# Stored data for newform 115.2.a.a, downloaded from the LMFDB on 19 April 2024.
{"label": "115.2.a.a", "space_label": "115.2.a", "level": 115, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 33554547, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 2195690488616595683, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [-2, 1]]], "qexp_display": "q+2q^{2}+2q^{4}-q^{5}+q^{7}-3q^{9}-2q^{10}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 460, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 0.9182796232447245, "hecke_ring_index": 1, "level_radical": 115, "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": "0.014", "prec": 17}, "analytic_rank_proved": true, "char_values": [115, 1, [47, 51], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [5, 23], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.009", "prec": 17}, {"__RealLiteral__": 0, "data": "0.972", "prec": 17}, {"__RealLiteral__": 0, "data": "0.033", "prec": 17}, {"__RealLiteral__": 0, "data": "1.882", "prec": 17}, {"__RealLiteral__": 0, "data": "0.131", "prec": 17}, {"__RealLiteral__": 0, "data": "4.551", "prec": 17}], "related_objects": ["EllipticCurve/Q/115/a"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[5, 1], [23, -1]], "trace_display": [2, 0, -1, 1], "traces": [0, 1, 2, 0, 2, -1, 0, 1, 0, -3, -2, 2, 0, -2, 2, 0, -4, 3, -6, -2, -2, 0, 4, 1, 0, 1, -4, 0, 2, 7, 0, -5, -8, 0, 6, -1, -6, 11, -4, 0, 0, 1, 0, 0, 4, 3, 2, 0, 0, -6, 2, 0, -4, 11, 0, -2, 0, 0, 14, -13, 0, -8, -10, -3, -8, 2, 0, 5, 6, 0, -2, 5, 0, 6, 22, 0, -4, 2, 0, -12, 4, 9, 2, 9, 0, -3, 0, 0, 0, 4, 6, -2, 2, 0, 0, 2, 0, -14, -12, -6, 2, -5, 0, -8, 0, 0, 22, -15, 0, -10, -4, 0, -4, -9, 0, -1, 14, 6, -26, 3, 0, -7, -16, 0, -10, -1, -6, -4, 0, 0, 4, 12, 0, -2, 10, 0, 0, 6, 0, -19, -2, 0, 10, -4, 12, -7, 12, 0, 22, 16, 0, 12, 0, -9, 4, 5, 0, 17, -24, 0, 8, 1, 18, -18, 2, 0, 18, -24, 0, -9, -6, 6, 0, 24, 0, 1, -8, 0, 8, 24, 6, 16, -4, 0, 0, -11, 0, 6, 0, 0, 4, 0, 0, 16, -28, 0, -12, -2, -12, 26, 0, 0, -10, 7, 0, -1, -16, -3, 8, -4, 0, 15, 22, 0, -30, 0, 0, -5, -20, 0, -4, -6, 0, 14, -8, -3, -18, 4, 0, 8, -2, 0, 0, 4, 12, 0, -26, 0, 6, -29, 0, -18, -14, 0, -16, 6, 0, 4, 0, 0, -2, -26, -6, 2, -8, 0, 16, -8, 0, 11, 4, -21, 24, 19, 0, -11, -4, 0, 10, 21, 0, 13, -12, 0, 12, 2, 0, 6, -38, 15, 0, -6, 0, 11, 10, 0, -8, 1, 24, -8, -14, 0, 12, 9, 0, 13, 0, 0, 32, -2, 0, 0, 24, 0, 8, 8, -18, -26, 4, 0, 10, -8, 0, -3, 34, 3, -24, 12, 0, 14, 8, 0, 2, -6, 18, -2, -36, 0, 0, 0, 0, 11, 18, -33, -48, -5, 0, 10, -18, 0, -6, -10, 12, -13, 0, 0, 48, -12, 0, 11, 2, 0, -16, -8, 0, -5, 8, 0, 48, -12, 0, -15, 32, 0, -4, -6, 0, -13, -4, -3, -22, 11, 0, -34, 12, 0, 0, -14, 0, 12, 4, 0, 0, 11, 0, -2, 32, 0, -28, 10, 0, 3, 0, 0, -4, 12, -12, 4, 52, 0, -4, 2, 0, 10, -10, -9, 14, 22, 0, -11, -2, 0, -16, -13, -6, -9, 16, 0, -8, -18, 0, -2, 30, 0, 0, 3, 0, -8, -30, 0, 0, 28, 