# Stored data for newform 475.2.a.a, downloaded from the LMFDB on 11 May 2026. {"Nk2": 1900, "analytic_conductor": 3.7928940960108184, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[5, -1], [19, -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": [475, 1, [77, 401], [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": 33554907, "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": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "475.2.a.a", "level": 475, "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": [5, 19], "level_radical": 95, "minimal_twist": "95.2.b.a", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q-q^{2}-q^{4}+2q^{7}+3q^{8}-3q^{9}-4q^{11}+\\cdots", "related_objects": ["EllipticCurve/Q/475/a"], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "475.2.a", "trace_display": [-1, 0, 0, 2], "trace_hash": 311833585263559080, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.994", "prec": 17}, {"__RealLiteral__": 0, "data": "0.050", "prec": 17}, {"__RealLiteral__": 0, "data": "1.940", "prec": 17}, {"__RealLiteral__": 0, "data": "0.134", "prec": 17}, {"__RealLiteral__": 0, "data": "4.728", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.014", "prec": 17}, "traces": [0, 1, -1, 0, -1, 0, 0, 2, 3, -3, 0, -4, 0, -2, -2, 0, -1, 4, 3, 1, 0, 0, 4, -6, 0, 0, 2, 0, -2, -6, 0, -4, -5, 0, -4, 0, 3, -10, -1, 0, 0, -10, 0, 2, 4, 0, 6, -6, 0, -3, 0, 0, 2, 10, 0, 0, 6, 0, 6, 0, 0, 2, 4, -6, 7, 0, 0, 8, -4, 0, 0, 4, -9, 4, 10, 0, -1, -8, 0, 4, 0, 9, 10, -18, 0, 0, -2, 0, -12, -2, 0, -4, 6, 0, 6, 0, 0, 6, 3, 12, 0, -6, 0, 16, -6, 0, -10, -4, 0, 6, 0, 0, -2, 6, 0, 0, 6, 6, 0, 8, 0, 5, -2, 0, 4, 0, 6, 0, 3, 0, 0, -12, 0, 2, -8, 0, 12, 12, 0, -4, 0, 0, -4, 8, 3, 0, -4, 0, 10, -10, 0, 24, 3, -12, 8, 0, 0, -8, -4, 0, 0, -12, -9, 10, 10, 0, 18, 12, 0, -9, 0, -3, -2, -6, 0, 0, 4, 0, 2, 0, 0, -18, 4, 0, -18, 0, 0, -16, 6, 0, 0, -24, 0, -26, -6, 0, 3, -12, -12, 16, 0, 0, 6, -12, 0, 0, -16, 18, 2, -4, 0, 20, -10, 0, 4, 0, 0, -8, -6, 0, 0, -8, 0, 16, -10, 0, -6, 20, 0, -10, 0, 0, -18, 16, -6, 0, 0, 0, -8, -16, 0, -2, -5, 0, -2, 0, 0, -2, -12, 0, 0, 4, 6, 24, 0, 0, -17, -6, 