# Stored data for newform 112.4.p.g, downloaded from the LMFDB on 18 April 2024.
{"label": "112.4.p.g", "space_label": "112.4.p", "level": 112, "weight": 4, "hecke_orbit": 7, "hecke_orbit_code": 27022628623482992, "dim": 6, "is_polredabs": true, "nf_label": "6.0.12258833328.1", "trace_hash": 2117534388217913822, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [97969, -17215, 5216, -241, 104, -7, 1]]], "qexp_display": "q+(-2\\beta _{3}-\\beta _{5})q^{3}+(-\\beta _{1}-\\beta _{2})q^{5}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 28, "char_orbit_label": "p", "char_is_real": false, "Nk2": 1792, "analytic_conductor": 6.608213920642949, "hecke_ring_index": 12, "level_radical": 14, "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": "0.167", "prec": 17}, "analytic_rank_proved": true, "char_values": [112, 6, [15, 85, 17], [3, 6, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 7], "conrey_indexes": [31, 47], "field_disc": -12258833328, "field_disc_factorization": [[-1, 1], [2, 4], [3, 3], [7, 2], [761, 2]], "field_poly": [576, -672, 808, -20, 29, -1, 1], "hecke_ring_index_factorization": [[2, 2], [3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.653", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "130.681", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5199.708", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "3.2.3.c6", "trace_display": [0, 7, -3, -52], "traces": [0, 6, 0, 7, 0, -3, 0, -52, 0, -78, 0, -99, 0, 0, 0, 0, 0, 9, 0, -143, 0, -15, 0, 15, 0, 306, 0, -362, 0, -348, 0, -205, 0, -471, 0, 1185, 0, -249, 0, -288, 0, 0, 0, 0, 0, 2118, 0, -75, 0, 702, 0, 2505, 0, -645, 0, -918, 0, -6, 0, -321, 0, -1707, 0, 1502, 0, -612, 0, -447, 0, 0, 0, 0, 0, 705, 0, -4138, 0, 555, 0, 3447, 0, 225, 0, -24, 0, 3786, 0, -3642, 0, -2607, 0, 2448, 0, -2991, 0, -2085, 0, 0, 0, 0, 0, -2079, 0, -2095, 0, 3258, 0, 4335, 0, 171, 0, -8762, 0, -1860, 0, -3897, 0, -3264, 0, 4263, 0, -2172, 0, 1236, 0, 0, 0, 0, 0, 6030, 0, -2043, 0, 3429, 0, 14649, 0, -4893, 0, -4408, 0, 6018, 0, -2736, 0, 2646, 0, 7843, 0, 759, 0, -339, 0, 0, 0, 0, 0, 1809, 0, -6471, 0, -7149, 0, 171, 0, -1059, 0, 9480, 0, 2574, 0, -1490, 0, -16323, 0, 238, 0, 801, 0, 3525, 0, 0, 0, 0, 0, 8841, 0, -4479, 0, 14688, 0, 5859, 0, 4731, 0, -1056, 0, 2964, 0, 6307, 0, 1761, 0, -984, 0, -5040, 0, -12066, 0, 0, 0, 0, 0, -7278, 0, 6798, 0, -3783, 0, -9675, 0, 2100, 0, -6848, 0, -24936, 0, -8613, 0, 6021, 0, -3063, 0, -5901, 0, -5913, 0, 0, 0, 0, 0, -2103, 0, 9184, 0, -13467, 0, -11952, 0, 10956, 0, -6528, 0, 6054, 0, 10593, 0, 24441, 0, 1595, 0, 6996, 0, 4929, 0, 0, 0, 0, 0, 1905, 0, 5441, 0, -4980, 0, -15858, 0, -5589, 0, -2068, 0, -18132, 0, 12667, 0, -7293, 0, -6408, 0, 14622, 0, 22020, 0, 0, 0, 0, 0, -4119, 0, 3552, 0, -5340, 0, -32511, 0, -2007, 0, 37960, 0, 28530, 0, 255, 0, 3705, 0, -34074, 0, 2151, 0, 12978, 0, 0, 0, 0, 0, -16296, 0, 19997, 0, 4809, 0, 1443, 0, -15066, 0, 48018, 0, -21588, 