# Stored data for newform 605.2.a.c, downloaded from the LMFDB on 15 November 2024. {"Nk2": 2420, "analytic_conductor": 4.830949322287463, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[5, -1], [11, -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": [605, 1, [122, 486], [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]], [3, [3, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9007199288296029, "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": true, "label": "605.2.a.c", "level": 605, "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, 11], "level_radical": 55, "minimal_twist": "605.2.a.a", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+q^{2}-3q^{3}-q^{4}+q^{5}-3q^{6}+3q^{7}+\\cdots", "related_objects": ["EllipticCurve/Q/605/c"], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "605.2.a", "trace_display": [1, -3, 1, 3], "trace_hash": 884153072314794808, "trace_moments": [{"__RealLiteral__": 0, "data": "0.007", "prec": 17}, {"__RealLiteral__": 0, "data": "0.987", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.007", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.115", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.010", "prec": 17}, "traces": [0, 1, 1, -3, -1, 1, -3, 3, -3, 6, 1, 0, 3, -4, 3, -3, -1, 0, 6, -4, -1, -9, 0, -8, 9, 1, -4, -9, -3, -6, -3, -2, 5, 0, 0, 3, -6, -8, -4, 12, -3, 5, -9, -5, 0, 6, -8, -3, 3, 2, 1, 0, 4, 4, -9, 0, -9, 12, -6, -2, 3, 11, -2, 18, 7, -4, 0, -13, 0, 24, 3, 2, -18, 8, -8, -3, 4, 0, 12, -10, -1, 9, 5, -4, 9, 0, -5, 18, 0, 1, 6, -12, 8, 6, -3, -4, -15, -8, 2, 0, -1, 5, 0, 8, 12, -9, 4, -9, 9, 9, 0, 24, -3, 6, 12, -8, 6, -24, -2, 0, 9, 0, 11, -15, 2, 1, 18, -11, -3, 15, -4, 0, 0, -12, -13, -9, 0, 0, 24, 18, -3, 9, 2, 0, -6, -6, 8, -6, 8, 17, -3, 14, 12, 0, 0, -2, -12, -8, -10, -12, 5, -24, 9, -17, -5, 0, -4, 7, 27, 3, 0, -24, 5, -24, 18, 3, 0, 6, 1, -26, -6, -19, -12, -33, 24, -8, 6, 0, 3, -27, -4, 8, -21, 10, -8, 12, -2, 14, 0, -6, -3, 39, 5, -18, 0, 5, 8, -48, 4, 0, -9, 22, -4, -6, -9, -5, 27, -6, 9, -24, 0, 0, 24, 5, 15, 6, 6, 1, -12, -1, -8, 0, 18, 24, -24, -3, 2, 30, 0, -4, 3, -23, 0, 0, -11, 2, -15, 16, 6, 12, 1, 18, -18, 0, -11, 0, -17, -6, 15, -24, 4, -36, 0, -12, 0, 4, -12, -3, 13, 21, -9, 0, 0, 36, 0, 0, -24, -14, 18, -12, -9, 6, 9, 13, -2, 