# Stored data for newform 588.3.p.b, downloaded from the LMFDB on 20 April 2024. {"label": "588.3.p.b", "space_label": "588.3.p", "level": 588, "weight": 3, "hecke_orbit": 2, "hecke_orbit_code": 4504630469853772, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 263683318755673434, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [0, 1]], [13, [-22, 1]]], "qexp_display": "q-3\\zeta_{6}q^{3}+(-9+9\\zeta_{6})q^{9}+22q^{13}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 21, "char_orbit_label": "p", "char_is_real": false, "Nk2": 5292, "analytic_conductor": 16.021839544385458, "hecke_ring_index": 1, "level_radical": 42, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [588, 6, [295, 197, 493], [6, 3, 4]], "hecke_ring_generator_nbound": 19, "inner_twist_count": 4, "level_primes": [2, 3, 7], "conrey_indexes": [557, 569], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.042", "prec": 17}, {"__RealLiteral__": 0, "data": "1.922", "prec": 17}, {"__RealLiteral__": 0, "data": "0.545", "prec": 17}, {"__RealLiteral__": 0, "data": "16.687", "prec": 20}, {"__RealLiteral__": 0, "data": "7.683", "prec": 17}, {"__RealLiteral__": 0, "data": "199.065", "prec": 24}], "related_objects": [], "self_twist_discs": [-3], "cm_discs": [-3], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "2.2.1.d6", "trace_display": [0, -3, 0, 0], "traces": [0, 2, 0, -3, 0, 0, 0, 0, 0, -9, 0, 0, 0, 44, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, -25, 0, 54, 0, 0, 0, -46, 0, 0, 0, 0, 0, -26, 0, -66, 0, 0, 0, -44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -156, 0, 0, 0, 74, 0, 0, 0, 0, 0, -122, 0, 0, 0, 0, 0, -46, 0, -75, 0, 0, 0, 142, 0, -81, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -138, 0, 0, 0, -4, 0, 0, 0, 0, 0, 194, 0, 0, 0, 0, 0, 214, 0, 156, 0, 0, 0, 0, 0, -198, 0, 0, 0, -121, 0, 0, 0, 0, 0, 292, 0, 66, 0, 0, 0, 0, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 286, 0, 0, 0, 0, 0, -118, 0, 0, 0, 0, 0, 262, 0, 0, 0, 0, 0, 630, 0, 234, 0, 0, 0, 0, 0, 0, 0, 0, 0, -628, 0, -444, 0, 0, 0, 0, 0, 0, 0, 0, 0, 382, 0, 0, 0, 0, 0, 386, 0, -366, 0, 0, 0, 0, 0, 0, 0, 0, 0, -332, 0, 0, 0, 0, 0, 0, 0, -138, 0, 0, 0, -676, 0, 450, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, -852, 0, 0, 0, -286, 0, -243, 0, 0, 0, 572, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 242, 0, 0, 0, 0, 0, -122, 0, 828, 0, 0, 0, 458, 0, 0, 0, 0, 0, -289, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 716, 0, -1164, 0, 0, 0, -142, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -550, 0, 642, 0, 0, 0, -362, 0, -234, 0, 0, 0, 964, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1004, 0, 1188, 0, 0, 0, 0, 0, 0, 0, 0, 0, -315, 0, 726, 0, 0, 0, -718, 0, 0, 0, 0, 0, -698, 0, 0, 0, 0, 0, -1388, 0, -438, 0, 0, 0, 0, 0, 198, 0, 0, 0, 0, 0, 0, 0, 0, 0, 362, 0, 0, 0, 0, 0, -1012, 0, 0, 0, 0, 0, 626, 0, 0, 0, 0, 0, 0, 0, -66, 0, 0, 0, -716, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1724, 0, 0, 0, 0, 0, -94, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 858, 0, 0, 0, 814, 0, 0, 0, 0, 0, -1052, 0, 0, 0, 0, 0, 0, 0, -354, 0, 0, 0, -1300, 0, 0, 0, 0, 0, -572, 0, 0, 0, 0, 0, -962, 0, -1572, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26, 0, 0, 0, 0, 0, 0, 0, -945, 0, 0, 0, 0, 0, 702, 0, 0, 0, 0, 0, 0, 0, 0, 0, -982, 0, 0, 0, 0, 0, -529, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1034, 0, 942, 0, 0, 0, 1012, 0, 666, 0, 0, 0, 0, 0, 0, 0, 0, 0, -968, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 886, 0, 0, 0, 0, 0, 962, 0, 1146, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2392, 0, 0, 0, 0, 0, 0, 0, 1158, 0, 0, 0, 1052, 0, 2196, 0, 0, 0, -814, 0, 0, 0, 0, 0, 1126, 0, 0, 0, 0, 0, -214, 0, 0, 0, 0, 0, -625, 0, 0, 0, 0, 0, 1348, 0, 498, 0, 0, 0, 0, 0, 0, 0, 0, 0, -628, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 828, 0, 0, 0, 122, 0, 0, 0, 0, 0, 0, 0, 1014, 0, 0, 0, 2308, 0, -675, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -156, 0, 0, 0, -1318, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 676, 0, 0, 0, 0, 0, 934, 0, 1278, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -858, 0, 0, 0, -964, 0, 1458, 0, 0, 0, 1034, 0, 0, 0, 0, 0, 1222, 0, -3432, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1202, 0, 0, 0, 0, 0, -1676, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3068, 0, 0, 0, 0, 0, -1150, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1562, 0, 0, 0, 0, 0, 1628, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3028, 0, -1452, 0, 0, 0, -572, 0, 0, 0, 0, 0, -1058, 0, 0, 0, 0, 0, 458, 0, -366, 0, 0, 0, 0, 0, -1242, 0, 0, 0, 1682, 0, 0, 0, 0, 0, 0, 0, 1374, 0, 0, 0, -3316, 0, 0, 0, 0, 0, 1418, 0, 0, 0, 0, 0, 0, 0, 1734, 0, 0, 0, -2684, 0, 18, 0, 0, 0, 598, 0, 0, 0, 0, 0, -3404, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 214, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -866, 0, -1074, 0, 0, 0, 1300, 0, 1746, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2396, 0, 852, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1012, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1155, 0, 0, 0, 0, 0, -3068, 0, 0, 0, 0, 0, 0, 0, -1650, 0, 0, 0, 0, 0, -3852, 0, 0, 0, 0, 0, 0, 0, 0, 0, 46, 0, 2172, 0, 0, 0, -1894, 0, -702, 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, 3, 2, -1, 2, -3], [1, 1, 7, 3, 1, 3, 0], [1, 1, 21, 8, -1, 6, 0]], "char_orbit_index": 16, "prim_orbit_index": 8, "minimal_twist": "12.3.c.a", "char_is_minimal": false, "conrey_index": 557, "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], [0, -3], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-9, 9], [0, 0], [0, 0], [0, 0], [22, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [26, -26], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -25], [0, 0], [27, 0], [0, 0], [0, 0], [0, 0], [0, -46], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-26, 26], [0, 0], [0, -66], [0, 0], [0, 0], [0, 0], [-22, 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, 0], [-78, 0], [0, 0], [0, 0], [0, 0], [74, -74], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -122], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, -46], [0, 0], [-75, 75], [0, 0], [0, 0], [0, 0], [142, -142], [0, 0], [0, -81], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-138, 138], [0, 0], [0, 0], [0, 0], [-2, 0], [0, 0], [0, 0], [0, 0]]}