# Stored data for newform 465.2.a.a, downloaded from the LMFDB on 07 June 2024.
{"Nk2": 1860, "analytic_conductor": 3.7130436939895377, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, -1], [5, -1], [31, 1]], "atkin_lehner_string": "--+", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [465, 1, [311, 187, 406], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 1, "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": 1, "has_non_self_twist": 0, "hecke_cutters": [[2, [1, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 33554897, "hecke_ring_generator_nbound": 1, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": true, "is_maximal": true, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": true, "label": "465.2.a.a", "level": 465, "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": true, "level_primes": [3, 5, 31], "level_radical": 465, "minimal_twist": "465.2.a.a", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}-4q^{7}+\\cdots", "related_objects": ["EllipticCurve/Q/465/a"], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "465.2.a", "trace_display": [-1, 1, 1, -4], "trace_hash": 511509967967797071, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.988", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.022", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.210", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.017", "prec": 17}, "traces": [0, 1, -1, 1, -1, 1, -1, -4, 3, 1, -1, -4, -1, 2, 4, 1, -1, -6, -1, -4, -1, -4, 4, 0, 3, 1, -2, 1, 4, -6, -1, -1, -5, -4, 6, -4, -1, 10, 4, 2, 3, -6, 4, -12, 4, 1, 0, 0, -1, 9, -1, -6, -2, -2, -1, -4, -12, -4, 6, -8, -1, 6, 1, -4, 7, 2, 4, 8, 6, 0, 4, -12, 3, 6, -10, 1, 4, 16, -2, -8, -1, 1, 6, 12, 4, -6, 12, -6, -12, 6, -1, -8, 0, -1, 0, -4, -5, -6, -9, -4, -1, -10, 6, 20, 6, -4, 2, 12, -1, -2, 4, 10, 4, 18, 4, 0, 6, 2, 8, 24, 3, 5, -6, -6, 1, 1, 4, -8, 3, -12, -2, 0, 4, 16, -8, 1, -18, 10, 0, 12, 4, 0, 12, -8, -1, -6, -6, 9, -10, 6, -1, 16, -12, -6, -16, -1, -2, -10, 8, -2, -5, 0, -1, -8, 6, -4, -12, -8, -12, -9, 6, -4, 12, -18, 6, -4, 4, -8, -6, -12, -1, -2, 8, 6, 0, 10, 1, 24, 0, -4, 4, -12, 7, 26, 6, 2, -9, -26, 4, 0, 3, 8, 10, 24, 6, -6, -20, 0, -2, 16, 4, -4, 2, -12, -12, -12, 3, 4, 2, 6, 4, -12, -10, -16, 20, 1, -18, 12, 4, -26, 0, 16, -18, -22, -2, 0, 8, -8, -24, -24, -1, 18, -5, 