# Stored data for newform 33.4.d.a, downloaded from the LMFDB on 20 April 2024.
{"label": "33.4.d.a", "space_label": "33.4.d", "level": 33, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 206225539105, "dim": 2, "is_polredabs": true, "nf_label": "2.0.11.1", "trace_hash": 1784193026071476463, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [0, 1]]], "qexp_display": "q+(-4-\\beta )q^{3}-8q^{4}-4\\beta q^{5}+(5+8\\beta )q^{9}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 33, "char_orbit_label": "d", "char_is_real": true, "Nk2": 528, "analytic_conductor": 1.9470630301894403, "hecke_ring_index": 2, "level_radical": 33, "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": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.760", "prec": 17}, "analytic_rank_proved": true, "char_values": [33, 2, [23, 13], [1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 4, "level_primes": [3, 11], "conrey_indexes": [32], "field_disc": -11, "field_disc_factorization": [[-1, 1], [11, 1]], "field_poly": [3, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.899", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "22.317", "prec": 20}, {"__RealLiteral__": 0, "data": "0.298", "prec": 17}, {"__RealLiteral__": 0, "data": "292.549", "prec": 24}], "related_objects": [], "self_twist_discs": [-11], "cm_discs": [-11], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.1.d2", "trace_display": [0, -8, 0, 0], "traces": [0, 2, 0, -8, -16, 0, 0, 0, 0, 10, 0, 0, 64, 0, 0, -88, 128, 0, 0, 0, 0, 0, 0, 0, 0, -102, 0, 136, 0, 0, 0, -680, 0, -242, 0, 0, -80, 868, 0, 0, 0, 0, 0, 0, 0, 704, 0, 0, -512, 686, 0, 0, 0, 0, 0, -968, 0, 0, 0, 0, 704, 0, 0, 0, -1024, 0, 0, 832, 0, -1276, 0, 0, 0, 0, 0, 408, 0, 0, 0, 0, 0, -1358, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2720, 0, 0, 0, -68, 0, 1936, 816, 0, 0, 2344, 0, 0, 0, 0, -1088, 0, 0, -3472, 0, 0, 0, -5104, 0, 0, 0, 0, 0, -2662, 0, 0, 5440, 0, 0, 0, 0, 0, 0, 0, 1936, 0, 0, -3256, 0, 0, 0, 0, 0, 4268, 0, 0, 640, 0, 0, -2744, -6944, 0, 0, 0, 0, 0, 0, 0, 0, 2668, 0, 1496, 0, 0, 0, 7456, 0, 3872, 0, 0, 0, 4394, 0, 0, 0, 0, 0, 0, 0, -3652, 0, 0, -5632, -4100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4096, 0, 0, 0, -5488, 0, 0, -7880, 0, -3328, 0, 0, 0, 0, 0, 10208, 0, 0, 0, 0, 0, -6820, 0, 0, 0, 0, 0, 0, 7744, 0, 0, 1336, 0, -510, 0, 0, 0, -6620, 0, 0, 0, 0, 0, 17072, 0, 0, 0, 0, -5632, 0, 0, 7192, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14036, 0, 0, 8192, 0, 0, 0, 0, 0, 0, 0, 0, 5984, 0, -880, -6656, 0, 0, 0, 0, 0, 0, 0, 10208, 0, 0, -3400, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9826, 0, 272, 0, 0, 0, -14608, 0, -8954, 0, 0, -3264, 0, 0, 0, 0, 0, 0, 0, 0, -9376, 0, 0, 0, 21964, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10864, 0, 0, 0, 0, 0, 0, 16240, 0, 4340, 0, 0, 0, 0, 0, -7216, 0, 0, 0, 0, 0, 20416, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27280, 0, 0, 0, 0, 0, 13718, 0, 10648, 0, 0, 0, -19832, 0, 0, 0, 0, -21760, 0, 0, -6512, 0, 0, 0, 25600, 0, 0, 0, 0, 0, 0, 0, 0, 544, 0, 0, 0, 0, 0, 0, 0, -15488, -4748, 0, 0, -6528, 0, 0, 0, 0, 7040, 0, 0, 0, 0, 0, 19712, -18752, 0, 0, 0, 0, 0, 0, 0, 0, 23260, 0, -34144, 0, 0, 0, 0, 0, 0, 0, 0, 8704, -26564, 0, 0, 0, 0, 0, 0, 0, 3430, 0, 0, 27776, -3520, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40832, 0, 0, 26536, 0, 29920, 0, 0, 0, 0, 0, -10672, 0, 0, 0, 0, 0, -11968, 0, 0, 0, 0, 0, 0, 21296, 0, 0, -33368, 0, -29824, 