12, 0, 15, 30, -17, -6, 24, -8, 34, -6, -2, 24, 0, 17, 32, 3, -15, 14, -15, 4, 11, 0, 8, 0, -24, -2, 24, -36, 8, -8, 18, 10, 18, -12, 0, 7, 27, -24, 0, -9, -4, -17, -27, -15, -9, 0, -20, 4, -48, 7, -13, 9, 12, 3, -18, 0, 0, -24, -15, 15, 24, -24, -7, -18, -22, 3, 36, 0, 6, 6, 2, -1, 0, -26, 28, -18, -3, -19, 0, 12, 8, -33, 1, 8, 30, -8, 12, -6, -18, 0, -3, 9, 24, -27, -22, 4, 33, 8, 0, 9, 0, 10, -30, 8, -3, 12, 0, -6, 0, 14, -10, 0, -12, -6, 36, -1, -37, 39, 8, -5, 9, -18, 0, 0, -21, 5, 0, -8, -6, -48, -4, -20, -54, 0, 32, 9, 3, 22, -18, -12, 0, -6, 33, 9, 0, -5, -18, 9, 14, -6, 18, -9, 32, -24, -8, 0, 12, 0, -25, -24, 1, 5, -51, 21, -13, 6, 0, -6, -42, 1, -12, -36, -26, -1, 0, 8, -7, 0, -15, 6, 6, 24, 27, 24, -39, -3, 24, 6, 0, 30, -4, 0, 24, -4, -6, -15, 32, -23, 72, 0, -8, 0, -8, -33, 51, 2, -22, 15, 0, 16, 0, 2, 6, 12, -42, -1, -21, 18, -13, -54, 5, 0, -9, 11, 23, 0, 24, -11, 36, -6, 8, -15, 0, -24, 72, 12, 15, -36, 4, 0, -9, -12, 0, 0, 41, 4, -12, 12, -20, -3, -9, 39, 78, 21, 0, 9, -31, 0, 57, 0, 9, 36, -36, 0, 66, 0, 24, -72, -30, -14, 24, -18, 28, -12, 20, -3, 0, 6, -21, -9, 6, 13, 27, -6, 11, 12, 18, 0, -24, 15, -8, 42, 14, -17, -30, 6, -12, 24, 0, -24, -24, 34, 21, 6, 8, -2, -42, 8, -44, 0, 0, -17, 18, 32, 24, 9, 2, -15, -78, -14, 0, -15, 40, -20, 54, 11, 12, 0, 22, 8, -15, 0, 26, -24, -8, 2, 72, 24, 3, -12, 1, 8, 0, 8, 0, 18, -44, 30, -66, 18, -11, 12, -8, 0, 12, -3, -14, 27, 35, 24, 15, 0, -25, -27, 0, -4, 18, 17, -34, -27, 0, -5, 48, -9, 42, 0, -37, -20, 0, 12, -12, -48, 48, -7, -15, -13, 0, -45, 10, 12, -9, -3, 28, -18, -24, 0, -3, 0, 47, 24, 0, -15, 3, 5, -16, 24, -40, 24, 0, -7, 18, -54, 0, -22, -72, -3, -38, 36, 32, 0, 9, 6, 15, -6, -25, 2, -60, -3, 16, 0, 0, 26, 12, 28, 0, -6, 24, -3, 69, 19, -6, 0, -17, 36, -27, 8, 0, 33, -36, 1, -6, -40, 0, 30, 10, 8, -48, 12, 7, -18, 17, -18, -24, 0, -27, -3, 10, 3, -54, 24, 14, 27, -12, -22, 0, 12, -26, 33, 27, -8, 0, 0, 8, 51, 26, 0, 18, -10, -22, -30, -2, 24, 72, -3, -20, -12, 0, 0, 54, -2, -8, 0, 43, -14, 36, -10, 18, 0, -44, -12, -12, 6, -50, 36, 0, 5, 6, -37, 0, -39, -24, 8, -63, -15, -54, 9, -42, 18, 0, 0, -17, 0, 20, -21, -72, -5, 3, 0, 51, -24, 0, -6, -45, 48, 13, -4, 42, -28, 0, -54, 7, 0, 18, 32, -14, 27, 7, 3, -18, -22, 3, -18, 0, -4, -39, 0, 64, 6, 32, 33, -24, 27, 18, 