1, -6, 9, 6, -8, -3, 12, -1, -20, 4, 0, 8, -6, -17, -14, 12, -40, -2, -6, 0, -8, -12, -2, -16, 6, -8, -6, -1, 16, 6, -8, -10, -4, 0, 2, -12, -1, -12, 18, 0, -32, 12, -4, 8, 24, -5, 19, 6, -6, -6, 6, -9, -8, 30, -4, -6, 0, -1, 48, -16, -10, 4, 6, 6, 0, -16, 20, 1, 12, 6, -10, 10, -4, 8, -2, 2, 24, 7, 12, 0, 24, -1, 2, 8, -2, -18, 0, 4, 4, -12, 10, 8, 8, 4, -10, 9, 18, 6, 4, 4, -8, -36, 0, 18, 12, 6, -2, 4, 2, 20, 10, 8, -12, -6, 24, 12, -4, 3, -3, 2, 5, 8, 6, -6, -16, 0, -6, -10, 8, 1, 14, -24, 1, 0, -12, 4, 36, 4, -8, 12, -8, 3, 16, -26, -12, 6, 2, -2, 0, 27, 0, 26, -8, 4, -18, 0, 16, -1, 6, -8, -2, 10, 1, -24, -40, -18, 34, 6, 10, -20, 32, 0, 12, -10, 12, -16, -24, 4, 6, 4, 0, -6, -6, 12, -24, -12, -8, 12, -28, -1, 30, -4, -6, 2, 0, -6, -8, -12, 9, 12, 36, -10, 6, 16, 6, -28, 6, -1, 24, -18, 16, -12, -8, -12, -42, 26, -6, 0, 2, -16, -40, 6, -1, 22, -12, -2, -32, 0, -10, -24, 48, 8, -4, -24, -2, 24, -4, -5, 20, -18, 0, -5, -6, -1, 16, 18, -8, -9, 36, 6, 36, 8, -4, 1, 48, -12, 4, -1, -8, 20, -8, -12, -10, 0, -9, 8, -14, 6, -24, 11, -4, 14, 20, 12, 0, 40, -18, 6, -38, 6, -12, 0, -4, 8, 6, 4, -23, 2, -8, -16, -12, -6, 12, 24, -12, 6, -36, -1, 14, -16, -2, 30, -2, 8, -8, -10, 6, 4, 24, 0, 32, -2, 10, -12, -10, 1, -24, 4, 24, -18, -28, 0, 18, 32, -4, -36, 30, 4, -36, 8, -12, -24, 0, 7, -30, -19, 26, 6, -48, 6, 8, 18, 2, -6, 12, -9, 4, 8, -26, -10, 18, 4, 24, -6, 0, 0, 12, 3, 34, -48, 8, -16, 5, 10, 28, 20, 24, -6, 0, 6, 2, 0, -6, 48, -22, -20, -28, 1, 0, -12, -24, -2, 1, 10, 16, 10, -60, 4, -8, -24, -4, 2, -8, 2, 18, -24, -12, 3, 22, -12, 28, 0, -12, -24, 24, 3, 32, -2, 4, 8, -18, 2, 0, 6, 6, 0, -40, 4, -26, -4, -12, 36, 16, -10, 0, 8, -16, -8, -24, 20, -26, 10, 1, 9, -18, -18, 24, -18, 12, -4, 20, 4, 10, 8, -26, 12, -4, 0, 4, 18, 16, -12, 12, -18, 36, 2, -22, 4, 22, -2, -40, -28, 0, -10, 40, 8, 6, 12, -8, 18, 0, -24, -8, 12, -24, 4, -48, -1, -80, 3, 18, 2, -6, -5, 28, -24, 1, -6, 72, -6, 30, 16, 9, 0, -32, 6, -20, -10, -8, -8, 24, -3, 6, -14, 12, -24, -48, -1, 32, 0, -20, 12, 16, 4, 42, -36, 0, -12, 14, 8, 8, 12, -6, 8, -16, -17, -30, -16, -14, -26, 30, 12, -1, -18, -40, -2, 24, -2, 48, 0, -6, -9, -10, 0, 4, 26, -8, 8, -72, -12, 12, 18, -2, 0, 46, -16, 0, -5, 6, -6, -24, -8, 0, 2, -6, -30, -18, -1, -28, -24, 16, 40, -8, 6, 48, -34, -8, 6, 18, -10, -48, 60, -4, -32, 36, 0, 