# Stored data for newform 84.4.a.a, downloaded from the LMFDB on 19 April 2024. {"label": "84.4.a.a", "space_label": "84.4.a", "level": 84, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 67108948, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 2263068300094914730, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [-6, 1]]], "qexp_display": "q-3q^{3}+6q^{5}+7q^{7}+9q^{9}+6^{2}q^{11}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 1344, "fricke_eigenval": 1, "atkin_lehner_string": "-+-", "analytic_conductor": 4.956160440482211, "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": [84, 1, [43, 29, 73], [1, 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": "0.002", "prec": 17}, {"__RealLiteral__": 0, "data": "0.993", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.006", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.077", "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": [0, -3, 6, 7], "traces": [0, 1, 0, -3, 0, 6, 0, 7, 0, 9, 0, 36, 0, 62, 0, -18, 0, 114, 0, -76, 0, -21, 0, -24, 0, -89, 0, -27, 0, 54, 0, -112, 0, -108, 0, 42, 0, -178, 0, -186, 0, 378, 0, -172, 0, 54, 0, -192, 0, 49, 0, -342, 0, -402, 0, 216, 0, 228, 0, 396, 0, 254, 0, 63, 0, 372, 0, -1012, 0, 72, 0, 840, 0, 890, 0, 267, 0, 252, 0, 80, 0, 81, 0, -108, 0, 684, 0, -162, 0, -1638, 0, 434, 0, 336, 0, -456, 0, 1010, 0, 324, 0, 6, 0, -472, 0, -126, 0, -972, 0, -1786, 0, 534, 0, -2286, 0, -144, 0, 558, 0, 798, 0, -35, 0, -1134, 0, -1284, 0, 1328, 0, 516, 0, -1212, 0, -532, 0, -162, 0, -1254, 0, -340, 0, 576, 0, 2232, 0, 324, 0, -147, 0, 1038, 0, 2936, 0, 1026, 0, -672, 0, -1330, 0, 1206, 0, -168, 0, -3364, 0, -648, 0, 3048, 0, 1647, 0, -684, 0, -2706, 0, -623, 0, -1188, 0, 4716, 0, 1910, 0, -762, 0, -1068, 0, 4104, 0, -189, 0, 4080, 0, -2686, 0, -1116, 0, 510, 0, 1352, 0, 3036, 0, 378, 0, 2268, 0, -216, 0, -2736, 0, -3364, 0, -2520, 0, -1032, 0, -784, 0, -2670, 0, 7068, 0, -4768, 0, -801, 0, 420, 0, -1882, 0, -756, 0, 5082, 0, -1152, 0, -240, 0, -5424, 0, -2590, 0, -243, 0, 294, 0, -4712, 0, 324, 0, -4932, 0, -864, 0, -2052, 0, -3438, 0, -1246, 0, 486, 0, 6120, 0, -2412, 0, 4914, 0, -18, 0, 6896, 0, -1302, 0, -3204, 0, 6254, 0, -1008, 0, 1194, 0, -7156, 0, 1368, 0, 2646, 0, 8083, 0, -3030, 0, -3738, 0, 2376, 0, -972, 0, -1488, 0, -1204, 0, -18, 0, 1524, 0, -844, 0, 1416, 0, 6312, 0, 8282, 0, 378, 0, 9318, 0, 1944, 0, 2916, 0, -8664, 0, -5518, 0, 5358, 0, -1344, 0, 1652, 0, -1602, 0, -6072, 0, -1294, 0, 6858, 0, -4032, 0, 343, 0, 432, 0, 3636, 0, 10478, 0, -1674, 0, -7566, 0, 5040, 0, -2394, 0, -8040, 0, -1083, 0, 105, 0, 5340, 0, 7568, 0, 3402, 0, -2814, 0, -13522, 0, 3852, 0, 3348, 0, 2468, 0, -3984, 0, -12336, 0, 1512, 0, -1548, 0, -3762, 0, -2736, 0, 3636, 0, 480, 0, -8770, 0, 1596, 0, 6642, 0, -6944, 0, 486, 0, -6408, 0, -1510, 0, 3762, 0, 2772, 0, -648, 0, 1020, 0, -1260, 0, 3998, 0, -1728, 0, -10146, 0, 1778, 0, -6696, 0, -2736, 0, 2690, 0, -972, 0, 1824, 0, -1240, 0, 441, 0, -3900, 0, -9828, 0, -3114, 0, -10878, 0, 13608, 0, -8808, 0, 2604, 0, 2330, 0, -3078, 0, 15150, 0, -2992, 0, 2016, 0, 8724, 0, -7084, 0, 3990, 0, -6192, 0, 6764, 0, -3618, 0, 9744, 0, -11036, 0, 504, 0, 6060, 0, 4136, 0, 10092, 0, 16212, 0, 6156, 0, 1944, 0, 