# Stored data for newform 136.4.a.b, downloaded from the LMFDB on 18 April 2024.
{"label": "136.4.a.b", "space_label": "136.4.a", "level": 136, "weight": 4, "hecke_orbit": 2, "hecke_orbit_code": 4503599694479496, "dim": 3, "is_polredabs": true, "nf_label": "3.3.8396.1", "trace_hash": 1805173798237581119, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[3, [28, -30, 4, 1]]], "qexp_display": "q+(-1+\\beta _{2})q^{3}+(-3+\\beta _{1}-2\\beta _{2})q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 2176, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 8.024259760780723, "hecke_ring_index": 2, "level_radical": 34, "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": [136, 1, [103, 69, 105], [1, 1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [2, 17], "conrey_indexes": [1], "field_disc": 8396, "field_disc_factorization": [[2, 2], [2099, 1]], "field_poly": [8, -20, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.895", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "23.195", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "272.525", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [17, 1]], "trace_display": [0, -4, -8, -2], "traces": [0, 3, 0, -4, 0, -8, 0, -2, 0, -5, 0, -84, 0, -50, 0, -148, 0, -51, 0, -224, 0, -16, 0, -234, 0, 161, 0, -292, 0, -72, 0, -2, 0, 148, 0, -428, 0, 100, 0, 156, 0, 218, 0, 44, 0, 768, 0, -16, 0, 403, 0, 68, 0, 462, 0, 460, 0, 688, 0, -68, 0, 460, 0, 586, 0, 408, 0, -1008, 0, 400, 0, 518, 0, 838, 0, 732, 0, -904, 0, 1238, 0, 455, 0, -1148, 0, 136, 0, 1108, 0, -2506, 0, -1416, 0, 648, 0, 40, 0, 2098, 0, -384, 0, -3810, 0, 648, 0, -1896, 0, 472, 0, -1440, 0, 2084, 0, -2074, 0, 268, 0, -906, 0, 34, 0, -989, 0, -3360, 0, -5040, 0, 1636, 0, -5120, 0, -960, 0, -904, 0, 1568, 0, -3102, 0, -1652, 0, 3176, 0, 2396, 0, 296, 0, 3624, 0, -582, 0, 980, 0, 85, 0, -5404, 0, 3690, 0, 1064, 0, 608, 0, -3448, 0, 5592, 0, 4210, 0, -4219, 0, -2184, 0, -136, 0, 10098, 0, 6896, 0, -2768, 0, 6084, 0, 7876, 0, -968, 0, 1428, 0, -1688, 0, -5504, 0, 3474, 0, 4816, 0, -5044, 0, 1794, 0, 3816, 0, -7348, 0, 8528, 0, 42, 0, 7104, 0, -1680, 0, -3976, 0, 7128, 0, 11712, 0, -8872, 0, 850, 0, -7436, 0, -2231, 0, -6904, 0, 6610, 0, -876, 0, 1790, 0, -2288, 0, -5088, 0, -8280, 0, 6586, 0, 11052, 0, -5824, 0, 5176, 0, -5296, 0, 560, 0, 6280, 0, 2516, 0, 2146, 0, -13484, 0, -8080, 0, -204, 0, -12608, 0, 1324, 0, 784, 0, -10712, 0, -1464, 0, -10996, 0, 10456, 0, 250, 0, -14966, 0, -3068, 0, 14272, 0, -5988, 0, 867, 0, -6664, 0, -8406, 0, -21752, 