# Stored data for newform 882.4.g.ba, downloaded from the LMFDB on 23 April 2024. {"label": "882.4.g.ba", "space_label": "882.4.g", "level": 882, "weight": 4, "hecke_orbit": 27, "hecke_orbit_code": 117094002695603058, "dim": 4, "is_polredabs": true, "nf_label": "4.0.576.2", "trace_hash": 966649027760431780, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [153664, 0, 392, 0, 1]], [11, [196, 14, 1]], [13, [-2592, 0, 1]]], "qexp_display": "q+(-2-2\\beta _{2})q^{2}+4\\beta _{2}q^{4}+14\\beta _{1}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": 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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.506", "prec": 17}, "analytic_rank_proved": true, "char_values": [882, 3, [785, 199], [3, 2]], "hecke_ring_generator_nbound": 25, "inner_twist_count": 4, "level_primes": [2, 3, 7], "conrey_indexes": [361, 667], "field_disc": 576, "field_disc_factorization": [[2, 6], [3, 2]], "field_poly": [4, 0, 2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.805", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "86.490", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2881.388", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c3", "trace_display": [-4, 0, 0, 0], "traces": [0, 4, -4, 0, -8, 0, 0, 0, 32, 0, 0, -28, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 112, 280, 0, -534, 0, 0, 0, 1144, 0, 0, -64, 0, 0, 0, 0, 76, 0, 0, 0, 0, 0, -136, -112, 0, 560, 0, 0, 0, 2136, 0, 0, -148, 0, 0, 0, 0, -1144, 0, 0, 0, 0, 0, 256, -2016, 0, -1368, 0, 0, 0, -2352, 0, 0, 152, 0, 0, 0, 0, -2440, 0, 0, 0, 0, 0, -112, 136, 0, -224, 0, 0, 0, -2240, 0, 0, 56, 0, 0, 0, 0, -2136, 0, 0, 0, 0, 0, 592, -3368, 0, 1636, 0, 0, 0, 2160, 0, 0, -2288, 0, 0, 0, 0, 2270, 0, 0, 0, 0, 0, 6880, -256, 0, -4032, 0, 0, 0, 5472, 0, 0, 1656, 0, 0, 0, 0, 2352, 0, 0, 0, 0, 0, -608, 4100, 0, 944, 0, 0, 0, -7392, 0, 0, -4880, 0, 0, 0, 0, -6572, 0, 0, 0, 0, 0, 1580, 112, 0, 272, 0, 0, 0, 896, 0, 0, 1080, 0, 0, 0, 0, 2240, 0, 0, 0, 0, 0, -224, 2056, 0, -9184, 0, 0, 0, -3176, 0, 0, -4272, 0, 0, 0, 0, -4984, 0, 0, 0, 0, 0, -10992, -592, 0, -6736, 0, 0, 0, -6544, 0, 0, 144, 0, 0, 0, 0, -2160, 0, 0, 0, 0, 0, 9152, 144, 0, 20720, 0, 0, 0, -17232, 0, 0, 4540, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, -7840, -6880, 0, -512, 0, 0, 0, 16128, 0, 0, 14280, 0, 0, 0, 0, -5472, 0, 0, 0, 0, 0, -6624, -7476, 0, -8012, 0, 0, 0, 23936, 0, 0, 4704, 0, 0, 0, 0, 9822, 0, 0, 