0, 29922, 0, 2721, 0, -26620, 0, 28269, 0, -33255, 0, 0, 0, 0, 0, -13215, 0, 13482, 0, 945, 0, -9933, 0, 11202, 0, -496, 0, 59658, 0, -4001, 0, 46920, 0, -16083, 0, -2433, 0, 37371, 0, 0, 0, 0, 0, -53910, 0, 6429, 0, -20712, 0, -24444, 0, -2301, 0, -27690, 0, -75654, 0, -465, 0, -99, 0, -17932, 0, -429, 0, 20304, 0, 0, 0, 0, 0, -6423, 0, 23757, 0, -4959, 0, -53892, 0, -5916, 0, 5064, 0, 9060, 0, 4038, 0, 60534, 0, -51, 0, 11892, 0, -38955, 0, 0, 0, 0, 0, 11661, 0, -4283, 0, -30294, 0, -16401, 0, 13893, 0, -10098, 0, 10956, 0, 7644, 0, -48975, 0, 14160, 0, -9693, 0, 36789, 0, 0, 0, 0, 0, 41631, 0, 7341, 0, 32475, 0, -19371, 0, 11370, 0, -13300, 0, -8988, 0, -5289, 0, -8340, 0, -21654, 0, -9888, 0, 29121, 0, 0, 0, 0, 0, -65826, 0, -16758, 0, -38484, 0, 29163, 0, -168, 0, 54960, 0, -16134, 0, 8227, 0, -5355, 0, 9579, 0, -7299, 0, -109173, 0, 0, 0, 0, 0, 46137, 0, -4975, 0, 78582, 0, 50829, 0, -13824, 0, 9660, 0, 48432, 0, 16983, 0, 9081, 0, 16017, 0, 21711, 0, 2796, 0, 0, 0, 0, 0, 36654, 0, 2586, 0, 3915, 0, 87729, 0, -9045, 0, 6144, 0, -55854, 0, -38553, 0, -86166, 0, 46835, 0, 8931, 0, 38469, 0, 0, 0, 0, 0, 62745, 0, -44123, 0, -31728, 0, 18621, 0, 26496, 0, -28488, 0, 39210, 0, -2490, 0, 19761, 0, 43092, 0, -47223, 0, -32439, 0, 0, 0, 0, 0, 47796, 0, -28763, 0, 15702, 0, -11088, 0, -15045, 0, -116280, 0, -55044, 0, -10849, 0, -83337, 0, 45777, 0, -28263, 0, 23427, 0, 0, 0, 0, 0, -33522, 0, 1770, 0, 13152, 0, 29004, 0, -12333, 0, -66536, 0, 88620, 0, -52113, 0, 14265, 0, 76285, 0, -47625, 0, 38439, 0, 0, 0, 0, 0, 30081, 0, -68208, 0, -543, 0, -5994, 0, 28056, 0, 47298, 0, -26100, 0, -53470, 0, 31029, 0, 4920, 0, 3993, 0, -61131, 0, 0, 0, 0, 0, 65124, 0, -18163, 0, 6876, 0, 146604, 0, 35664, 0, -85434, 0, 4548, 0, 523, 0, -46593, 0, -9393, 0, -30297, 0, -87570, 0, 0, 0, 0, 0, -105246, 0, 4929, 0, 64545, 0, 96093, 0, -95412, 0, -100000, 0, 7638, 0, -84822, 0, -2547, 0, 22440, 0, -21747, 0, -21027, 0, 0, 0, 0, 0, -122607, 0, -53592, 0, -6201, 0, 58035, 0, -4356, 0, 139338, 0, 74004, 0, 9183, 0, -86031, 0, -26831, 0, 14334, 0, 25344, 0, 0, 0, 0, 0, 96609, 0, -62354, 0, 136152, 0, 48516, 0, 31206, 0, 62076, 0, 17130, 0, 58943, 0, -14991, 0, -6792, 0, 41268, 0, 130851, 0, 0, 0, 0, 0, 106854, 0, -26499, 0, -19755, 0, -14691, 0, -60741, 0, -26968, 0, 113154, 0, -76221, 0, 6102, 0, 66960, 0, 4767, 0, -11319, 0, 0, 0, 0, 0, 27177, 0, 28753, 0, -148743, 0, -70596, 0, -35649, 0, 100992, 0, 24234, 0, 44802, 0, -90615, 0, 51880, 0, -46863, 0, -41397, 0, 0, 0, 0, 0, -3423, 0, 9985, 0, 4584, 0, 48159, 0, 10593, 0, -126388, 0, -112170, 0, 13728, 0, 43464, 0, 26526, 0, 43311, 0, 28404, 0, 0, 0, 0, 0, 3591, 0, 72357, 0, 34572, 0, -24093, 0, -12747, 0, -130950, 0, 22728, 0, -65010, 0, 83169, 0, -74958, 0, 26460, 0, 120321, 0, 0, 0, 0, 0, 21348, 0, -21249, 0, 11205, 0, -10173, 0, 92148, 0, 154752, 0, -233196, 0, 56798, 0, 94257, 0, 9229, 0, 14553, 0, -144549, 0, 0, 0, 0, 0, -33063, 0, 