# Stored data for newform 588.2.i.b, downloaded from the LMFDB on 05 October 2024. {"Nk2": 2352, "analytic_conductor": 4.695203638851287, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 7, "char_degree": 2, "char_is_minimal": false, "char_is_real": false, "char_orbit_index": 9, "char_orbit_label": "i", "char_order": 3, "char_parity": 1, "char_values": [588, 3, [295, 197, 493], [3, 3, 2]], "cm_discs": [], "conrey_index": 361, "dim": 2, "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 6, "has_non_self_twist": 1, "hecke_cutters": [[5, [4, 2, 1]], [13, [-3, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4504149416739404, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 3, 1, 3, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "588.2.i.b", "level": 588, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 3, 7], "level_radical": 42, "minimal_twist": "84.2.i.a", "nf_label": "2.0.3.1", "prim_orbit_index": 3, "qexp_display": "q+(-1+\\zeta_{6})q^{3}-2\\zeta_{6}q^{5}-\\zeta_{6}q^{9}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "588.2.i", "trace_display": [0, -1, -2, 0], "trace_hash": 74835991873416206, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.025", "prec": 17}, {"__RealLiteral__": 0, "data": "0.224", "prec": 17}, {"__RealLiteral__": 0, "data": "12.099", "prec": 20}, {"__RealLiteral__": 0, "data": "2.499", "prec": 17}, {"__RealLiteral__": 0, "data": "108.668", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.015", "prec": 17}, "traces": [0, 2, 0, -1, 0, -2, 0, 0, 0, -1, 0, -2, 0, 6, 0, 4, 0, 8, 0, -1, 0, 0, 0, -8, 0, 1, 0, 2, 0, 8, 0, 3, 0, -2, 0, 0, 0, 1, 0, -3, 0, -12, 0, 22, 0, -2, 0, 6, 0, 0, 0, 8, 0, 12, 0, 8, 0, 2, 0, 4, 0, -6, 0, 0, 0, -6, 0, -13, 0, 16, 0, -20, 0, -11, 0, 1, 0, 0, 0, 3, 0, -1, 0, -4, 0, -32, 0, -4, 0, 0, 0, 0, 0, 3, 0, -2, 0, -20, 0, 4, 0, 10, 0, 11, 0, 0, 0, 0, 0, 11, 0, -2, 0, -28, 0, -16, 0, -3, 0, 0, 0, 7, 0, 6, 0, -24, 0, 6, 0, -11, 0, -2, 0, 0, 0, -2, 0, -4, 0, 10, 0, -12, 0, -6, 0, -8, 0, 0, 0, 12, 0, 8, 0, -16, 0, -12, 0, 2, 0, 12, 0, 0, 0, 4, 0, -4, 0, 4, 0, -8, 0, -1, 0, 16, 0, 0, 0, 4, 0, -6, 0, 30, 0, 12, 0, 2, 0, 16, 0, 0, 0, -6, 0, -11, 0, 12, 0, 16, 0, 8, 0, -13, 0, 0, 0, 12, 0, -8, 0, 4, 0, -8, 0, 10, 0, -22, 0, 0, 0, -11, 0, 24, 0, -16, 0, -2, 0, -18, 0, 1, 0, 0, 0, -14, 0, 12, 0, -6, 0, 36, 0, 14, 0, -1, 0, 0, 0, -3, 0, 2, 0, 0, 0, 32, 0, 16, 0, 18, 0, 0, 0, -4, 0, -12, 0, -48, 0, 0, 0, -2, 0, -24, 0, 0, 0, 2, 0, -17, 0, -6, 0, 40, 0, 19, 0, -2, 0, 0, 0, -47, 0, 10, 0, 48, 0, -16, 0, -2, 0, -24, 0, 0, 0, 10, 0, -12, 0, 46, 0, -22, 0, -2, 0, -17, 0, 0, 0, 24, 0, -8, 0, 0, 0, -16, 0, 3, 0, 11, 0, 0, 0, -17, 0, 1, 0, 52, 0, 42, 0, 14, 0, 6, 0, 0, 0, -16, 0, -24, 0, 28, 0, 6, 0, -6, 0, 20, 0, 0, 0, 20, 0, 18, 0, -14, 0, 44, 0, 5, 0, 6, 0, 0, 0, 5, 0, 12, 0, 24, 0, 26, 0, -3, 0, -28, 0, 0, 0, -11, 0, -10, 0, -128, 0, 4, 0, 6, 0, 3, 0, 0, 0, 12, 0, 9, 0, 4, 0, -4, 0, -19, 0, -4, 0, 0, 0, 4, 0, -5, 0, -36, 