# Stored data for newform 574.2.a.b, downloaded from the LMFDB on 19 April 2024.
{"label": "574.2.a.b", "space_label": "574.2.a", "level": 574, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503599660925502, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 2064916703469562942, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[3, [1, 1]], [5, [-1, 1]], [11, [0, 1]]], "qexp_display": "q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 2296, "fricke_eigenval": 1, "atkin_lehner_string": "+++", "analytic_conductor": 4.583413076021494, "hecke_ring_index": 1, "level_radical": 574, "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": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.011", "prec": 17}, "analytic_rank_proved": true, "char_values": [574, 1, [493, 211], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 7, 41], "conrey_indexes": [1], "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": "0.953", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.860", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.574", "prec": 17}], "related_objects": ["EllipticCurve/Q/574/b"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [7, 1], [41, 1]], "trace_display": [-1, -1, 1, -1], "traces": [0, 1, -1, -1, 1, 1, 1, -1, -1, -2, -1, 0, -1, 2, 1, -1, 1, -5, 2, -4, 1, 1, 0, 6, 1, -4, -2, 5, -1, -9, 1, 3, -1, 0, 5, -1, -2, -8, 4, -2, -1, -1, -1, 7, 0, -2, -6, -10, -1, 1, 4, 5, 2, -13, -5, 0, 1, 4, 9, -14, -1, -5, -3, 2, 1, 2, 0, 4, -5, -6, 1, -15, 2, -6, 8, 4, -4, 0, 2, -3, 1, 1, 1, 16, 1, -5, -7, 9, 0, 13, 2, -2, 6, -3, 10, -4, 1, 17, -1, 0, -4, 18, -5, 7, -2, 1, 13, 3, 5, -2, 0, 8, -1, 1, -4, 6, -9, -4, 14, 5, 1, -11, 5, 1, 3, -9, -2, 18, -1, -7, -2, -18, 0, 4, -4, 5, 5, -18, 6, 14, -1, 10, 15, 0, -2, -9, 6, -1, -8, 7, -4, -5, 4, 10, 0, 3, -2, 0, 3, 13, -1, -6, -1, 12, -1, 0, -16, 12, -1, -9, 5, 8, 7, 9, -9, 4, 0, 14, -13, -24, -2, 0, 2, 5, -6, -8, 3, 0, -10, -5, 4, -15, -1, 16, -17, -2, 1, 0, 0, 4, 4, -4, -18, 9, 5, -1, -7, -12, 2, 0, -1, 20, -13, 15, -3, 7, -5, -3, 2, 6, 0, -10, -8, 3, 1, 8, -1, 7, 4, 8, -6, 0, 9, -12, 4, -10, -14, 3, -5, 0, -1, -20, 11, -16, -5, 1, -1, -8, -3, -16, 9, -8, 2, 0, -18, 5, 1, 3, 7, 8, 2, 18, 18, -24, 0, -13, -4, -13, 4, 10, -5, 16, -5, 2, 18, 0, -6, 20, -14, -6, 1, -22, -10, -12, -15, 4, 0, 1, 2, 8, 9, -17, -6, 24, 1, -14, 8, 0, -7, 12, 4, -7, 5, -18, -4, -5, -10, -16, 0, -7, -3, 18, 2, -6, 0, 2, -3, -22, -13, 0, 1, -3, 6, 20, 1, -8, -12, 2, 1, 10, 0, 26, 16, 16, -12, 4, 1, -35, 9, -1, -5, 0, -8, -1, -7, -6, -9, 24, 9, 2, -4, 10, 0, -2, -14, -15, 13, -5, 24, 0, 2, -3, 0, 11, -2, -6, -5, -19, 6, 2, 8, 13, -3, -16, 0, 9, 10, -18, 5, -15, -4, -18, 15, -8, 1, 0, -16, -14, 17, 20, 2, -30, -1, 18, 0, -3, 0, -2, -4, -4, -4, -5, 4, 6, 18, 1, -9, 0, -5, 32, 1, 18, 7, 14, 12, 16, -2, -14, 0, -14, 1, -7, -20, 20, 13, 20, -15, 5, 3, 0, -7, 8, 5, 6, 3, 9, -2, -24, -6, -28, 0, -2, 10, 39, 8, 13, -3, -7, -1, -33, -8, 0, 1, 