31548, 0, -122667, 0, -50541, 0, 46044, 0, -177306, 0, 20748, 0, 106155, 0, 95094, 0, 2433, 0, -10794, 0, -57426, 0, 0, 0, 0, 0, -164745, 0, 113709, 0, 181056, 0, -223776, 0, -68997, 0, 14442, 0, -23244, 0, -43653, 0, -34866, 0, -105756, 0, -47142, 0, 31305, 0, 0, 0, 0, 0, -71343, 0, 78967, 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, 28, 6, 1, 6, 0]], "char_orbit_index": 16, "prim_orbit_index": 6, "minimal_twist": "112.4.p.f", "char_is_minimal": true, "conrey_index": 31, "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, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, -2, 0, -1], [0, 0, 0, 0, 0, 0], [0, -1, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-4, 0, 0, 9, -1, 0], [0, 0, 0, 0, 0, 0], [-25, -1, 1, -25, -2, 0], [0, 0, 0, 0, 0, 0], [-22, -1, 0, -11, 1, -1], [0, 0, 0, 0, 0, 0], [-23, 0, -1, -46, 1, 0], [0, 0, 0, 0, 0, 0], [19, 1, -7, 38, 7, 2], [0, 0, 0, 0, 0, 0], [0, 11, 0, 0, -5, 8], [0, 0, 0, 0, 0, 0], [-49, 2, -1, -49, 2, 1], [0, 0, 0, 0, 0, 0], [-1, 2, -5, -3, -1, 16], [0, 0, 0, 0, 0, 0], [0, 5, 6, 0, 0, 1], [0, 0, 0, 0, 0, 0], [0, 0, 0, -94, 0, -24], [0, 0, 0, 0, 0, 0], [-53, -15, -7, 0, -7, 0], [0, 0, 0, 0, 0, 0], [-51, -22, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0], [0, 1, 2, 77, -1, -23], [0, 0, 0, 0, 0, 0], [-51, -4, 4, 51, 0, 8], [0, 0, 0, 0, 0, 0], [200, 22, 8, 19, -9, 1], [0, 0, 0, 0, 0, 0], [-73, -26, 2, -73, -4, -24], [0, 0, 0, 0, 0, 0], [-54, -37, 0, -27, 7, -22], [0, 0, 0, 0, 0, 0], [141, -8, -9, 282, 9, -16], [0, 0, 0, 0, 0, 0], [-20, 22, 16, -40, -16, 44], [0, 0, 0, 0, 0, 0], [438, 73, 0, 219, 25, 24], [0, 0, 0, 0, 0, 0], [-33, 22, -1, -33, 2, 21], [0, 0, 0, 0, 0, 0], [126, 26, 19, 28, -1, 40], [0, 0, 0, 0, 0, 0], [289, -32, -11, -289, 0, 21], [0, 0, 0, 0, 0, 0], [0, 6, 12, 237, -6, -48], [0, 0, 0, 0, 0, 0], [-162, 11, 16, 0, 16, 0], [0, 0, 0, 0, 0, 0], [7, -32, 8, 0, 8, 0], [0, 0, 0, 0, 0, 0], [0, 2, 4, 108, -2, 3], [0, 0, 0, 0, 0, 0], [-189, -2, 6, 189, 0, 8], [0, 0, 0, 0, 0, 0], [487, 13, -15, 481, 32, 20], [0, 0, 0, 0, 0, 0], [-219, -1, -23, -219, 46, -24], [0, 0, 0, 0, 0, 0], [-88, 8, 0, -44, -42, 25], [0, 0, 0, 0, 0, 0], [-66, -8, 39, -132, -39, -16], [0, 0, 0, 0, 0, 0], [322, -26, 14, 644, -14, -52], [0, 0, 0, 0, 0, 0], [190, -58, 0, 95, -42, -8], [0, 0, 0, 0, 0, 0], [-1340, -70, 24, -1340, -48, -46], [0, 0, 0, 0, 0, 0], [-33, -11, -25, -246, 30, -32], [0, 0, 0, 0, 0, 0], [372, 33, -14, -372, 0, -47], [0, 0, 0, 0, 0, 0], [0, -23, -46, -122, 23, 72], [0, 0, 0, 0, 0, 0], [-42, 92, 22, 0, 22, 0], [0, 0, 0, 0, 0, 0], [639, 16, -40, 0, -40, 0], [0, 0, 0, 0, 0, 0], [0, -17, -34, 1197, 17, 0], [0, 0, 0, 0, 0, 0], [-291, 4, -28, 291, 0, -32], [0, 0, 0, 0, 0, 0], [525, -54, -47, 210, 15, -68], [0, 0, 0, 0, 0, 0], [-1007, 90, 30, -1007, -60, 120], [0, 0, 0, 0, 0, 0], [-476, -6, 0, -238, 44, -25], [0, 0, 0, 0, 0, 0], [45, 48, -1, 90, 1, 96], [0, 0, 0, 0, 0, 0], [113, 4, -23, 226, 23, 8], [0, 0, 0, 0, 0, 0]]}