0, 0, 0, 0, 0, -4840, -43520, 0, 0, -8240, 0, 0, 0, 0, 0, 0, 0, -17576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 46948, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -15488, -49674, 0, 29216, 0, 0, 0, 0, 0, 28820, 0, 0, 26048, 0, 0, 16400, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -38192, 0, 0, 0, 0, 0, 0, 0, 0, -34144, -28864, 0, 0, 0, 0, 0, 0, 0, -5236, 0, 0, -5120, 44932, 0, 0, 0, 0, 0, 16456, 0, 0, 0, 0, 21952, 0, 0, 0, 55552, 0, 0, 0, 0, 31520, 0, 0, 0, 0, 0, 4160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3712, 0, -47212, 0, 0, 0, -38798, 0, 0, -21344, 0, 0, 25816, 0, 0, 0, 0, -11968, 0, 0, 54560, 0, 0, 0, -20336, 0, 0, 0, 0, 0, -40172, 0, 0, -59648, 0, 0, 0, 0, 0, 0, 0, -30976, 47164, 0, 0, 0, 0, 0, 0, 0, -5344, 0, 0, 0, 0, 0, -6936, -35152, 0, 0, 0, 0, 0, 0, 0, 0, 78848, 0, 26480, 0, 0, 0, -60656, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -68288, 0, 0, 29216, 67108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 45056, 0, 0, 0, 32800, 0, 0, 66568, 0, -20870, 0, 0, 0, 0, 0, -30184, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -79304, 0, 52580, 0, 0, 0, -62852, 0, 56144, 0, 0, 0, 0, 0, 0, 0, 0, -32768, 0, 0, 11792, 0, 0, 0, 34680, 0, 0, 0, 0, 0, -75020, 0, 0, 43904, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23936, 63040, 0, 0, 0, 0, 7040, 0, 0, 26624, 0, 0, -55528, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6664, 0, 12342, 0, 0, -81664, -95468, 0, 0, 0, 0, 0, 0, 0, -46240, 0, 0, 0, -48778, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54560, 0, 0, 0, 0, 0, 0, 100192, 0, 0, 0, 0, 0, 0, 0, 39304, 0, 0, 0, 0, 0, -340, 0, 0, 0, 0, 0, 0, -61952, 0, 0, 54544, 0, 58432, 0, 0, 0, 0, 0, 19360, -10688, 0, 0, 115280, 0, 0, 0, 0, 4080, 0, 0, 0, 0, 0, 0, -42512, 0, 0, 0, 0, 0, 0, 0, 0, 52960, 0, 0, 0, 0, 0, 0, 0, 0, -44268, 0, 11720, 0, 0, 0, 0, 0, 36740, 0, 0, 0, 0, 0, -87856, -136576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -63448, 0, 0, 0, -20944, 0, 0, 0, 0, 45056, 171618, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -57536, 0, 0, 0, 0, 0, 0, -9680, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -102920, 0, -64960, 0, 0, 0, 0, 0, 59024, 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": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 11, 2, -1, 2, -11], [1, 1, 3, 2, -1, 2, 0], [1, 1, 33, 4, 1, 2, 0]], "char_orbit_index": 4, "prim_orbit_index": 4, "minimal_twist": "33.4.d.a", "char_is_minimal": true, "conrey_index": 32, "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], [1, 0], [0, 0], [-4, -1], [-8, 0], [0, -4], [0, 0], [0, 0], [0, 0], [5, 8], [0, 0], [0, -11], [32, 8], [0, 0], [0, 0], [-44, 16], [64, 0], [0, 0], [0, 0], [0, 0], [0, 32], [0, 0], [0, 0], [0, -58], [0, 0], [-51, 0], [0, 0], [68, -37], [0, 0], [0, 0], [0, 0], [-340, 0], [0, 0], [-121, 44], [0, 0], [0, 0], [-40, -64], [434, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 88], [352, -20], [0, 0], [0, 194], [-256, -64], [343, 0], [0, 0], [0, 0], [0, 0], [0, 68], [0, 0], [-484, 0], [0, 0], [0, 0], [0, 0], [0, -166], [352, -128], [0, 0], [0, 0], [0, 0], [-512, 0], [0, 0], [0, 0], [416, 0], [0, 0], [-638, 232], [0, 0], [0, -310], [0, 0], [0, 0], [0, 0], [204, 51], [0, 0], [0, 0], [0, 0], [0, 0], [0, -256], [-679, 80], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -40], [0, 0], [0, 0], [0, 464], [1360, 340], [0, 0], [0, 0], [0, 0], [-34, 0], [0, 0], [968, -55], [408, 0]]}