0, 4, 5, -45, -18, 31, -45, -24, 14, 51, 6, 0, 18, 52, -27, -48, 32, 3, 24, -22, -8, -102, 0, -15, 12, 20, 0, 6, -25, -1, -72, -33, 1, 0, -5, 12, -51, -26, -9, -96, -13, 12, -6, 0, 0, 45, -18, -19, -42, -43, -1, 30, -12, -34, -12, 0, -26, -33, 1, 0, 0, -12, 24, -24, -7, -8, 0, -8, -15, 48, -30, -26, 6, -8, -24, -72, 27, 0, 72, 18, -39, -24, 3, 13, 24, -40, 2, -27, 0, -12, -30, -32, -4, -54, 0, 36, 24, 8, 4, 0, -6, 0, -21, -27, 32, -54, 23, 10, 72, 32, 0, 0, -8, 12, 0, 54, -8, 12, -11, 28, 51, 0, -2, 54, -22, -61, 45, 14, 0, 27, -16, 40, 0, 20, -10, 60, 6, -6, -12, -52, -42, 72, -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, -3, -1, 1, -3, 3, -3, 6, 1, 0, 3, -4, 3, -3, -1, 0, 6, -4, -1, -9, 0, -8, 9, 1, -4, -9, -3, -6, -3, -2, 5, 0, 0, 3, -6, -8, -4, 12, -3, 5, -9, -5, 0, 6, -8, -3, 3, 2, 1, 0, 4, 4, -9, 0, -9, 12, -6, -2, 3, 11, -2, 18, 7, -4, 0, -13, 0, 24, 3, 2, -18, 8, -8, -3, 4, 0, 12, -10, -1, 9, 5, -4, 9, 0, -5, 18, 0, 1, 6, -12, 8, 6, -3, -4, -15, -8, 2, 0, -1, 5, 0, 8, 12, -9, 4, -9, 9, 9, 0, 24, -3, 6, 12, -8, 6, -24, -2, 0, 9, 0, 11, -15, 2, 1, 18, -11, -3, 15, -4, 0, 0, -12, -13, -9, 0, 0, 24, 18, -3, 9, 2, 0, -6, -6, 8, -6, 8, 17, -3, 14, 12, 0, 0, -2, -12, -8, -10, -12, 5, -24, 9, -17, -5, 0, -4, 7, 27, 3, 0, -24, 5, -24, 18, 3, 0, 6, 1, -26, -6, -19, -12, -33, 24, -8, 6, 0, 3, -27, -4, 8, -21, 10, -8, 12, -2, 14, 0, -6, -3, 39, 5, -18, 0, 5, 8, -48, 4, 0, -9, 22, -4, -6, -9, -5, 27, -6, 9, -24, 0, 0, 24, 5, 15, 6, 6, 1, -12, -1, -8, 0, 18, 24, -24, -3, 2, 30, 0, -4, 3, -23, 0, 0, -11, 2, -15, 16, 6, 12, 1, 18, -18, 0, -11, 0, -17, -6, 15, -24, 4, -36, 0, -12, 0, 4, -12, -3, 13, 21, -9, 0, 0, 36, 0, 0, -24, -14, 18, -12, -9, 6, 9, 13, -2, 12, 0, 15, 30, -17, -6, 24, -8, 34, -6, -2, 24, 0, 17, 32, 3, -15, 14, -15, 4, 11, 0, 8, 0, -24, -2, 24, -36, 8, -8, 18, 10, 18, -12, 0, 7, 27, -24, 0, -9, -4, -17, -27, -15, -9, 0, -20, 4, -48, 7, -13, 9, 12, 3, -18, 0, 0, -24, -15, 15, 24, -24, -7, -18, -22, 3, 36, 0, 6, 6, 2, -1, 0, -26, 28, -18, -3, -19, 0, 12, 8, -33, 1, 8, 30, -8, 12, -6, -18, 0, -3, 9, 24, -27, -22, 4, 33, 8, 0, 9, 0, 10, -30, 8, -3, 12, 0, -6, 0, 14, -10, 0, -12, -6, 36, -1, -37, 39, 8, -5, 9, -18, 0, 0, -21, 5, 0, -8, -6, -48, -4, -20, -54, 0, 32, 9, 3, 22, -18, -12, 0, -6, 33, 9, 0, -5, -18, 9, 14, -6, 