# Stored data for newform 315.5.e.a, downloaded from the LMFDB on 24 April 2024.
{"label": "315.5.e.a", "space_label": "315.5.e", "level": 315, "weight": 5, "hecke_orbit": 1, "hecke_orbit_code": 274961793339, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 2174907550204942762, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [0, 1]], [13, [-23, 1]]], "qexp_display": "q+2^{4}q^{4}-5^{2}q^{5}+7^{2}q^{7}+73q^{11}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 35, "char_orbit_label": "e", "char_is_real": true, "Nk2": 7875, "analytic_conductor": 32.56153837141096, "hecke_ring_index": 1, "level_radical": 105, "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": "0.513", "prec": 17}, "analytic_rank_proved": true, "char_values": [315, 2, [281, 127, 136], [2, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 2, "level_primes": [3, 5, 7], "conrey_indexes": [244], "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": "0.944", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.785", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.165", "prec": 17}], "related_objects": [], "self_twist_discs": [-35], "cm_discs": [-35], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "4.2.1.d2", "trace_display": [0, 0, -25, 49], "traces": [0, 1, 0, 0, 16, -25, 0, 49, 0, 0, 0, 73, 0, 23, 0, 0, 256, -263, 0, 0, -400, 0, 0, 0, 0, 625, 0, 0, 784, 1153, 0, 0, 0, 0, 0, -1225, 0, 0, 0, 0, 0, 0, 0, 0, 1168, 0, 0, 3457, 0, 2401, 0, 0, 368, 0, 0, -1825, 0, 0, 0, 0, 0, 0, 0, 0, 4096, -575, 0, 0, -4208, 0, 0, 10078, 0, -9502, 0, 0, 0, 3577, 0, 12167, -6400, 0, 0, 6382, 0, 6575, 0, 0, 0, 0, 0, 1127, 0, 0, 0, 0, 0, 3383, 0, 0, 10000, 0, 0, 18383, 0, 0, 0, 0, 0, -14353, 0, 0, 12544, 0, 0, 0, 18448, 0, 0, -12887, 0, -9312, 0, 0, 0, -15625, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -19600, 0, 0, 1679, 0, -28825, 0, 0, 0, -24242, 0, -45433, 0, 0, 0, 0, 0, -31342, 0, 0, 0, 0, 0, 0, 0, 0, 0, -17663, 0, -28032, 0, 0, 0, 11017, 0, 30625, 18688, 0, 0, 16558, 0, 0, 0, 0, 0, 0, 0, -19199, 55312, 0, 0, -47447, 0, 0, 0, 0, 38416, 0, 0, 0, 0, 0, 0, 56497, 0, 0, 0, 0, 5888, 0, 0, -77593, 0, 0, 0, 0, 0, 0, 0, 0, -29200, -6049, 0, 61343, 0, 0, 0, -49823, 0, 0, 0, 0, 0, 0, 0, -86425, 0, 0, 0, -43367, 0, 0, 0, 0, 0, -60025, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 65536, -111938, 0, 0, -9200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -67328, 0, 0, 45625, 0, 0, 0, 0, 0, -119807, 0, 152303, 161248, 0, 0, 0, 0, -14352, 0, 0, -152032, 171337, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 135263, 57232, 0, 0, 0, 0, -147097, 0, 0, 194672, 0, 0, 84169, -102400, 0, 0, 0, 0, 14375, 0, 0, 0, 169393, 0, 138482, 102112, 0, 0, 0, 0, 0, 0, 0, 105200, 0, 0, 117649, 0, 0, 0, 0, 0, 0, 0, 0, 0, 229897, 0, -251950, 0, 0, 0, -76322, 0, 130321, 0, 0, 18032, 237550, 0, -116497, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26519, 0, -35278, 0, 0, 0, 29182, 0, -89425, 0, 0, 54128, -249407, 0, 0, 0, 0, 0, -304175, 0, -163897, 0, 0, 160000, 316273, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 294128, 0, 0, -159550, 0, 0, 0, 0, 0, -76753, 0, 0, 0, -164375, 0, 0, 0, 0, 0, -356087, 0, 193538, 0, 0, -229648, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200704, -264287, 0, 0, 0, 0, 0, -28175, 