5, -7, -2, -4, -18, -8, -25, 6, 21, 0, -24, -9, -3, 12, 32, -4, -4, 10, 0, 14, 0, -3, 16, 5, 26, 0, -26, 1, -16, 20, 6, -11, 17, 16, 26, 5, -12, -1, 5, 1, 45, 8, 0, 3, 15, 16, -2, -9, -12, 8, -10, -2, 18, 0, 9, 18, -42, -5, 6, -1, -20, -3, 7, -7, 0, -8, -9, -2, 14, -18, 6, -18, -4, 24, -15, 0, 13, 13, 28, 4, -2, 13, 3, -4, 24, -10, 0, 5, 12, -16, 0, 5, -2, -2, -36, -18, 10, 0, 36, 6, 3, -20, 8, 14, 13, 6, 14, -1, 0, 22, 20, 10, 1, 12, -1, 15, 27, -4, -26, 0, 15, -1, -24, -2, -42, -8, -16, -9, -16, 17, 0, 6, -4, -24, -15, -1, -12, 14, 0, -8, 15, 0, 5, 7, -4, -12, 6, -4, -37, 7, -8, -5, -11, 18, 3, 4, -9, 5, -20, 10, 28, 16, 1, 0, -26, 7, -4, 3, 30, -18, -13, -2, 11, 6, 0, 0, 40, -2, 14, 3, -20, 22, 18, 13, 2, 0, 30, -1, 38, 3, 19, -6, -7, -20, 39, -1, 0, 8, 3, 12, -9, -2, -18, -1, 12, -10, -18, 0, -50, -26, 10, -16, 4, -16, -54, 12, -3, -4, 0, -1, -32, 35, -20, -9, -6, 1, -17, 5, -7, 0, -12, 8, -18, 1, -8, 7, -26, 6, -13, 9, 0, -24, 14, -9, 5, -2, 12, 4, -42, -10, 32, 0, 10, 2, -18, 14, -1, 15, 6, -13, 18, 5, 0, -24, 0, 0, -30, -2, -7, 3, 20, 0, 36, -11, -32, 2, 13, 6, -35, 5, 19, 19, -1, -6, 0, -2, 19, -8, 8, -13, 2, 3, 7, 16, -32, 0, -3, -9, -32, -10, 8, 18, -5, -5, 15, 15, 0, 4, -14, 18, 2, -15, 10, 8, -28, -1, -42, 0, -3, 16, -2, 14, -12, -17, -8, -20, 4, -2, 0, 30, -45, 1, 0, -18, -40, 0, 24, 3, -1, 0, -10, 2, 13, 4, -17, 4, 50, 4, -26, 5, 0, -4, -6, -6, -10, -18, 32, -1, -6, 9, -16, 0, 12, 5, -28, -32, 4, -1, 52, -18, 5, -7, 0, -14, 6, -12, 37, -16, -20, 2, -5, 14, 12, 0, 15, 14, 20, -1, 52, 7, 22, 20, -9, -20, 11, -13, 12, -20, -48, 15, -7, -5, 8, -3, -30, 0, 22, 7, -1, -8, -34, -5, 9, -6, -8, -3, 0, -9, 8, 2, -34, 24, 9, 6, 12, 28, -24, 0, 40, 2, 0, -10, 14, -39, -10, -8, -18, -13, 0, 3, 40, 7, -24, 1, -12, 33, -27, 8, 65, 0, 7, -1, 0, -5, 35, 7, -36, 2, 36, 4, 0, 18, 5, 8, 18, 25, -9, -6, 16, -21, -30, 0, 32, 24, -14, 9, 34, 3, -4, -12, -18, -32, 0, 4, 9, 4, 6, -10, 10, 0, -6, -14, -5, 0, -36, 3, -12, -16, 22, -5, -26, -26, -15, 0, 0, 26, 18, -1, -22, 16, -6, -20, 16, -6, -27, 11, -20, -17, -21, -16, -14, -26, 8, -5, -6, 12, 0, 1, 4, -5, -21, -1, 0, -45, -10, -8, 42, 0, 8, -3, -26, -15, 4, -16, -14, 2, -40, 9], "weight_parity": 1, "has_non_self_twist": 0, "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]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "574.2.a.b", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0], [1], [-1], [-1], [1], [1], [1], [-1], [-1], [-2], [-1], [0], [-1], [2], [1], [-1], [1], [-5], [2], [-4], [1], [1], [0], [6], [1], [-4], [-2], [5], [-1], [-9], [1], [3], [-1], [0], [5], [-1], [-2], [-8], [4], [-2], [-1], [-1], [-1], [7], [0], [-2], [-6], [-10], [-1], [1], [4], [5], [2], [-13], [-5], [0], [1], [4], [9], [-14], [-1], [-5], [-3], [2], [1], [2], [0], [4], [-5], [-6], [1], [-15], [2], [-6], [8], [4], [-4], [0], [2], [-3], [1], [1], [1], [16], [1], [-5], [-7], [9], [0], [13], [2], [-2], [6], [-3], [10], [-4], [1], [17], [-1], [0], [-4]]}