0, -1, -10, 0, -20, -2, 0, 8, 0, 18, -12, -32, 0, -4, 28, 0, -8, -21, -6, 2, -18, 0, 8, 2, 0, 25, 16, 0, -2, -2, 0, -10, -28, 0, 8, 33, 12, 5, 0, 0, 0, 0, 0, -2, 6, -33, -58, 12, 0, -22, -36, 0, -14, 14, 0, -28, 0, 0, 12, 9, 0, 21, 8, 6, 20, 5, 0, 1, -2, 0, -52, -33, 0, 5, 4, 0, -8, 18, 0, 6, 32, 0, -16, 8, 0, 0, 22, 0, 0, -42, -42, -4, 24, 0, 38, -15, 0, 1, -22, 39, -4, -2, 0, 15, 0, 0, 42, -12, 0, -26, 26, 0, -24, 10, 0, 24, 12, 24, 4, -14, 0, -12, 12, 0, -38, 11, 30, 0, 4, 0, -12, 31, 0, 9, 22, 9, 0, -6, 0, -16, -8, 0, 2, 1, 24, 20, -16, 0, -14, 9, 0, 22, 0, -6, 18, 2, 0, 10, 26, 0, -44, -4, 0, -3, 32, 0, -4, -24, 0, -21, 0, -15, 24, 7, 0, 32, 16, 0, 16, 0, -18, -26, -52, 0, 0, 13, 0, 36, 10, 0, -16, 4, 0, 1, -6, 0, 34, 33, 6, 40, 0, 0, 24, 4, 0, 12, 28, -15, 0, 14, 0, 25, 2, 0, -12, -50, 0, -26, -4, 0, -36, 18, 0, -12, -4, -18, 0, -30, 0, -14, 22, 0, 0, 2, -66, 7, -48, 0, -10, -16, 0, 28, 20, 0, -18, -27, 0, -14, 0, 0, -20, -28, 12, -6, -26, 0, 0, -22, 0, -44, 48, -6, -24, 19, 0, 3, 22, 0, 2, 0, 0, -22, -16, 0, -16, -5, 0, 12, -10, 36, 0, -5, 0, 4, 48, 0, -24, -37, -12, -8, -30, 0, 32, 7, 0, 19, 0, -27, -12, 0, 0, 11, -26, 0, -8, 10, -6, 23, -22, 0, 22, 16, 0, -16, -68, -27, 12, -15, 0, -22, 0, 0, -28, -12, 0, 37, 24, 0, 0, 45, 0, -10, 0, 9, 22, 26, 0, 32, -4, 0, 32, -10, 0, -5, 0, 0, 20, -2, 0, 10, 6, 0, 24, -17, 0, -7, -4, 0, 24, -9, 0, 16, 8, 0, 52, 53, 0, 0, -8, -12, 4, 12, 0, -1, 20, 0, 0, 15, -18, 15, 14, 0, 44, 18, 0, 0, -22, 6, -2, 10, 0, -16, 0, 0, -26, -29, -6, 45, -18, 0, 16, -18, 0, 24, -8, 0, -36, 54, 0, 20, -4, 0, 30, 9, 0, -7, -44, 0, 6, 11, 0, -14, -16, -6, 0, 22, 0, -5, 0, 0, 56, -18, 0, -24, -2, 0, -10, -24, 0, -10, 0, 42, -4, -1, 0, -2, 16, 0, 8, -32, 36, -56, -12, 0, -64, -26, 0, -4, -8, 18, 28, 0, 0, -24, 0, 0, -42, -35, -6, 33, 4, 0, 0, -16, 0, 5, 8, 15, 4, -40, 0, 18, 50, 0, 16, 12, 0, -4, 0, 0, -4, -10, 0, 11, -20, 24, -56, 27, 0, 12, 8, 0, 66, -6, 0, -22, 10, 0, 0, -24, 0, 1, 52, 0, 0, -52, 0, -12, -4, 0, 0, 26, -66, 0, -58, 0, 24, 6, 0, -6, -44, 45, -36, -16, 0, 44, 0, 0, 28, 12, 0, -19, -56, 0, 32, -39, 0, 8, 12, 30, 18, 9, 0, 2, 42, 0, 8, 0, 12, -1, 40, 0, 10, -26, 0, -40, 2, 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": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "115.2.a.a", "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], [2], [0], [2], [-1], [0], [1], [0], [-3], [-2], [2], [0], [-2], [2], [0], [-4], [3], [-6], [-2], [-2], [0], [4], [1], [0], [1], [-4], [0], [2], [7], [0], [-5], [-8], [0], [6], [-1], [-6], [11], [-4], [0], [0], [1], [0], [0], [4], [3], [2], [0], [0], [-6], [2], [0], [-4], [11], [0], [-2], [0], [0], [14], [-13], [0], [-8], [-10], [-3], [-8], [2], [0], [5], [6], [0], [-2], [5], [0], [6], [22], [0], [-4], [2], [0], [-12], [4], [9], [2], [9], [0], [-3], [0], [0], [0], [4], [6], [-2], [2], [0], [0], [2], [0], [-14], [-12], [-6], [2]]}