0, -20, 0, 18, 12, -6, 0, 0, -2, 0, -8, -18, 0, 24, -4, 0, -12, 0, 0, 8, 4, 12, 0, -26, 0, 14, -4, 0, -8, -20, 15, -1, 0, 0, -4, -14, 0, 0, -30, 0, 10, 12, 0, 4, -24, 0, -1, 0, 12, -20, 8, 0, 0, 24, 0, -24, 8, 0, -4, 22, 0, 24, 0, 0, 12, 4, -9, 0, -10, 0, -30, -12, 0, -4, 18, 30, -12, 0, 0, 22, 9, 0, 0, 16, 3, -20, 6, 0, 6, -6, 0, 2, 0, 0, 20, 4, 0, 0, 2, 0, 0, -8, 0, 1, 18, 0, 4, 0, 0, -22, 6, 30, 0, 20, 0, -6, 16, 0, -18, 12, 0, 28, 0, 0, 24, 12, 0, 0, 26, -6, -6, -30, 0, -24, -9, 0, 12, 0, -12, -8, -16, 0, 0, 18, 0, 8, 6, 0, 12, 40, 0, -14, 0, 0, -16, 0, -18, 0, 10, 0, 4, 36, 0, -30, -20, 18, 30, 0, 0, 4, 4, 0, 0, 0, 0, -34, 8, 0, -6, -6, 0, 20, 0, 9, 8, -2, 0, 0, -16, 0, 14, 10, 0, 40, -6, 0, -20, 0, 0, -8, 10, 0, 0, 14, 0, 2, 6, 0, -16, -38, -6, 16, 0, 0, 0, -8, 0, 0, -8, -30, 16, -24, 0, 20, 2, 0, -5, 0, 0, -20, 6, 0, 0, -20, 0, -24, 2, 0, 4, 8, 0, 4, 0, 0, -4, 10, -18, 0, -24, 0, 0, -6, 0, 8, 11, 0, 6, 0, 0, 24, 20, 0, 0, 42, -18, -44, 12, 0, 6, -16, 0, 13, 0, 0, -2, 20, 0, 0, 24, 0, 18, 12, 0, -22, -24, 0, -20, 0, 0, 28, -12, -6, 0, -6, 0, 8, -8, 0, 4, -16, -12, -4, 0, 0, 26, 12, 0, 0, -14, 18, 12, 42, 0, 4, -8, 0, 20, 0, -21, 24, 1, 0, 0, -36, 0, -40, 12, 0, 14, 18, 0, -4, 0, 0, 10, -8, 0, 0, 10, 0, -12, 12, 0, 14, -4, -24, -24, 0, 0, -44, -5, 0, 0, 12, 12, -24, 20, 0, -24, 12, 0, -20, 0, 0, -24, -4, 0, 0, 24, 0, 8, -40, 0, -8, 12, 0, -22, 0, 0, 6, -24, -12, 0, 6, 0, 38, 12, 0, -4, 30, 27, 0, 0, 0, -10, 16, 0, 0, 10, -12, 12, -16, 0, -30, 4, 0, -54, 0, -30, 36, -12, 0, 0, -8, 0, 34, -22, 0, 9, 18, 0, 12, 0, 0, -16, 12, 3, 0, 20, 0, -2, -20, 0, -12, 6, 24, 6, 0, 0, -40, -2, 0, 0, -30, 0, -10, -28, 0, -4, -12, 0, -38, 0, -12, -6, 24, 0, 0, 0, 0, 8, 0, 0, 32, -1, 0, 18, 0, 0, 2, -12, -27, 0, 8, 0, -12, 22, 0, 30, -32, -30, 4, 0, 0, -20, -4, 0, 0, 6, 54, 16, -8, 0, -40, 6, 0, -12, 0, 0, -4, -28, 0, 0, 6, 0, 12, 24, 0, -12, 0, 0, 26, 0, 0, 26, 46, 6, 0, 18, 0, 30, -10, 0, -16, 24, 0, 3, 0, 0, -44, 12, 0, 0, 12, 36, -4, 8, 0, -16, -6, 0, -24, 0, 6, -18, -16, 0, 0, -8, 0, -18, -10, 0, -24, 12, 0, -40, 0, 0, 2, 14, 12, 0, -42, 0, -42, 48, 0, 0, 24, -18, 14, 0, 0, -14, -12, 0, 0, 4, 0, -36, -12, 