5880, 0, 2396, 0, -9144, 0, 13128, 0, 36, 0, -4941, 0, 12798, 0, 6230, 0, 2052, 0, -2832, 0, -6912, 0, 8118, 0, 7386, 0, 5180, 0, 1869, 0, -12768, 0, -11591, 0, 3564, 0, 23436, 0, -5832, 0, -14148, 0, 1764, 0, 4070, 0, -5730, 0, -10716, 0, 14780, 0, 2286, 0, -4104, 0, 560, 0, 3204, 0, -6858, 0, -10664, 0, -12312, 0, 6660, 0, -13716, 0, 567, 0, -150, 0, -8188, 0, -12240, 0, 2136, 0, -5854, 0, 8058, 0, -756, 0, -14472, 0, 3348, 0, 17580, 0, 8512, 0, -1530, 0, 17154, 0, 4788, 0, -4056, 0, -18120, 0, 17546, 0, -9108, 0, -210, 0, -14560, 0, -1134, 0, -11904, 0, -4498, 0, -6804, 0, -5478, 0, 6044, 0, 648, 0, -11466, 0, 3421, 0, 8208, 0, -20292, 0, -15352, 0, 10092, 0, 7968, 0, 3038, 0, 7560, 0, -22398, 0, 3764, 0, 3096, 0, -17688, 0, 14256, 0, 2352, 0, 19878, 0, -7272, 0, 8010, 0, -20004, 0, -1306, 0, -21204, 0, -3192, 0, -1296, 0, 14304, 0, 9144, 0, -13054, 0, 2403, 0, 5046, 0, 7070, 0, -1260, 0, 12468, 0, -7524, 0, 5646, 0, -24924, 0, -23212, 0, 2268, 0, -2040, 0, 43092, 0, -15246, 0, 35958, 0, 13528, 0, 3456, 0, 42, 0, 6446, 0, 720, 0, 2688, 0, 13392, 0, 16272, 0, -4704, 0, -3304, 0, 7770, 0, -4806, 0, -10600, 0, 729, 0, -19608, 0, 12542, 0, -882, 0, -36432, 0, 23324, 0, 14136, 0, -6312, 0, 6228, 0, -972, 0, -6804, 0, 35840, 0, 14796, 0, 17616, 0, -34594, 0, 2592, 0, 23946, 0, -12502, 0, 6156, 0, 24552, 0, 18770, 0, 10314, 0, 30342, 0, 9968, 0, 3738, 0, -28728, 0, 30240, 0, -1458, 0, -7980, 0, -26188, 0, -18360, 0, -16002, 0, 15748, 0, 7236, 0, -34818, 0, -21888, 0, -14742, 0, 32040, 0, -1008, 0, 54, 0, -21702, 0, -20356, 0, -20688, 0, -20184, 0, 13072, 0, 3906, 0, -19890, 0, 4232, 0, 9612, 0, 9636, 0, 35294, 0, -18762, 0, 5586, 0, 18288, 0, 3024, 0, -3768, 0, -21473, 0, -3582, 0, 9882, 0, -245, 0, 21468, 0, 4272, 0, -39466, 0, -4104, 0, -34038, 0, -3364, 0, -7938, 0, 13104, 0, -16236, 0, -24249, 0, 2880, 0, -62744, 0, 9090, 0, -8988, 0, -40858, 0, 11214, 0, -37374, 0, 9788, 0, -7128, 0, 50424, 0, 9296, 0, 2916, 0, 14592, 0, 28296, 0, 4464, 0, -6048, 0, -45828, 0, 3612, 0, 11460, 0, -12412, 0, 54, 0, 6576, 0, -3888, 0, -4572, 0, -8484, 0, 8264, 0, 2532, 0, 52080, 0, 15842, 0, -4248, 0, 39426, 0, -3724, 0, -18936, 0, 24624, 0, -4678, 0, -24846, 0, -17346, 0, -9072, 0, -1134, 0, 19452, 0, 55180, 0, -27954, 0, 4458, 0, 24480, 0, -5832, 0, -8778, 0, -17247, 0, -8748, 0, -16116, 0, 52520, 0, 25992, 0, -10404, 0, -2380, 0, 16554, 0, -7566, 0, -58968, 0, -16074, 0, 44376, 0, 3060, 0, 4032, 0, 4128, 0, -27328, 0, -4956, 0, 8112, 0, 2774, 0, 4806, 0], "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": "84.4.a.a", "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], [0], [-3], [0], [6], [0], [7], [0], [9], [0], [36], [0], [62], [0], [-18], [0], [114], [0], [-76], [0], [-21], [0], [-24], [0], [-89], [0], [-27], [0], [54], [0], [-112], [0], [-108], [0], [42], [0], [-178], [0], [-186], [0], [378], [0], [-172], [0], [54], [0], [-192], [0], [49], [0], [-342], [0], [-402], [0], [216], [0], [228], [0], [396], [0], [254], [0], [63], [0], [372], [0], [-1012], [0], [72], [0], [840], [0], [890], [0], [267], [0], [252], [0], [80], [0], [81], [0], [-108], [0], [684], [0], [-162], [0], [-1638], [0], [434], [0], [336], [0], [-456], [0], [1010], [0], [324], [0]]}