0, 9408, 0, 3536, 0, 13664, 0, 3948, 0, -24248, 0, -2460, 0, -18016, 0, 10842, 0, 2746, 0, 11740, 0, 3172, 0, 7284, 0, 10276, 0, 3808, 0, -11942, 0, -5620, 0, -15080, 0, -908, 0, -17204, 0, 13296, 0, 12678, 0, -2160, 0, -7536, 0, -14464, 0, 11352, 0, 21680, 0, -17090, 0, 6680, 0, 8794, 0, -2084, 0, 272, 0, -7740, 0, -1073, 0, 880, 0, 24048, 0, 2442, 0, 15082, 0, 22060, 0, -12858, 0, 1368, 0, 9608, 0, 9964, 0, -9712, 0, 7252, 0, 17064, 0, 33172, 0, -4798, 0, 3978, 0, -22364, 0, 8060, 0, 13644, 0, 2424, 0, -8350, 0, -11032, 0, -4144, 0, 6884, 0, -16910, 0, 9620, 0, 18208, 0, 14904, 0, -7012, 0, 27332, 0, 13310, 0, -22880, 0, -2737, 0, 9332, 0, -4144, 0, -23162, 0, 18078, 0, 18136, 0, 17640, 0, 4238, 0, -29213, 0, -4112, 0, 18024, 0, 30408, 0, -19046, 0, -3232, 0, -14080, 0, 13520, 0, 8470, 0, 4964, 0, 15518, 0, -39376, 0, -12504, 0, 19472, 0, -48456, 0, -25568, 0, -12048, 0, -13776, 0, -2834, 0, -25686, 0, 13968, 0, 2676, 0, -20992, 0, -542, 0, -9700, 0, -25352, 0, 1224, 0, -30140, 0, 24760, 0, -15872, 0, 2000, 0, 11082, 0, 3672, 0, 5500, 0, -8446, 0, -25124, 0, 22688, 0, 46288, 0, 11560, 0, -8748, 0, -9886, 0, -18328, 0, 23408, 0, 34, 0, -17981, 0, -32396, 0, -860, 0, -31764, 0, -30352, 0, 24, 0, 15068, 0, -24220, 0, 39304, 0, -47728, 0, -45660, 0, 15704, 0, -10848, 0, 23304, 0, 24558, 0, -19488, 0, -2516, 0, -4572, 0, 9936, 0, -17934, 0, 18334, 0, 16668, 0, 36040, 0, -7894, 0, 8890, 0, 8032, 0, 13024, 0, -27288, 0, -26456, 0, 42400, 0, -4216, 0, -43252, 0, 45662, 0, 7276, 0, 27936, 0, -12744, 0, 3646, 0, -28704, 0, -11744, 0, 34334, 0, -4184, 0, 18512, 0, -12270, 0, -17288, 0, -11954, 0, -2568, 0, 22056, 0, -18232, 0, 30995, 0, -23624, 0, -1700, 0, -13732, 0, 2092, 0, 43912, 0, 12326, 0, 26122, 0, 21538, 0, 10252, 0, -44048, 0, 17056, 0, -7936, 0, 24476, 0, 30800, 0, 52796, 0, 34358, 0, 9556, 0, 36686, 0, -2652, 0, 24704, 0, 4500, 0, -14408, 0, -16476, 0, -41022, 0, -30540, 0, -11700, 0, 71860, 0, 27900, 0, 420, 0, -8952, 0, 15628, 0, -28388, 0, 13476, 0, 3504, 0, -5004, 0, -3706, 0, 39024, 0, -5298, 0, 13304, 0, 35632, 0, 29928, 0, -13576, 0, 14074, 0, 4920, 0, -18832, 0, 58712, 0, 45206, 0, -24416, 0, -10224, 0, -42584, 0, -29720, 0, -36665, 0, -748, 0, 24582, 0, 19380, 0, 61800, 0, -27432, 0, -21664, 0, -58466, 0, -87792, 0, 44684, 0, 14864, 0, -1706, 0, -29576, 0, 17512, 0, -41846, 0, -15076, 0, -24830, 0, -52652, 0, -13056, 0, -10224, 0, 38650, 0, 8316, 0, -33846, 0, 95666, 0, -5896, 0, -28752, 0, -32336, 0, 15520, 0, 13392, 0, -28644, 0, -68992, 0, 22644, 