6, -12, 2, 14, -54, -12, -8, -16, -1, 24, 28, -12, 7, -6, 18, 4, -9, 0, -20, 2, -32, 6, 0, 12, -26, 24, -4, 36, -54, 8, 28, 12, 24, 28, 32, -5, -18, -30, 19, -4, 32, 6, 16, -6, -6, 0, -4, -6, -2, 8, 6, 4, 14, -9, 52, 12, -8, -36, -16, 30, 32, -6, -4, 16, 0, -6, -12, -12, 0, -6, 6, -1, 12, -24, 48, 54, -2, -16, -40, -12, -10, 8, -48, 4, -48, 42, 6, 26, 0, 6, 32, 0, 0, -2, -24, -16, 10, 40, 20, 30, -18, 1, -36, 22, 12, 12, 24, 6, 2, 32, -10, 0, 10, 10, 0, 8, -4, -48, 12, 8, 12, 4, -2, 72, -22, 2, -12, 24, 24, 4, -40, 7, 1, -20, 12, -18, 26, 0, -8, 15, 24, 6, 0, -1, -48, -16, 2, -6, 18, 8, -24, -9, -2, -36, 24, -18, -26, -36, 0, 8, 0, 4, -32, 5, 4, -48, 0, -12, 30, -4, 10, 3], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0], 1, -1, 1, -1, 1, -1, -4, 3, 1, -1, -4, -1, 2, 4, 1, -1, -6, -1, -4, -1, -4, 4, 0, 3, 1, -2, 1, 4, -6, -1, -1, -5, -4, 6, -4, -1, 10, 4, 2, 3, -6, 4, -12, 4, 1, 0, 0, -1, 9, -1, -6, -2, -2, -1, -4, -12, -4, 6, -8, -1, 6, 1, -4, 7, 2, 4, 8, 6, 0, 4, -12, 3, 6, -10, 1, 4, 16, -2, -8, -1, 1, 6, 12, 4, -6, 12, -6, -12, 6, -1, -8, 0, -1, 0, -4, -5, -6, -9, -4, -1, -10, 6, 20, 6, -4, 2, 12, -1, -2, 4, 10, 4, 18, 4, 0, 6, 2, 8, 24, 3, 5, -6, -6, 1, 1, 4, -8, 3, -12, -2, 0, 4, 16, -8, 1, -18, 10, 0, 12, 4, 0, 12, -8, -1, -6, -6, 9, -10, 6, -1, 16, -12, -6, -16, -1, -2, -10, 8, -2, -5, 0, -1, -8, 6, -4, -12, -8, -12, -9, 6, -4, 12, -18, 6, -4, 4, -8, -6, -12, -1, -2, 8, 6, 0, 10, 1, 24, 0, -4, 4, -12, 7, 26, 6, 2, -9, -26, 4, 0, 3, 8, 10, 24, 6, -6, -20, 0, -2, 16, 4, -4, 2, -12, -12, -12, 3, 4, 2, 6, 4, -12, -10, -16, 20, 1, -18, 12, 4, -26, 0, 16, -18, -22, -2, 0, 8, -8, -24, -24, -1, 18, -5, 1, -6, 9, 6, -8, -3, 12, -1, -20, 4, 0, 8, -6, -17, -14, 12, -40, -2, -6, 0, -8, -12, -2, -16, 6, -8, -6, -1, 16, 6, -8, -10, -4, 0, 2, -12, -1, -12, 18, 0, -32, 12, -4, 8, 24, -5, 19, 6, -6, -6, 6, -9, -8, 30, -4, -6, 0, -1, 48, -16, -10, 4, 6, 6, 0, -16, 20, 1, 12, 6, -10, 10, -4, 8, -2, 2, 24, 7, 12, 0, 24, -1, 2, 8, -2, -18, 0, 4, 4, -12, 10, 8, 8, 4, -10, 9, 18, 6, 4, 4, -8, -36, 0, 18, 12, 6, -2, 4, 2, 20, 10, 8, -12, -6, 24, 12, -4, 3, -3, 2, 5, 8, 6, -6, -16, 0, -6, -10, 8, 1, 14, -24, 1, 0, -12, 4, 36, 4, -8, 12, -8, 3, 16, -26, -12, 6, 2, -2, 0, 27, 0, 26, -8, 4, -18, 0, 16, -1, 6, -8, -2, 10, 1, -24, -40, -18, 34, 6, 10, -20, 32, 0, 12, -10, 12, -16, -24, 4, 