0, 7, 30, 0, -20, 0, -18, 10, -10, 0, 0, 60, 0, -4, -4, 0, -12, -6, 0, -20, 0, 0, 0, -28, 0, 0, 34, 0, 8, -16, 0, -16, 18, -18, 6, 0, 0, 2, -20, 0, 0, -2, -9, 34, 8, 0, 2, 8, 0, 0, 0, -36, -16, -6, 0, 0, 6, 0, -10, 24, 0, 40, -40, 0, 18, 0, 0, 12, -20, 18, 0, 8, 0, 72, 8, 0, 10, -24, 0, 16, 0, 0, -14, -8, 0, 0, -2, -48, 30, 6, 0, -3, -16, 0, 38, 0, 18, -20, -16, 0, 0, 14, 0, 60, 0, 0, 8, -30, 0, -8, 0, 0, 24, -30, 30, 0, 16, 0, 24, 24, 0, -15, -20, 12, 2, 0, 0, -2, 15, 0, 0, 24, 0, -8, 20, 0, -2, -14, 0, 8, 0, -18, 20, -12, 0, 0, 24, 0, 2, -12, 0, 32, 20, 0, -8, 0, 0, 32, -4, 0, 0], "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, 0, -1, 0, 0, 2, 3, -3, 0, -4, 0, -2, -2, 0, -1, 4, 3, 1, 0, 0, 4, -6, 0, 0, 2, 0, -2, -6, 0, -4, -5, 0, -4, 0, 3, -10, -1, 0, 0, -10, 0, 2, 4, 0, 6, -6, 0, -3, 0, 0, 2, 10, 0, 0, 6, 0, 6, 0, 0, 2, 4, -6, 7, 0, 0, 8, -4, 0, 0, 4, -9, 4, 10, 0, -1, -8, 0, 4, 0, 9, 10, -18, 0, 0, -2, 0, -12, -2, 0, -4, 6, 0, 6, 0, 0, 6, 3, 12, 0, -6, 0, 16, -6, 0, -10, -4, 0, 6, 0, 0, -2, 6, 0, 0, 6, 6, 0, 8, 0, 5, -2, 0, 4, 0, 6, 0, 3, 0, 0, -12, 0, 2, -8, 0, 12, 12, 0, -4, 0, 0, -4, 8, 3, 0, -4, 0, 10, -10, 0, 24, 3, -12, 8, 0, 0, -8, -4, 0, 0, -12, -9, 10, 10, 0, 18, 12, 0, -9, 0, -3, -2, -6, 0, 0, 4, 0, 2, 0, 0, -18, 4, 0, -18, 0, 0, -16, 6, 0, 0, -24, 0, -26, -6, 0, 3, -12, -12, 16, 0, 0, 6, -12, 0, 0, -16, 18, 2, -4, 0, 20, -10, 0, 4, 0, 0, -8, -6, 0, 0, -8, 0, 16, -10, 0, -6, 20, 0, -10, 0, 0, -18, 16, -6, 0, 0, 0, -8, -16, 0, -2, -5, 0, -2, 0, 0, -2, -12, 0, 0, 4, 6, 24, 0, 0, -17, -6, 0, -20, 0, 18, 12, -6, 0, 0, -2, 0, -8, -18, 0, 24, -4, 0, -12, 0, 0, 8, 4, 12, 0, -26, 0, 14, -4, 0, -8, -20, 15, -1, 0, 0, -4, -14, 0, 0, -30, 0, 10, 12, 0, 4, -24, 0, -1, 0, 12, -20, 8, 0, 0, 24, 0, -24, 8, 0, -4, 22, 0, 24, 0, 0, 12, 4, -9, 0, -10, 0, -30, -12, 0, -4, 18, 30, -12, 0, 0, 22, 9, 0, 0, 16, 3, -20, 6, 0, 6, -6, 0, 2, 0, 0, 20, 4, 0, 0, 2, 0, 0, -8, 0, 1, 18, 0, 4, 0, 0, -22, 6, 30, 0, 20, 0, -6, 16, 0, -18, 12, 0, 28, 0, 0, 24, 12, 0, 0, 26, -6, -6, -30, 0, -24, -9, 0, 12, 0, -12, -8, -16, 0, 0, 18, 0, 8, 6, 0, 12, 40, 0, -14, 0, 0, -16, 0, -18, 0, 10, 0, 4, 36, 0, -30, -20, 