# Stored data for newform 27.3.b.a, downloaded from the LMFDB on 24 April 2024.
{"label": "27.3.b.a", "space_label": "27.3.b", "level": 27, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 68769808411, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1350997177047738507, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [0, 1]]], "qexp_display": "q+4q^{4}-13q^{7}-q^{13}+2^{4}q^{16}+11q^{19}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 3, "char_orbit_label": "b", "char_is_real": true, "Nk2": 243, "analytic_conductor": 0.7356967137728017, "hecke_ring_index": 1, "level_radical": 3, "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": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [27, 2, [2], [1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 2, "level_primes": [3], "conrey_indexes": [26], "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": "0.966", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.857", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.408", "prec": 17}], "related_objects": [], "self_twist_discs": [-3], "cm_discs": [-3], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "2.2.1.d2", "trace_display": [0, 0, 0, -13], "traces": [0, 1, 0, 0, 4, 0, 0, -13, 0, 0, 0, 0, 0, -1, 0, 0, 16, 0, 0, 11, 0, 0, 0, 0, 0, 25, 0, 0, -52, 0, 0, -46, 0, 0, 0, 0, 0, 47, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, 120, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -121, 0, 0, 64, 0, 0, -109, 0, 0, 0, 0, 0, -97, 0, 0, 44, 0, 0, 131, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 167, 0, 0, 100, 0, 0, -37, 0, 0, 0, 0, 0, -214, 0, 0, -208, 0, 0, 0, 0, 0, 0, 0, 0, 121, 0, 0, -184, 0, 0, 146, 0, 0, 0, 0, 0, -143, 0, 0, 0, 0, 0, 251, 0, 0, 0, 0, 0, 0, 0, 0, 188, 0, 0, 59, 0, 0, 0, 0, 0, -118, 0, 0, 0, 0, 0, 299, 0, 0, 0, 0, 0, -168, 0, 0, -88, 0, 0, -325, 0, 0, 0, 0, 0, -313, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 143, 0, 0, 480, 0, 0, -277, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, -253, 0, 0, 0, 0, 0, 598, 0, 0, 0, 0, 0, 338, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -193, 0, 0, -484, 0, 0, -11, 0, 0, 0, 0, 0, 0, 0, 0, 256, 0, 0, -611, 0, 0, 0, 0, 0, 0, 0, 0, -436, 0, 0, 299, 0, 0, 0, 0, 0, 122, 0, 0, 0, 0, 0, 458, 0, 0, 0, 0, 0, 289, 0, 0, -388, 0, 0, 0, 0, 0, 0, 0, 0, 286, 0, 0, 176, 0, 0, -358, 0, 0, 0, 0, 0, 599, 0, 0, 524, 0, 0, 0, 0, 0, 0, 0, 0, -25, 0, 0, 0, 0, 0, -661, 0, 0, 0, 0, 0, -649, 0, 0, 0, 0, 0, -923, 0, 0, 0, 0, 0, 671, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -240, 0, 0, 52, 0, 0, 491, 0, 0, 0, 0, 0, -577, 0, 0, 0, 0, 0, 83, 0, 0, 0, 0, 0, 0, 0, 0, 668, 0, 0, 0, 0, 0, 0, 0, 0, 362, 0, 0, 400, 0, 0, 46, 0, 0, 0, 0, 0, 143, 0, 0, -148, 0, 0, 0, 0, 0, 0, 0, 0, -481, 0, 0, 0, 0, 0, 1573, 0, 0, 0, 0, 0, -862, 0, 0, -856, 0, 0, -94, 0, 0, 0, 0, 0, 0, 0, 0, -832, 0, 0, 0, 0, 0, 0, 0, 0, -814, 0, 0, 0, 0, 0, -397, 0, 0, 0, 0, 0, 1417, 0, 0, 0, 0, 0, 275, 0, 0, 0, 0, 0, -47, 0, 0, 484, 0, 0, -349, 0, 0, 0, 0, 0, 0, 0, 0, -736, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 584, 0, 0, 1261, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 803, 0, 0, 0, 0, 0, 529, 0, 0, -572, 0, 0, 0, 0, 0, 0, 0, 0, -241, 0, 0, 0, 0, 0, -1093, 0, 0, 0, 0, 0, -1703, 0, 0, 1004, 0, 0, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -181, 0, 0, 0, 0, 0, -1033, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -506, 0, 0, 752, 0, 0, 0, 0, 0, 0, 0, 0, -526, 0, 0, 236, 0, 0, 1187, 0, 0, 0, 0, 0, 983, 0, 0, 0, 0, 0, -949, 0, 0, 0, 0, 0, 625, 0, 0, -472, 0, 0, 587, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 314, 0, 0, 0, 0, 0, 0, 0, 0, 1196, 0, 0, 0, 0, 0, 0, 0, 0, 1079, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 0, 0, -672, 0, 0, -2171, 0, 0, 0, 0, 0, 0, 0, 0, -352, 0, 0, -1318, 0, 0, 0, 0, 0, 0, 0, 0, -1300, 0, 0, 517, 0, 0, 0, 0, 0, 1391, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 481, 0, 0, -1252, 0, 0, 482, 0, 0, 0, 0, 0, 1034, 0, 0, 0, 0, 0, -1222, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 179, 0, 0, 0, 0, 0, -673, 0, 0, 0, 0, 0, 2782, 0, 0, 0, 0, 0, 863, 0, 0, 572, 0, 0, -1150, 0, 0, 0, 0, 0, 0, 0, 0, 1920, 0, 0, -613, 0, 0, 0, 0, 0, 121, 0, 0, -1108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1514, 0, 0, 0, 0, 0, -242, 0, 0, 0, 0, 0, -1621, 0, 0, 0, 0, 0, -1609, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 841, 0, 0, -1012, 0, 0, -1573, 0, 0, 0, 0, 0, -481, 0, 0, 0, 0, 0, -1549, 0, 0, 0, 0, 0, 0, 0, 0, 2392, 0, 0, 109, 0, 0, 0, 0, 0, 1727, 0, 0, 0, 0, 0, 443, 0, 0, 0, 0, 0, -1898, 0, 0, 1352, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1453, 0, 0, 0, 0, 0, 0, 0, 0, 104, 0, 0, 866, 0, 0, 0, 0, 0, 1175, 0, 0, 0, 0, 0, 1320, 0, 0, 0, 0, 0, 1847, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1155, 0, 0, -772, 0, 0, -253, 0, 0, 0, 0, 0, -3263, 0, 0, -1936, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -44, 0, 0, 1739, 0, 0, 0, 0, 0, -1894, 0, 0, 0], "weight_parity": -1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "27.3.b.a", "char_is_minimal": true, "conrey_index": 26, "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], [4], [0], [0], [-13], [0], [0], [0], [0], [0], [-1], [0], [0], [16], [0], [0], [11], [0], [0], [0], [0], [0], [25], [0], [0], [-52], [0], [0], [-46], [0], [0], [0], [0], [0], [47], [0], [0], [0], [0], [0], [-22], [0], [0], [0], [0], [0], [120], [0], [0], [-4], [0], [0], [0], [0], [0], [0], [0], [0], [-121], [0], [0], [64], [0], [0], [-109], [0], [0], [0], [0], [0], [-97], [0], [0], [44], [0], [0], [131], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [13], [0], [0], [0], [0], [0], [167], [0], [0], [100]]}