 0, 672, 0, 0, 7015, 2352, 0, 2520, -7542, 0, 17980, 5406, 0, 1836, 1311, 0, 0, 1984, 0, 6534, -8709, 0, -12964, 0, 0, 1824, 2133, 0, 864, -8136, 0, 5148, 3849, 0, 6834, 5348, 0, 0, -5634, 0, 6491, 1104, 0, -9108, 0, 0, -923, 5814, 0, 1608, -15960, 0, 12688, -180, 0, -8370, 5007, 0, 0, 340, 0, -7336, 12291, 0, -7038, 0, 0, 780, 4149, 0, 887, -11332, 0, -1408, 11955, 0, 1610, 1140, 0, 0, -28842, 0, -3421, 756, 0, 3992, 0, 0, -5292, 2240, 0, -570, -10920, 0, 15460, -248, 0, 3144, 2244, 0, 0, 8856, 0, 2232, -11313, 0, -8428, 0, 0, -3692, -345, 0, 16553, 8208, 0, -14280, -16395, 0, -9153, -112, 0, 0, 30180, 0, 2394, 6168, 0, 12228, 0, 0, 14785, 1922, 0, -2484, 5796, 0, 928, 1824, 0, 5658, -4233, 0, 0, 7236, 0, 1752, 7068, 0, 440, 0, 0, 7080, -2739, 0, 17710, 20924, 0, 15344, 16506, 0, -17051, 5672, 0, 0, 8592, 0, 5814, -700, 0, -736, 0, 0, -3401, -6084, 0, 10080, 33600, 0, 5130, -7866, 0, 8224, -1839, 0, 0, -1024, 0, -2874, 4491, 0, 22914, 0, 0, -5040, -303, 0, -21667, 16392, 0, -9300, 1173, 0, 7406, -7074, 0, 0, -5880, 0, 9963, 3352, 0, 9540, 0, 0, -5039, 662, 0, 1632, -16614, 0, -4784, -564, 0, -5016, -570, 0, 0, -19484, 0, 5936, -22149, 0, -17360, 0, 0, 14052, 8349, 0, -13878, -21412, 0, -1536, -15345, 0, 11593, -15960, 0, 0, 6072, 0, -14593, -4624, 0, 8208, 0, 0, -22401, 2504, 0, 8316, -30744, 0, 230, -3942, 0, 4048, 14373, 0, 0, 456, 0, -9660, 2547, 0, 14084, 0, 0, -3356, 17262, 0, -22591, 320, 0, 25524, -14070, 0, 8485, 19208, 0, 0, 36564, 0, 2291, -828, 0, -40524, 0, 0, 8189, -21598, 0, -11332, -25806, 0, -13856, 3688, 0, -1062, -18504, 0, 0, 25992, 0, -1152, 24975, 0, -19096, 0, 0, -510, -10131, 0, -12483, 12320, 0, -18488, 16659, 0, 18441, 672, 0, 0, -59112, 0, 191, -14030, 0, 9408, 0, 0, -7866, -5040, 0, -7542, 80826, 0, 5212, 17980, 0, -10812, 4209, 0, 0, 7344, 0, -2622, 24303, 0, -2538, 0, 0, 1984, -27510, 0, 15041, 26136, 0, -34836, -13356, 0, 2142, -12964, 0, 0, -49452, 0, -1265, -3648, 0, 8532, 0, 0, 4957, -1728, 0, -8136, 3174, 0, -71820, 5148, 0, -7698, -27669, 0, 0, 27336, 0, -10696, -5016, 0, 27776, 0, 0, -5634, 6324, 0, 14243, 25964, 0, 4416, -23883, 0, -36959, -9108, 0, 0, 25056, 0, 513, 1846, 0, 23256, 0, 0, 17767, -3216, 0, -15960, -15102, 0, -57452, 12688, 0, 360, 26469, 0, 0, -33480, 0, -10014, -15330, 0, -10108, 0, 0, 340, 35565, 0, -1012, -29344, 0, 49164, -210, 0, -5472, -7038, 0, 0, -50994, 0, -8629, -1560, 0, 16596, 0, 0, -49630, -1774, 0, -11332, 41412, 0, 20502, -1408, 0, -23910, -17841, 0, 0, 6440, 0, -2280, -16185, 0, 23576, 0, 0, -28842, -20799, 0, -620, -13684, 0, 3024, -29793, 0, -30323, 3992, 0, 0, -42312, 0, -5269, 10584, 0, 8960, 0, 0, 11340, 1140, 0, -10920, -79632, 0, -22786, 15460, 0, 496, 24327, 0, 0, 12576, 0, -4488, -17457, 0, -29092, 0, 0, 8856, 31449, 0, -24523, 8928, 0, -45252, -8163, 0, 29403, -8428, 0, 0, 52554, 0, -29330, 7384, 0, -1380, 0, 0, -4367, -33106, 0, 8208, -100380, 0, 24616, -14280, 0, 32790, -31617, 0, 0, -36612, 0, 224, 1005, 0, 23166, 0, 0, 30180, -2622, 0, -20043, 9576, 0, 24672, 24066, 0, 13525, 12228, 0, 0, 38496, 0, 33516, -29570, 0, 7688, 0, 0, 8695, 4968, 0, 5796, 13440, 0, 22264, 928, 0, -3648, -19479, 0, 0, 22632, 0, 8466, 26163, 0, 25004, 0, 0, 7236, 15993, 0, -2898, 7008, 0, 28272, 44001, 0, -21910, 440, 0, 0, 8004, 0, -37665, -14160, 0, -10956, 0, 0, 29262, -35420, 0, 20924, 1530, 0, 21088, 15344, 0, -33012, 6183, 0, 0, -68204, 0, -11344, 3723, 0, -115938, 0, 0, 8592, 45897, 0, 3510, 23256, 0, -2800, -8556, 0, -6467, -736, 0, 0, -50994, 0, 23039, 6802, 0, -24336], "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, 7, 3, 1, 3, 0]], "char_orbit_index": 7, "prim_orbit_index": 3, "minimal_twist": "14.4.c.a", "char_is_minimal": false, "conrey_index": 361, "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, 0], [-4, 4], [0, 9], [0, 0], [0, 0], [-8, 0], [0, 0], [-18, 18], [-57, 57], [0, 0], [70, 0], [0, 0], [0, 0], [0, -16], [-51, 51], [0, 0], [0, 5], [-36, 0], [0, 0], [-114, 0], [0, 69], [0, 0], [44, -44], [0, 140], [0, 0], [0, 0], [-114, 0], [0, 0], [23, -23], [32, -32], [0, 0], [-102, 0], [0, 0], [0, 0], [0, 253], [-10, 10], [0, 0], [0, -72], [-42, 0], [0, 0], [-124, 0], [0, -228], [0, 0], [-138, 138], [0, -201], [0, 0], [0, 0], [88, 0], [0, 0], [-280, 280], [-393, 393], [0, 0], [-513, 0], [0, 0], [0, 0], [0, -228], [-219, 219], [0, 0], [0, -709], [46, 0], [0, 0], [64, 0], [0, 630], [0, 0], [-419, 419], [0, -204], [0, 0], [0, 0], [96, 0], [0, 0], [-313, 313], [-506, 506], [0, 0], [-20, 0], [0, 0], [0, 0], [0, -461], [144, -144], [0, 0], [0, -84], [-588, 0], [0, 0], [-459, 0], [0, -248], [0, 0], [456, -456], [0, 1017], [0, 0], [0, 0], [-276, 0], [0, 0], [402, -402], [-45, 45], [0, 0], [1834, 0], [0, 0], [0, 0], [0, 176]]}