0, 0, 0, -34384, 608, 0, 8200, 0, 0, 0, -3776, 0, 0, -560, 0, 0, 0, 0, 7392, 0, 0, 0, 0, 0, 19520, 19652, 0, -8008, 0, 0, 0, 8, 0, 0, -13144, 0, 0, 0, 0, 11476, 0, 0, 0, 0, 0, -9016, -1580, 0, 224, 0, 0, 0, -1088, 0, 0, -3972, 0, 0, 0, 0, -896, 0, 0, 0, 0, 0, -4320, 11888, 0, 13714, 0, 0, 0, -21392, 0, 0, 4480, 0, 0, 0, 0, 11452, 0, 0, 0, 0, 0, 41320, 224, 0, 4112, 0, 0, 0, 36736, 0, 0, 10420, 0, 0, 0, 0, 3176, 0, 0, 0, 0, 0, 17088, -996, 0, 9504, 0, 0, 0, -2128, 0, 0, -9968, 0, 0, 0, 0, 16744, 0, 0, 0, 0, 0, 43416, 10992, 0, -1184, 0, 0, 0, 26944, 0, 0, -10728, 0, 0, 0, 0, 6544, 0, 0, 0, 0, 0, -576, 11992, 0, 24472, 0, 0, 0, -10488, 0, 0, -4320, 0, 0, 0, 0, -22416, 0, 0, 0, 0, 0, 15808, -9152, 0, 288, 0, 0, 0, -82880, 0, 0, 952, 0, 0, 0, 0, 17232, 0, 0, 0, 0, 0, -18160, -58744, 0, -1944, 0, 0, 0, 29616, 0, 0, 288, 0, 0, 0, 0, 24488, 0, 0, 0, 0, 0, -89376, 7840, 0, -13760, 0, 0, 0, 2048, 0, 0, 34384, 0, 0, 0, 0, -16128, 0, 0, 0, 0, 0, -57120, -264, 0, -14866, 0, 0, 0, 25632, 0, 0, -10944, 0, 0, 0, 0, -4100, 0, 0, 0, 0, 0, 58216, 6624, 0, -14952, 0, 0, 0, 32048, 0, 0, 13908, 0, 0, 0, 0, -23936, 0, 0, 0, 0, 0, -18816, -14284, 0, 41212, 0, 0, 0, -149520, 0, 0, 19644, 0, 0, 0, 0, -2072, 0, 0, 0, 0, 0, 528, 34384, 0, 1216, 0, 0, 0, -32800, 0, 0, -22592, 0, 0, 0, 0, 3776, 0, 0, 0, 0, 0, 2240, 53280, 0, -33924, 0, 0, 0, 76136, 0, 0, 14784, 0, 0, 0, 0, -44578, 0, 0, 0, 0, 0, -58864, -19520, 0, 39304, 0, 0, 0, 32032, 0, 0, 9460, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 52576, 7548, 0, -68712, 0, 0, 0, 84600, 0, 0, 22952, 0, 0, 0, 0, 80080, 0, 0, 0, 0, 0, -4656, 9016, 0, -3160, 0, 0, 0, -896, 0, 0, -33192, 0, 0, 0, 0, 1088, 0, 0, 0, 0, 0, 15888, 16856, 0, 356, 0, 0, 0, 11016, 0, 0, -1792, 0, 0, 0, 0, -58868, 0, 0, 0, 0, 0, 56448, 4320, 0, 23776, 0, 0, 0, -54856, 0, 0, -152724, 0, 0, 0, 0, 21392, 0, 0, 0, 0, 0, -17920, -19152, 0, -41340, 0, 0, 0, 101600, 0, 0, 22904, 0, 0, 0, 0, -58360, 0, 0, 0, 0, 0, -104824, -41320, 0, 448, 0, 0, 0, -16448, 0, 0, 44208, 0, 0, 0, 0, -36736, 0, 0, 0, 0, 0, -41680, 356, 0, 16464, 0, 0, 0, -175168, 0, 0, 6352, 0, 0, 0, 0, -1440, 0, 0, 0, 0, 0, 2960, -17088, 0, -1992, 0, 0, 0, -38016, 0, 0, 7552, 0, 0, 0, 0, 2128, 0, 0, 0, 0, 0, 39872, -32820, 0, -44144, 0, 0, 0, 46512, 0, 0, 33488, 0, 0, 0, 0, -59024, 0, 0, 0, 0, 0, 229628, -43416, 0, 21984, 0, 0, 0, 4736, 0, 0, -10640, 0, 0, 0, 0, -26944, 0, 0, 0, 0, 0, 42912, -10904, 0, -81984, 0, 0, 0, 68320, 0, 