# Stored data for newform 336.4.bc.d, downloaded from the LMFDB on 19 April 2024. {"label": "336.4.bc.d", "space_label": "336.4.bc", "level": 336, "weight": 4, "hecke_orbit": 4, "hecke_orbit_code": 13512723094569296, "dim": 12, "is_polredabs": true, "trace_hash": 474316101557812143, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [2962842624, 0, 1937507040, 0, 1245448953, 0, 13986756, 0, 121221, 0, 396, 0, 1]], [13, [82121472, 0, 1731204, 0, 4335, 0, 1]]], "qexp_display": "q+\\beta _{1}q^{3}+\\beta _{4}q^{5}+(4+2\\beta _{1}+3\\beta _{2}+\\cdots)q^{7}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 21, "char_orbit_label": "bc", "char_is_real": false, "Nk2": 5376, "analytic_conductor": 19.824641761928845, "hecke_ring_index": 432, "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": "0.590", "prec": 17}, "analytic_rank_proved": true, "char_values": [336, 6, [127, 85, 113, 241], [6, 6, 3, 1]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 4, "level_primes": [2, 3, 7], "conrey_indexes": [17, 257], "field_disc": 1666117098337039248466944, "field_disc_factorization": [[2, 10], [3, 6], [7, 6], [2087, 4]], "field_poly": [531441, -59049, 0, -21141, 486, -441, 1564, -49, 6, -29, 0, -1, 1], "hecke_ring_index_factorization": [[2, 4], [3, 3]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "10.564", "prec": 20}, {"__RealLiteral__": 0, "data": "10.434", "prec": 20}, {"__RealLiteral__": 0, "data": "1047.143", "prec": 27}, {"__RealLiteral__": 0, "data": "3243.088", "prec": 27}, {"__RealLiteral__": 0, "data": "200087.822", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "3.2.3.c6", "trace_display": [0, 3, 0, 56], "traces": [0, 12, 0, 3, 0, 0, 0, 56, 0, -3, 0, 0, 0, 0, 0, -6, 0, 0, 0, -300, 0, 357, 0, 0, 0, -42, 0, 0, 0, 0, 0, 930, 0, -855, 0, 0, 0, 764, 0, 426, 0, 0, 0, 1012, 0, 2367, 0, 0, 0, -336, 0, 1341, 0, 0, 0, 0, 0, 270, 0, 0, 0, 2358, 0, -1071, 0, 0, 0, -792, 0, 0, 0, 0, 0, -2904, 0, 2418, 0, 0, 0, -1674, 0, 837, 0, 0, 0, 348, 0, -1638, 0, 0, 0, 1218, 0, -1479, 0, 0, 0, 0, 0, 3354, 0, 0, 0, -888, 0, 1302, 0, 0, 0, -3184, 0, 0, 0, 0, 0, -30, 0, 4122, 0, 0, 0, -1498, 0, 210, 0, 0, 0, -13968, 0, -174, 0, 0, 0, 84, 0, -1638, 0, 0, 0, 0, 0, -7386, 0, 0, 0, -13566, 0, 10563, 0, 0, 0, -428, 0, 0, 0, 0, 0, -4794, 0, -15273, 0, 0, 0, 5550, 0, 3489, 0, 0, 0, 9024, 0, 1449, 0, 0, 0, -19180, 0, 8277, 0, 0, 0, 0, 0, 14850, 0, 0, 0, 16998, 0, -5418, 0, 0, 0, 1142, 0, 0, 0, 0, 0, -9990, 0, 21777, 0, 0, 0, -11676, 0, -2649, 0, 0, 0, -11840, 0, -6426, 0, 0, 0, -3864, 0, -7929, 0, 0, 0, 0, 0, -19812, 0, 0, 0, -21456, 0, 11697, 0, 0, 0, 10326, 0, 0, 0, 0, 0, 20364, 0, -9747, 0, 0, 0, 306, 0, 6510, 0, 0, 0, 16028, 0, -11439, 0, 0, 0, -7056, 0, 11928, 0, 0, 0, 0, 0, 24606, 0, 0, 0, 16752, 0, 7056, 0, 0, 0, -10800, 0, 0, 0, 0, 0, 60696, 0, 2925, 0, 0, 0, 4956, 0, 4164, 0, 0, 0, -28488, 0, 7182, 0, 0, 0, 27174, 0, 13353, 0, 0, 0, 0, 0, -11322, 0, 0, 0, 13530, 0, 13923, 0, 0, 0, -31598, 0, 0, 0, 0, 0, 13926, 0, -14889, 0, 0, 0, -4964, 0, 3897, 0, 0, 0, 13016, 0, -39564, 0, 0, 0, 28616, 0, -15123, 0, 0, 0, 0, 0, -1620, 0, 0, 0, 7140, 0, 16947, 0, 0, 0, -35166, 0, 0, 0, 0, 0, 20166, 0, -34398, 0, 0, 0, 28596, 0, 11841, 0, 0, 0, 19324, 0, -11094, 0, 0, 0, -41874, 0, 17226, 0, 0, 0, 0, 0, -14862, 0, 0, 0, 52296, 0, 1890, 0, 0, 0, -2550, 0, 0, 0, 0, 0, -47214, 0, 225, 0, 0, 0, -8778, 0, 28512, 0, 0, 0, 41436, 0, -42057, 0, 0, 0, -59094, 0, -13308, 0, 0, 0, 0, 0, -31920, 0, 0, 0, 13812, 0, 25935, 0, 0, 0, 35202, 0, 0, 0, 0, 0, -17388, 0, -48741, 0, 0, 0, -26914, 0, 9828, 0, 0, 0, 33156, 0, -24975, 0, 0, 