# Stored data for newform 35.3.c.b, downloaded from the LMFDB on 23 April 2024. {"label": "35.3.c.b", "space_label": "35.3.c", "level": 35, "weight": 3, "hecke_orbit": 2, "hecke_orbit_code": 4503737116655651, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1504593162416961282, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [0, 1]], [3, [-1, 1]]], "qexp_display": "q+q^{3}+4q^{4}-5q^{5}+7q^{7}-8q^{9}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 35, "char_orbit_label": "c", "char_is_real": true, "Nk2": 315, "analytic_conductor": 0.9536809252610392, "hecke_ring_index": 1, "level_radical": 35, "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": 1, "is_self_dual": true, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.512", "prec": 17}, "analytic_rank_proved": true, "char_values": [35, 2, [22, 31], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 2, "level_primes": [5, 7], "conrey_indexes": [34], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.958", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.827", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.316", "prec": 17}], "related_objects": [], "self_twist_discs": [-35], "cm_discs": [-35], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "2.2.1.d2", "trace_display": [0, 1, -5, 7], "traces": [0, 1, 0, 1, 4, -5, 0, 7, 0, -8, 0, -13, 4, -19, 0, -5, 16, 29, 0, 0, -20, 7, 0, 0, 0, 25, 0, -17, 28, 23, 0, 0, 0, -13, 0, -35, -32, 0, 0, -19, 0, 0, 0, 0, -52, 40, 0, -31, 16, 49, 0, 29, -76, 0, 0, 65, 0, 0, 0, 0, -20, 0, 0, -56, 64, 95, 0, 0, 116, 0, 0, 2, 0, -34, 0, 25, 0, -91, 0, -157, -80, 55, 0, 86, 28, -145, 0, 23, 0, 0, 0, -133, 0, 0, 0, 0, 0, 149, 0, 104, 100, 0, 0, -199, 0, -35, 0, 0, -68, -97, 0, 0, 112, 0, 0, 0, 92, 152, 0, 203, 0, 48, 0, 0, 0, -125, 0, 0, 0, 0, 0, 0, -52, 0, 0, 85, 0, 0, 0, 0, -140, -31, 0, 247, -128, -115, 0, 49, 0, -262, 0, -13, 0, -232, 0, 0, -76, 134, 0, 0, 0, 0, 0, 0, 0, 65, 0, -271, 0, 192, 0, 0, 0, 221, 0, 175, -208, 0, 0, 218, 160, 0, 0, 0, 0, 0, 0, -377, -124, -119, 0, 347, 64, 0, 0, 95, 196, 0, 0, 0, 0, 0, 0, 161, 116, 0, 0, 0, -304, 0, 0, 107, 0, 2, 0, 0, 0, 0, 0, -34, 260, -551, 0, 401, 0, -200, 0, -391, 0, 0, 0, -91, 0, 0, 0, 155, 0, -157, 0, -397, -80, 0, 0, 208, 0, -245, 0, 0, 0, 86, 0, 0, -224, 0, 0, -145, 256, 494, 0, 0, 380, -184, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 464, -133, 0, -325, 0, 0, 0, 0, 0, 527, 0, -559, 8, 0, 0, 0, 0, 552, 0, 149, -136, -19, 0, 0, 0, 221, 0, 0, 100, 0, 0, 0, 0, 0, 0, 569, -364, -199, 0, 0, 0, 221, 0, 280, -628, 0, 0, -299, -320, 0, 0, 0, 220, -475, 0, -97, 0, -217, 0, -598, 344, 0, 0, 0, 112, 0, 0, 0, -580, 0, 0, 343, 0, 0, 0, 0, 92, 0, 0, 323, 0, -139, 0, -10, 0, 203, 0, 578, 0, 361, 0, 48, -532, 170, 0, -391, 0, 0, 0, 0, 0, 0, 0, -125, 0, -437, 0, -502, 0, 0, 0, -514, 0, 455, 0, 0, 596, 743, 0, 0, 0, 0, 0, 785, 416, 389, 0, 0, 400, -73, 0, 0, 0, -275, 0, 0, 0, 0, 0, 0, -796, 0, 0, -430, 0, 0, 0, 0, -140, 527, 0, 248, 0, 725, 0, 0, 0, 247, 0, -853, -272, -754, 0, -115, -388, 0, 0, 0, 0, -392, 0, 0, 0, 0, 0, -262, 448, -817, 0, 0, 0, -13, 0, 665, 0, 0, 