18, -9, 32, -24, -8, 0, 12, 0, -25, -24, 1, 5, -51, 21, -13, 6, 0, -6, -42, 1, -12, -36, -26, -1, 0, 8, -7, 0, -15, 6, 6, 24, 27, 24, -39, -3, 24, 6, 0, 30, -4, 0, 24, -4, -6, -15, 32, -23, 72, 0, -8, 0, -8, -33, 51, 2, -22, 15, 0, 16, 0, 2, 6, 12, -42, -1, -21, 18, -13, -54, 5, 0, -9, 11, 23, 0, 24, -11, 36, -6, 8, -15, 0, -24, 72, 12, 15, -36, 4, 0, -9, -12, 0, 0, 41, 4, -12, 12, -20, -3, -9, 39, 78, 21, 0, 9, -31, 0, 57, 0, 9, 36, -36, 0, 66, 0, 24, -72, -30, -14, 24, -18, 28, -12, 20, -3, 0, 6, -21, -9, 6, 13, 27, -6, 11, 12, 18, 0, -24, 15, -8, 42, 14, -17, -30, 6, -12, 24, 0, -24, -24, 34, 21, 6, 8, -2, -42, 8, -44, 0, 0, -17, 18, 32, 24, 9, 2, -15, -78, -14, 0, -15, 40, -20, 54, 11, 12, 0, 22, 8, -15, 0, 26, -24, -8, 2, 72, 24, 3, -12, 1, 8, 0, 8, 0, 18, -44, 30, -66, 18, -11, 12, -8, 0, 12, -3, -14, 27, 35, 24, 15, 0, -25, -27, 0, -4, 18, 17, -34, -27, 0, -5, 48, -9, 42, 0, -37, -20, 0, 12, -12, -48, 48, -7, -15, -13, 0, -45, 10, 12, -9, -3, 28, -18, -24, 0, -3, 0, 47, 24, 0, -15, 3, 5, -16, 24, -40, 24, 0, -7, 18, -54, 0, -22, -72, -3, -38, 36, 32, 0, 9, 6, 15, -6, -25, 2, -60, -3, 16, 0, 0, 26, 12, 28, 0, -6, 24, -3, 69, 19, -6, 0, -17, 36, -27, 8, 0, 33, -36, 1, -6, -40, 0, 30, 10, 8, -48, 12, 7, -18, 17, -18, -24, 0, -27, -3, 10, 3, -54, 24, 14, 27, -12, -22, 0, 12, -26, 33, 27, -8, 0, 0, 8, 51, 26, 0, 18, -10, -22, -30, -2, 24, 72, -3, -20, -12, 0, 0, 54, -2, -8, 0, 43, -14, 36, -10, 18, 0, -44, -12, -12, 6, -50, 36, 0, 5, 6, -37, 0, -39, -24, 8, -63, -15, -54, 9, -42, 18, 0, 0, -17, 0, 20, -21, -72, -5, 3, 0, 51, -24, 0, -6, -45, 48, 13, -4, 42, -28, 0, -54, 7, 0, 18, 32, -14, 27, 7, 3, -18, -22, 3, -18, 0, -4, -39, 0, 64, 6, 32, 33, -24, 27, 18, 0, 4, 5, -45, -18, 31, -45, -24, 14, 51, 6, 0, 18, 52, -27, -48, 32, 3, 24, -22, -8, -102, 0, -15, 12, 20, 0, 6, -25, -1, -72, -33, 1, 0, -5, 12, -51, -26, -9, -96, -13, 12, -6, 0, 0, 45, -18, -19, -42, -43, -1, 30, -12, -34, -12, 0, -26, -33, 1, 0, 0, -12, 24, -24, -7, -8, 0, -8, -15, 48, -30, -26, 6, -8, -24, -72, 27, 0, 72, 18, -39, -24, 3, 13, 24, -40, 2, -27, 0, -12, -30, -32, -4, -54, 0, 36, 24, 8, 4, 0, -6, 0, -21, -27, 32, -54, 23, 10, 72, 32, 0, 0, -8, 12, 0, 54, -8, 12, -11, 28, 51, 0, -2, 54, -22, -61, 45, 14, 0, 27, -16, 40, 0, 20, -10, 60, 6, -6, -12, -52, -42, 72, -3]}