0, -86254, 0, -7131, 0, 0, 0, 0, 0, -46194, 0, 0, 0, -15906, 0, 16926, 0, 0, 0, 13810, 0, 0, 0, 0, 0, 63924, 0, -38079, 0, 0, 0, -16388, 0, 1680, 0, 0, 0, -7884, 0, -51819, 0, 0, 0, -39774, 0, 7344, 0, 0, 0, 0, 0, -48306, 0, 0, 0, -45576, 0, 22050, 0, 0, 0, -44380, 0, 0, 0, 0, 0, 144996, 0, 34299, 0, 0, 0, -37848, 0, 54018, 0, 0, 0, -21192, 0, -78309, 0, 0, 0, 63560, 0, -20037, 0, 0, 0, 0, 0, -6714, 0, 0, 0, 3696, 0, 78687, 0, 0, 0, -97224, 0, 0, 0, 0, 0, 141282, 0, -20685, 0, 0, 0, 34924, 0, 41544, 0, 0, 0, -40872, 0, 25452, 0, 0, 0, -2436, 0, 50811, 0, 0, 0, 0, 0, -71670, 0, 0, 0, 134394, 0, 59934, 0, 0, 0, -83670, 0, 0, 0, 0, 0, -65220, 0, -27972, 0, 0, 0, 31998, 0, 22095, 0, 0, 0, 79692, 0, -132852, 0, 0, 0, -37842, 0, -13566, 0, 0, 0, 0, 0, -4776, 0, 0, 0, 50664, 0, 41643, 0, 0, 0, 15660, 0, 0, 0, 0, 0, 60600, 0, -20592, 0, 0, 0, 4900, 0, 31830, 0, 0, 0, -46456, 0, -34326, 0, 0, 0, -109326, 0, 17265, 0, 0, 0, 0, 0, 70878, 0, 0, 0, 20028, 0, 70140, 0, 0, 0, 16380, 0, 0, 0, 0, 0, -53508, 0, -14013, 0, 0, 0, -51862, 0, 19959, 0, 0, 0, 72888, 0, -87066, 0, 0, 0, -153552, 0, 66789, 0, 0, 0, 0, 0, 173556, 0, 0, 0, 110508, 0, 88788, 0, 0, 0, -61860, 0, 0, 0, 0, 0, 185754, 0, -6804, 0, 0, 0, -28190, 0, 44226, 0, 0, 0, 86096, 0, -36891, 0, 0, 0, -58170, 0, 14157, 0, 0, 0, 0, 0, -68298, 0, 0, 0, -40314, 0, 85344, 0, 0, 0, -29764, 0, 0, 0, 0, 0, 291654, 0, -164529, 0, 0, 0, 5112, 0, 93027, 0, 0, 0, 143796, 0, -68697, 0, 0, 0, -67998, 0, 36747, 0, 0, 0, 0, 0, 111570, 0, 0, 0, -9102, 0, 9702, 0, 0, 0, -138594, 0, 0, 0, 0, 0, 33384, 0, 65415, 0, 0, 0, -81564, 0, 15660, 0, 0, 0, -187336, 0, -131544, 0, 0, 0, -30394, 0, 621, 0, 0, 0, 0, 0, -68130, 0, 0, 0, -159270, 0, 142674, 0, 0, 0, -74586, 0, 0, 0, 0, 0, -23550, 0, -143550, 0, 0, 0, 49806, 0, 82236, 0, 0, 0, -38804, 0, -49545, 0, 0, 0, -268996, 0, 106425, 0, 0, 0, 0, 0, 22944, 0, 0, 0, 219882, 0, 79128, 0, 0, 0, -2444, 0, 0, 0, 0, 0, -56574, 0, 104301, 0, 0, 0, -82412, 0, 78996, 0, 0, 0, -30580, 0, -143451, 0, 0, 0, 3066, 0, -19065, 0, 0, 0, 0, 0, -241098, 0, 0, 0, -26460, 0, 177408, 0, 0, 0, -47178, 0, 0, 0, 0, 0, 159486, 0, -65016, 0, 0, 0, -94680, 0, 122343, 0, 0, 0, -16992, 0, -86157, 0, 0, 0, -152670, 0, 1398, 0, 0, 0, 0, 0, -64746, 0, 0, 0, 145572, 0, 48300, 0, 0, 0, -97154, 0, 0, 0, 0, 0, 99576, 0, 49176, 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, 21, 7, 1, 6, 0], [1, 1, 3, 2, -1, 2, 0], [1, 1, 7, 4, -1, 6, 0]], "char_orbit_index": 29, "prim_orbit_index": 7, "minimal_twist": "21.4.g.a", "char_is_minimal": false, "conrey_index": 17, "id": null, "nf_label": 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, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 2, 3, -1, 0, 0, 1, 1, 0, 0, -1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 3, 0, 1, 0, 1, 2, 0, 2, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 2, 1, -2, 2, 0, 1, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9, -3, -3, 18, 0, 0, 5, 0, 0, 0, -3, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, -1, 0, 0, -1, 3, -4, -8, -3, 1, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -8, 0, 0, 0, -1, -9, -9, 2, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-34, 1, 1, -17, 0, 0, 1, 0, 0, 0, -2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [44, 4, 5, 31, -3, 1, -12, 1, 4, -1, -4, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -5, 0, 0, 0, 0, -10, -5, -1, 0, 0, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-13, 11, 0, -13, 0, 0, -4, -11, 0, 0, 15, 7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [21, -3, 3, 42, -3, 6, -3, 0, 