0, 13088, 0, 0, 0, 0, -62212, 0, 0, 0, 0, 0, 139184, 576, 0, 23984, 0, 0, 0, -97888, 0, 0, -1480, 0, 0, 0, 0, 10488, 0, 0, 0, 0, 0, 17280, -149856, 0, 59512, 0, 0, 0, -85760, 0, 0, -44832, 0, 0, 0, 0, 16576, 0, 0, 0, 0, 0, -40584, -15808, 0, -18304, 0, 0, 0, -1152, 0, 0, 784, 0, 0, 0, 0, 82880, 0, 0, 0, 0, 0, -3808, 28068, 0, 27504, 0, 0, 0, 170792, 0, 0, 34464, 0, 0, 0, 0, 42158, 0, 0, 0, 0, 0, -193968, 18160, 0, -117488, 0, 0, 0, 7776, 0, 0, -110760, 0, 0, 0, 0, -29616, 0, 0, 0, 0, 0, -1152, -9520, 0, 79424, 0, 0, 0, 196896, 0, 0, 48976, 0, 0], "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], [1, 1, 7, 4, -1, 6, 0], [1, 1, 7, 2, -1, 2, 0]], "char_orbit_index": 7, "prim_orbit_index": 3, "minimal_twist": "98.4.a.g", "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, 0, 0], [1, 0, 0, 0], [-2, 0, -2, 0], [0, 0, 0, 0], [0, 0, 4, 0], [0, 14, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [8, 0, 0, 0], [0, 0, 0, 0], [0, -28, 0, -28], [0, 0, 14, 0], [0, 0, 0, 0], [0, 0, 0, 36], [0, 0, 0, 0], [0, 0, 0, 0], [-16, 0, -16, 0], [0, 1, 0, 1], [0, 0, 0, 0], [0, -1, 0, 0], [0, 0, 0, 56], [0, 0, 0, 0], [28, 0, 0, 0], [140, 0, 140, 0], [0, 0, 0, 0], [0, 0, 267, 0], [0, 72, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [286, 0, 0, 0], [0, 0, 0, 0], [0, 66, 0, 66], [0, 0, 32, 0], [0, 0, 0, 0], [0, 0, 0, -2], [0, 0, 0, 0], [0, 0, 0, 0], [38, 0, 38, 0], [0, 2, 0, 2], [0, 0, 0, 0], [0, 112, 0, 0], [0, 0, 0, 89], [0, 0, 0, 0], [-34, 0, 0, 0], [-56, 0, -56, 0], [0, 0, 0, 0], [0, 0, -280, 0], [0, -370, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [534, 0, 0, 0], [0, 0, 0, 0], [0, -144, 0, -144], [0, 0, 74, 0], [0, 0, 0, 0], [0, 0, 0, 196], [0, 0, 0, 0], [0, 0, 0, 0], [-572, 0, -572, 0], [0, 307, 0, 307], [0, 0, 0, 0], [0, 10, 0, 0], [0, 0, 0, -132], [0, 0, 0, 0], [64, 0, 0, 0], [-1008, 0, -1008, 0], [0, 0, 0, 0], [0, 0, 684, 0], [0, -4, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-588, 0, 0, 0], [0, 0, 0, 0], [0, 191, 0, 191], [0, 0, -76, 0], [0, 0, 0, 0], [0, 0, 0, -4], [0, 0, 0, 0], [0, 0, 0, 0], [-1220, 0, -1220, 0], [0, -224, 0, -224], [0, 0, 0, 0], [0, 178, 0, 0], [0, 0, 0, -299], [0, 0, 0, 0], [-28, 0, 0, 0], [68, 0, 68, 0], [0, 0, 0, 0], [0, 0, 112, 0], [0, -437, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-560, 0, 0, 0], [0, 0, 0, 0], [0, 740, 0, 740], [0, 0, -28, 0], [0, 0, 0, 0], [0, 0, 0, 1049], [0, 0, 0, 0], [0, 0, 0, 0], [-1068, 0, -1068, 0]]}