0, -493, 0, 0, 0, 0, 368, 0, 0, -871, 608, 0, 0, 134, 0, 0, 0, 0, 812, 0, 0, 0, 0, 0, 0, 0, 192, -745, 0, 0, 0, 0, 0, 107, 0, 667, 0, -520, 0, 14, 0, 683, -500, -271, 0, -439, 0, 0, 0, 192, 0, 0, 0, -238, 0, 0, 0, 995, 0, 403, 0, 221, 0, 0, 0, 326, 0, 175, 0, 0, -208, 529, 0, 0, 0, 0, 0, 0, 0, 218, 0, -637, 340, 767, 0, 0, 0, 485, 0, 0, 0, 0, 0, 0, 0, -1099, 0, 0, 0, 0, 0, 0, -560, -377, 0, -874, -124, 0, 0, 385, 0, -1102, 0, -118, 988, 347, 0, 0, -512, 29, 0, 0, -460, 602, 0, 0, 0, -760, 0, 1094, 196, 0, 0, 0, 0, -619, 0, -1015, -1048, 0, 0, 323, 0, 0, 0, 0, -52, -240, 0, 809, 0, 161, 0, 589, -928, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -304, 625, 0, 0, 536, 0, 0, 947, 0, 107, 0, 0, 0, -931, 0, -16, 0, -958, 0, 1241, 0, 0, 0, 974, 0, 0, 0, 0, 0, 0, 0, 0, 0, 272, 0, 1283, 260, 0, 0, -551, 0, 0, 0, 0, -1084, 401, 0, 0, 0, 0, 0, -425, 768, -1291, 0, 1043, 0, -391, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 884, 728, 0, 0, 0, 0, 0, 0, 700, -313, 0, 0, -832, 155, 0, 0, 0, -1417, 0, 1256, 0, 0, 0, -1235, 872, -397, 0, 0, 640, -1393, 0, 0, 0, 575, 0, -1426, 0, -287, 0, 0, 0, 1061, 0, -245, 0, 0, 0, -1357, 0, 0, 0, 0, 0, 1310, 0, -688, -1508, 0, 0, -1333, -496, 0, 0, 65, -476, 0, 0, 0, 0, 0, 0, -679, 1388, 1160, 0, 0, 256, 0, 0, 494, 0, 1541, 0, 0, 0, 0, 0, 0, 380, -26, 0, -391, 784, -670, 0, 449, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1531, 0, -899, 0, 0, 0, 442, 0, 0, 0, 0, 0, -97, 0, 0, 644, 0, 0, 0, 464, 0, 0, 1064, 0, 1607, 0, 0, 0, -325, 0, 0, 0, 0, 0, 0, -1216, 1421, 0, 1355, 0, 0, 0, 0, 0, -312, 0, 527, 428, -960, 0, 336, 0, -559, 0, 0, 8, 86, 0, 0, 0, -706, 0, 0, 0, 0, 0, 0, 0, -1105, 0, 552, 0, 2041, 0, 0, 0, -1192, 0, -875, -136, 0, 0, -19, 1040, 0, 0, 0, -2204, 0, 0, 494, 0, 0, 0, -715, 1604, 0, 0, -1090, 0, 0, 0, 0, -800, 0, 0, 0, 0, 0, 0, 0, -1564, 0, 0, -1678, 0, -1118, 0, 0, 0, 0, 0, -997, 0, 569, 0, -38, -364, 0, 0, 1592, 0, 0, 0, 0, 0, 0, 0, 1885, 0, 1829, 0, 221, 620, 0, 0, 0, 0, 595, 0, 0, -628, 646, 0, 0, 0, 0, 0, -1735, -1588, -299, 0, 0, -320, 961, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 832, 0, 0, -475, 0, 0, 0, 0, -980, 776, 0, 1121, 0, 0, 0, -217, 0, 0, 0, 722, 0, -598, 0, 0, 344, -1651, 0, 0, 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": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 35, 3, -1, 2, -35]], "char_orbit_index": 3, "prim_orbit_index": 3, "minimal_twist": "35.3.c.a", "char_is_minimal": true, "conrey_index": 34, "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], [1], [0], [1], [4], [-5], [0], [7], [0], [-8], [0], [-13], [4], [-19], [0], [-5], [16], [29], [0], [0], [-20], [7], [0], [0], [0], [25], [0], [-17], [28], [23], [0], [0], [0], [-13], [0], [-35], [-32], [0], [0], [-19], [0], [0], [0], [0], [-52], [40], [0], [-31], [16], [49], [0], [29], [-76], [0], [0], [65], [0], [0], [0], [0], [-20], [0], [0], [-56], [64], [95], [0], [0], [116], [0], [0], [2], [0], [-34], [0], [25], [0], [-91], [0], [-157], [-80], [55], [0], [86], [28], [-145], [0], [23], [0], [0], [0], [-133], [0], [0], [0], [0], [0], [149], [0], [104], [100]]}