0, -8816, 0, -44776, 0, 50150, 0, 272, 0, 8974, 0, -9672, 0, 27144, 0, -16020, 0, -69974, 0, -78152, 0, -13528, 0, 64108, 0, -39408, 0, 19432, 0, -68868, 0, 60846, 0, -35396, 0, -19040, 0, -86686, 0, -25772, 0, -6851, 0, -12004, 0, -16280, 0, -41786, 0, -21303, 0, 46768, 0, 2344, 0, 46874, 0, 64196, 0, -9316, 0, 14064, 0, -73000, 0, -57718, 0, 11244, 0, -34432, 0, -31520, 0, 33560, 0, -1156, 0, -29128, 0, 68400, 0, 42834, 0, -72216, 0, 37088, 0, 12184, 0, 17774, 0, -37088, 0, 10896, 0, -2574, 0, -93200, 0, 272, 0, 28080, 0, 109480, 0, -15352, 0, -50116, 0, -7854, 0, -16216, 0, 47032, 0, 21308, 0, 21894, 0, -26586, 0, 21696, 0, 4072, 0, 15440, 0, 40128, 0, 47672, 0, -37024, 0, -59028, 0, 88120, 0, -59406, 0, 2024, 0, 84192, 0, -7820, 0, 19346, 0, 11056, 0, 57828, 0, -23044, 0, 56752, 0, -100820, 0, 2844, 0, 92076, 0, -9906, 0, -27904, 0, -31576, 0, 15352, 0, 15531, 0, -57524, 0, -47520, 0, 93708, 0, -11696, 0, 76148, 0, 93832, 0, -33004, 0, 54, 0, 82764, 0, 27256, 0, -10362, 0, 92872, 0, -880, 0, -5616, 0, -17962, 0, 48336, 0, -58780, 0, -18052, 0, 5200, 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": "136.4.a.b", "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, 0, 0], [1, 0, 0], [0, 0, 0], [-1, 0, 1], [0, 0, 0], [-3, 1, -2], [0, 0, 0], [-2, -3, -1], [0, 0, 0], [-4, -1, -6], [0, 0, 0], [-27, 2, 1], [0, 0, 0], [-15, 3, 2], [0, 0, 0], [-46, 4, 6], [0, 0, 0], [-17, 0, 0], [0, 0, 0], [-72, 2, 6], [0, 0, 0], [-5, -5, 6], [0, 0, 0], [-78, -1, 1], [0, 0, 0], [49, -22, 8], [0, 0, 0], [-96, 4, 0], [0, 0, 0], [-13, 15, 18], [0, 0, 0], [-8, -25, 3], [0, 0, 0], [39, 3, -34], [0, 0, 0], [-146, 20, -30], [0, 0, 0], [55, 27, 38], [0, 0, 0], [44, 4, -28], [0, 0, 0], [64, 14, -40], [0, 0, 0], [-20, -26, -78], [0, 0, 0], [239, -25, -26], [0, 0, 0], [22, 30, 52], [0, 0, 0], [166, 29, 66], [0, 0, 0], [17, 0, -17], [0, 0, 0], [142, -48, 12], [0, 0, 0], [166, -40, 78], [0, 0, 0], [194, -2, -104], [0, 0, 0], [-8, -42, 86], [0, 0, 0], [183, -25, 114], [0, 0, 0], [216, 65, -3], [0, 0, 0], [148, -32, 68], [0, 0, 0], [-282, 102, 60], [0, 0, 0], [105, -3, -82], [0, 0, 0], [136, -51, -59], [0, 0, 0], [266, 56, -96], [0, 0, 0], [237, -52, 31], [0, 0, 0], [-285, 63, -14], [0, 0, 0], [406, 23, -43], [0, 0, 0], [184, 35, 62], [0, 0, 0], [-424, -22, -102], [0, 0, 0], [51, -17, 34], [0, 0, 0], [334, 12, -118], [0, 0, 0], [-827, 43, -18], [0, 0, 0], [-482, 14, -44], [0, 0, 0], [199, -53, 2], [0, 0, 0], [56, -60, 188], [0, 0, 0], [618, -152, -92], [0, 0, 0], [-73, -14, 179], [0, 0, 0]]}