6, 4, 0, -6, -6, 12, -24, -12, -8, 12, -28, -1, 30, -4, -6, 2, 0, -6, -8, -12, 9, 12, 36, -10, 6, 16, 6, -28, 6, -1, 24, -18, 16, -12, -8, -12, -42, 26, -6, 0, 2, -16, -40, 6, -1, 22, -12, -2, -32, 0, -10, -24, 48, 8, -4, -24, -2, 24, -4, -5, 20, -18, 0, -5, -6, -1, 16, 18, -8, -9, 36, 6, 36, 8, -4, 1, 48, -12, 4, -1, -8, 20, -8, -12, -10, 0, -9, 8, -14, 6, -24, 11, -4, 14, 20, 12, 0, 40, -18, 6, -38, 6, -12, 0, -4, 8, 6, 4, -23, 2, -8, -16, -12, -6, 12, 24, -12, 6, -36, -1, 14, -16, -2, 30, -2, 8, -8, -10, 6, 4, 24, 0, 32, -2, 10, -12, -10, 1, -24, 4, 24, -18, -28, 0, 18, 32, -4, -36, 30, 4, -36, 8, -12, -24, 0, 7, -30, -19, 26, 6, -48, 6, 8, 18, 2, -6, 12, -9, 4, 8, -26, -10, 18, 4, 24, -6, 0, 0, 12, 3, 34, -48, 8, -16, 5, 10, 28, 20, 24, -6, 0, 6, 2, 0, -6, 48, -22, -20, -28, 1, 0, -12, -24, -2, 1, 10, 16, 10, -60, 4, -8, -24, -4, 2, -8, 2, 18, -24, -12, 3, 22, -12, 28, 0, -12, -24, 24, 3, 32, -2, 4, 8, -18, 2, 0, 6, 6, 0, -40, 4, -26, -4, -12, 36, 16, -10, 0, 8, -16, -8, -24, 20, -26, 10, 1, 9, -18, -18, 24, -18, 12, -4, 20, 4, 10, 8, -26, 12, -4, 0, 4, 18, 16, -12, 12, -18, 36, 2, -22, 4, 22, -2, -40, -28, 0, -10, 40, 8, 6, 12, -8, 18, 0, -24, -8, 12, -24, 4, -48, -1, -80, 3, 18, 2, -6, -5, 28, -24, 1, -6, 72, -6, 30, 16, 9, 0, -32, 6, -20, -10, -8, -8, 24, -3, 6, -14, 12, -24, -48, -1, 32, 0, -20, 12, 16, 4, 42, -36, 0, -12, 14, 8, 8, 12, -6, 8, -16, -17, -30, -16, -14, -26, 30, 12, -1, -18, -40, -2, 24, -2, 48, 0, -6, -9, -10, 0, 4, 26, -8, 8, -72, -12, 12, 18, -2, 0, 46, -16, 0, -5, 6, -6, -24, -8, 0, 2, -6, -30, -18, -1, -28, -24, 16, 40, -8, 6, 48, -34, -8, 6, 18, -10, -48, 60, -4, -32, 36, 0, 6, -12, 2, 14, -54, -12, -8, -16, -1, 24, 28, -12, 7, -6, 18, 4, -9, 0, -20, 2, -32, 6, 0, 12, -26, 24, -4, 36, -54, 8, 28, 12, 24, 28, 32, -5, -18, -30, 19, -4, 32, 6, 16, -6, -6, 0, -4, -6, -2, 8, 6, 4, 14, -9, 52, 12, -8, -36, -16, 30, 32, -6, -4, 16, 0, -6, -12, -12, 0, -6, 6, -1, 12, -24, 48, 54, -2, -16, -40, -12, -10, 8, -48, 4, -48, 42, 6, 26, 0, 6, 32, 0, 0, -2, -24, -16, 10, 40, 20, 30, -18, 1, -36, 22, 12, 12, 24, 6, 2, 32, -10, 0, 10, 10, 0, 8, -4, -48, 12, 8, 12, 4, -2, 72, -22, 2, -12, 24, 24, 4, -40, 7, 1, -20, 12, -18, 26, 0, -8, 15, 24, 6, 0, -1, -48, -16, 2, -6, 18, 8, -24, -9, -2, -36, 24, -18, -26, -36, 0, 8, 0, 4, -32, 5, 4, -48, 0, -12, 30, -4, 10, 3]}