0, 0, 0, 0, 0, 0, 0, 0, 295168, 0, 0, -322463, 0, 0, 0, 0, 0, 0, 0, 0, -206192, 0, 0, 0, 0, 0, 0, 0, -148992, -84575, 0, 0, 0, 0, 0, 470713, 0, -303239, 0, 0, 0, 493822, 0, -31513, -250000, 0, 0, 313297, 0, 0, 0, 0, 0, 0, 0, -465598, 0, 0, 0, -459575, 0, 252361, 0, 0, 0, 0, 0, -440782, 0, 0, 0, 0, 0, 279841, 0, 0, 0, 0, 0, 0, 0, 0, 0, 175273, 0, 2927, 0, 0, 0, 358825, 0, 0, 0, 0, 0, 0, 0, 596183, 0, 0, 0, 0, 0, 0, -313600, 0, 0, -129938, 0, 0, 0, 0, 0, -566882, 0, -638158, 26864, 0, 0, 0, 0, -665017, 0, 0, -461200, 312718, 0, 0, 0, 0, 0, -507698, 0, 0, 0, 0, 0, 320137, 0, 322175, -387872, 0, 0, 613273, 0, 0, 0, 0, -726928, 232800, 0, -82417, 0, 0, 0, 79511, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 390625, 0, 0, -501472, 0, 0, 100487, 0, 0, 0, 0, 0, 55223, 0, 0, 0, -96002, 0, 713183, 0, 0, 0, -111458, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -777527, 0, 0, 0, 0, 0, 0, 0, 0, -282608, 0, 0, 0, 0, 0, 0, 0, -448512, -750023, 0, 165767, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 176272, 0, 0, 0, 0, 0, 0, 0, 490000, 884833, 0, 0, 299008, 0, 0, 0, 0, 1002527, 0, 0, 0, 0, 0, -41975, 264928, 0, 0, 0, 0, 900767, 0, 0, 0, 720625, 0, 976418, 0, 0, 0, 0, 0, 51143, 0, 0, 0, 0, 0, 749207, 0, 0, 0, 0, 0, 606050, 0, 0, -307184, 0, 0, 648887, 884992, 0, 0, 1135825, 0, 0, 0, 0, 0, 0, 0, -703297, -759152, 0, 0, 0, 0, 0, 0, 0, 0, -1179623, 0, 0, 0, 0, 0, 0, 0, 735694, 0, 0, 614656, 783550, 0, -1037137, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1073543, 0, -909191, 0, 0, 0, -693646, 0, 0, 0, 0, 0, 1299553, 0, 0, 903952, 0, 0, 0, 0, 0, 0, 0, 0, -1234367, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 94208, -631463, 0, 441575, 0, 0, 0, 0, 0, 622128, 0, 0, -1241488, 700800, 0, -456288, 0, 0, 0, 0, 0, -1447822, 0, 0, 0, 970462, 0, 0, 0, 0, 0, 0, 0, -275425, 0, 0, 0, 888191, 0, 0, 0, 0, 0, -765625, 0, 0, 0, 0, -467200, 0, 0, 0, -96784, 0, 0, 1329502, 0, 0, 0, 0, 981488, 0, 0, -413950, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -797168, 0, 0, -1155842, 0, 465886, 0, 0, 0, 0, 0, -695113, 0, 0, 0, 231794, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 479975, 0, 1589303, 0, 0, -1382800, 0, 0, 0, 0, 0, 0, 0, 0, -218546, 0, 0, 0, 0, 0, 1186175, -693872, 0, 0, 0, 0, 923521, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -960400, 0, 0, 675937, 0, 0, 0, 0, 0, 0, 0, -1442878, 0, 0, 0, 0, 0, 737783, 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": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 35, 3, -1, 2, -35]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "35.5.c.a", "char_is_minimal": true, "conrey_index": 244, "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], [0], [16], [-25], [0], [49], [0], [0], [0], [73], [0], [23], [0], [0], [256], [-263], [0], [0], [-400], [0], [0], [0], [0], [625], [0], [0], [784], [1153], [0], [0], [0], [0], [0], [-1225], [0], [0], [0], [0], [0], [0], [0], [0], [1168], [0], [0], [3457], [0], [2401], [0], [0], [368], [0], [0], [-1825], [0], [0], [0], [0], [0], [0], [0], [0], [4096], [-575], [0], [0], [-4208], [0], [0], [10078], [0], [-9502], [0], [0], [0], [3577], [0], [12167], [-6400], [0], [0], [6382], [0], [6575], [0], [0], [0], [0], [0], [1127], [0], [0], [0], [0], [0], [3383], [0], [0], [10000]]}