18, 30, 0, 0, 4, 4, 0, 0, 0, 0, -34, 8, 0, -6, -6, 0, 20, 0, 9, 8, -2, 0, 0, -16, 0, 14, 10, 0, 40, -6, 0, -20, 0, 0, -8, 10, 0, 0, 14, 0, 2, 6, 0, -16, -38, -6, 16, 0, 0, 0, -8, 0, 0, -8, -30, 16, -24, 0, 20, 2, 0, -5, 0, 0, -20, 6, 0, 0, -20, 0, -24, 2, 0, 4, 8, 0, 4, 0, 0, -4, 10, -18, 0, -24, 0, 0, -6, 0, 8, 11, 0, 6, 0, 0, 24, 20, 0, 0, 42, -18, -44, 12, 0, 6, -16, 0, 13, 0, 0, -2, 20, 0, 0, 24, 0, 18, 12, 0, -22, -24, 0, -20, 0, 0, 28, -12, -6, 0, -6, 0, 8, -8, 0, 4, -16, -12, -4, 0, 0, 26, 12, 0, 0, -14, 18, 12, 42, 0, 4, -8, 0, 20, 0, -21, 24, 1, 0, 0, -36, 0, -40, 12, 0, 14, 18, 0, -4, 0, 0, 10, -8, 0, 0, 10, 0, -12, 12, 0, 14, -4, -24, -24, 0, 0, -44, -5, 0, 0, 12, 12, -24, 20, 0, -24, 12, 0, -20, 0, 0, -24, -4, 0, 0, 24, 0, 8, -40, 0, -8, 12, 0, -22, 0, 0, 6, -24, -12, 0, 6, 0, 38, 12, 0, -4, 30, 27, 0, 0, 0, -10, 16, 0, 0, 10, -12, 12, -16, 0, -30, 4, 0, -54, 0, -30, 36, -12, 0, 0, -8, 0, 34, -22, 0, 9, 18, 0, 12, 0, 0, -16, 12, 3, 0, 20, 0, -2, -20, 0, -12, 6, 24, 6, 0, 0, -40, -2, 0, 0, -30, 0, -10, -28, 0, -4, -12, 0, -38, 0, -12, -6, 24, 0, 0, 0, 0, 8, 0, 0, 32, -1, 0, 18, 0, 0, 2, -12, -27, 0, 8, 0, -12, 22, 0, 30, -32, -30, 4, 0, 0, -20, -4, 0, 0, 6, 54, 16, -8, 0, -40, 6, 0, -12, 0, 0, -4, -28, 0, 0, 6, 0, 12, 24, 0, -12, 0, 0, 26, 0, 0, 26, 46, 6, 0, 18, 0, 30, -10, 0, -16, 24, 0, 3, 0, 0, -44, 12, 0, 0, 12, 36, -4, 8, 0, -16, -6, 0, -24, 0, 6, -18, -16, 0, 0, -8, 0, -18, -10, 0, -24, 12, 0, -40, 0, 0, 2, 14, 12, 0, -42, 0, -42, 48, 0, 0, 24, -18, 14, 0, 0, -14, -12, 0, 0, 4, 0, -36, -12, 0, 7, 30, 0, -20, 0, -18, 10, -10, 0, 0, 60, 0, -4, -4, 0, -12, -6, 0, -20, 0, 0, 0, -28, 0, 0, 34, 0, 8, -16, 0, -16, 18, -18, 6, 0, 0, 2, -20, 0, 0, -2, -9, 34, 8, 0, 2, 8, 0, 0, 0, -36, -16, -6, 0, 0, 6, 0, -10, 24, 0, 40, -40, 0, 18, 0, 0, 12, -20, 18, 0, 8, 0, 72, 8, 0, 10, -24, 0, 16, 0, 0, -14, -8, 0, 0, -2, -48, 30, 6, 0, -3, -16, 0, 38, 0, 18, -20, -16, 0, 0, 14, 0, 60, 0, 0, 8, -30, 0, -8, 0, 0, 24, -30, 30, 0, 16, 0, 24, 24, 0, -15, -20, 12, 2, 0, 0, -2, 15, 0, 0, 24, 0, -8, 20, 0, -2, -14, 0, 8, 0, -18, 20, -12, 0, 0, 24, 0, 2, -12, 0, 32, 20, 0, -8, 0, 0, 32, -4, 0, 0]}