6, -3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 5, 13, 7, 14, -13, -5, 0, -6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [55, -12, -4, -55, 0, 0, 10, 8, 0, 0, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-98, -5, 10, -49, -5, 8, 10, 4, -4, 0, -20, 5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -3, 0, 0, 3, 6, 9, 3, 3, -13, 0, -12], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -15, -11, -135, 0, 0, 19, 4, 0, 0, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [63, 10, 0, 63, -4, -9, 20, -5, 0, -2, -15, 26], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -8, 0, 0, -16, 8, -6, 0, 8, -16, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [87, 5, 31, 0, 0, 0, 13, 26, 0, 0, -31, 18], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [135, 9, 30, -135, 0, 0, 15, 30, 0, -12, -15, 15], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 17, 0, 0, -14, 10, 0, 27, -5, 0, 0, 17], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-133, 28, 7, -175, 0, 0, 14, -21, 0, 0, -35, 42], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -26, -39, -219, -5, 0, -5, -22, 3, -10, 0, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 38, 0, 0, -6, -10, -28, 28, 0, -3, 0, 66], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-150, 19, 19, -300, 0, 0, 9, 0, 0, 0, 19, 28], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [30, -31, 6, 0, -1, -3, -1, -2, 3, 1, -6, -11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -50, 0, 0, 0, -4, -54, -54, 8, -19, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [228, 51, -38, 114, 0, 0, -38, -89, 0, 0, 76, 13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-237, 35, 6, -282, 25, -6, 7, 20, 18, 20, -30, 46], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 14, 0, 12, 6, 21, 28, 0, -6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-181, 62, 0, -181, 0, 0, 23, -62, 0, 0, 39, 85], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-143, -10, -11, -286, -19, -1, -4, 0, -1, -19, -11, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 19, 0, 0, -4, 17, 18, 36, -17, 4, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-145, -38, 22, 145, 0, 0, 49, 60, 0, 0, -11, 11], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [294, -28, 3, 147, -18, 30, 3, 81, -15, 0, -6, -25], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -30, 0, 0, 23, -24, -15, -54, 37, -18, 0, -15], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 38, -12, 325, 0, 0, -88, -50, 0, 0, 0, -50], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [144, -24, 0, 144, 42, 18, 24, 57, 0, 21, -81, 51], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -14, 0, 0, -13, 14, 27, 0, 14, -13, 0, -41], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [54, -46, 12, 0, 0, 0, 29, 58, 0, 0, -12, -17], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-100, 60, 146, 100, 0, 28, -39, 34, -56, -16, -73, 45], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -103, 0, 0, -48, 52, 0, -51, -26, 0, 0, -103], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [356, -46, -55, 499, 0, 0, 75, -9, 0, 0, 2, 29], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 33, -36, 276, -10, 0, 8, -14, -6, -20, 0, -69], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -12, 0, 0, -32, 9, 3, -3, 0, -16, 0, -15], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [156, 81, 81, 312, 0, 0, -44, 0, 0, 0, 81, 37], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [303, -66, 87, 0, 18, -33, 12, 24, 33, -18, -87, 27], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}