0, -54, 0, 6, 0, -8, 0, 0, 0, -6, 0, 30, 0, 50, 0, 16, 0, -8, 0, 24, 0, 0, 0, 4, 0, 0, 0, -24, 0, 44, 0, 12, 0, 8, 0, 0, 0, -13, 0, 8, 0, -8, 0, -22, 0, 6, 0, 34, 0, 0, 0, 2, 0, -22, 0, -2, 0, -24, 0, -28, 0, 3, 0, 0, 0, 20, 0, 19, 0, -8, 0, -72, 0, 32, 0, -4, 0, 0, 0, 29, 0, -2, 0, 60, 0, -40, 0, 4, 0, 18, 0, 0, 0, -1, 0, 22, 0, -24, 0, -32, 0, -36, 0, -31, 0, 0, 0, -24, 0, -41, 0, -8, 0, -36, 0, 0, 0, -6, 0, 0, 0, 15, 0, -15, 0, -44, 0, -24, 0, -6, 0, -4, 0, 0, 0, 2, 0, -22, 0, 66, 0, -32, 0, -46, 0, 28, 0, 0, 0, -6, 0, 21, 0, 12, 0, -16, 0, -41, 0, -11, 0, 0, 0, 24, 0, -6, 0, -64, 0, -6, 0, -8, 0, -6, 0, 0, 0, 8, 0, 12, 0, 2, 0, 26, 0, 14, 0, -3, 0, 0, 0, 18, 0, 30, 0, -24, 0, 52, 0, -11, 0, -8, 0, 0, 0, 19, 0, -2, 0, 16, 0, -32, 0, 4, 0, -6, 0, 0, 0, 10, 0, 40, 0, -70, 0, 44, 0, 6, 0, 8, 0, 0, 0, 6, 0, -4, 0, 22, 0, -56, 0, -29, 0, 24, 0, 0, 0, -32, 0, 8, 0, 24, 0, -2, 0, 1, 0, 12, 0, 0, 0, -18, 0, -36, 0, 16, 0, -2, 0, 36, 0, -43, 0, 0, 0, -10, 0, -48, 0, 28, 0, -16, 0, 1, 0, 12, 0, 0, 0, -14, 0, 3, 0, -48, 0, 24, 0, -18, 0, -6, 0, 0, 0, 14, 0, 4, 0, 46, 0, 2, 0, 88, 0, 45, 0, 0, 0, -26, 0, 9, 0, 6, 0, -36, 0, 24, 0, 2, 0, 0, 0, -15, 0, 0, 0, -32, 0, 84, 0, -16, 0, 8, 0, 0, 0, 16, 0, 12, 0, -62, 0, -36, 0, 22, 0, -3, 0, 0, 0, 6, 0, 20, 0, 8, 0, -8, 0, 24, 0, -12, 0, 0, 0, -18, 0, 24, 0, 96, 0, 96, 0, 0, 0, -22, 0, 0, 0, -2, 0, -22, 0, 64, 0, 48, 0, 8, 0, -11, 0, 0, 0, -2, 0, -40, 0, -4, 0, 108, 0, -11, 0, -17, 0, 0, 0, -4, 0, 3, 0, 8, 0, -26, 0, -20, 0, 8, 0, 0, 0, 19, 0, 8, 0, -46, 0, 4, 0, 0, 0, 8, 0, 0, 0, -46, 0, 32, 0, 94, 0, -12, 0, -39, 0, 10, 0, 0, 0, 38, 0, -24, 0, -96, 0, 58, 0, 8, 0, -6, 0, 0, 0, -2, 0, 6, 0, 24, 0, 48, 0, 12, 0, -96, 0, 0, 0, -30, 0, -21, 0, -20, 0, 96, 0, 4, 0, -12, 0, 0, 0, 11, 0, -23, 0, -60, 0, 2, 0, 11, 0, 6, 0, 0, 0, -2, 0, 32, 0, 98, 0, 34, 0, 52, 0, 48, 0, 0, 0, -10, 0, -33, 0, -48, 0, -56, 0, -12, 0, -8, 0, 0, 0, 22, 0, 0, 0, 44, 0, -62, 0, 8, 0, 36, 0, 0, 0, 3, 0, 18, 0, 0, 0, -22, 0, -12, 0, -16, 0, 0, 0, -88, 0, -11, 0, 34, 0, -32, 0, -1, 0, 1, 0], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0], [1, 0], [0, 0], [-1, 1], [0, 0], [0, -2], [0, 0], [0, 0], [0, 0], [0, -1], [0, 0], [-2, 2], [0, 0], [3, 0], [0, 0], [2, 0], [0, 0], [8, -8], [0, 0], [0, -1], [0, 0], [0, 0], [0, 0], [0, -8], [0, 0], [1, -1], [0, 0], [1, 0], [0, 0], [4, 0], [0, 0], [3, -3], [0, 0], [0, -2], [0, 0], [0, 0], [0, 0], [0, 1], [0, 0], [-3, 3], [0, 0], [-6, 0], [0, 0], [11, 0], [0, 0], [-2, 2], [0, 0], [0, 6], [0, 0], [0, 0], [0, 0], [0, 8], [0, 0], [12, -12], [0, 0], [4, 0], [0, 0], [1, 0], [0, 0], [4, -4], [0, 0], [0, -6], [0, 0], [0, 0], [0, 0], [0, -6], [0, 0], [-13, 13], [0, 0], [8, 0], [0, 0], [-10, 0], [0, 0], [-11, 11], [0, 0], [0, 1], [0, 0], [0, 0], [0, 0], [0, 3], [0, 0], [-1, 1], [0, 0], [-2, 0], [0, 0], [-16, 0], [0, 0], [-4, 4], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 3], [0, 0], [-2, 2], [0, 0], [-10, 0], [0, 0], [2, 0], [0, 0]]}