# Stored data for newform 605.2.a.a, downloaded from the LMFDB on 16 April 2024.
{"label": "605.2.a.a", "space_label": "605.2.a", "level": 605, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 33555037, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1311679285348292577, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [1, 1]], [3, [3, 1]]], "qexp_display": "q-q^{2}-3q^{3}-q^{4}+q^{5}+3q^{6}-3q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 2420, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 4.830949322287463, "hecke_ring_index": 1, "level_radical": 55, "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": "0.010", "prec": 17}, "analytic_rank_proved": true, "char_values": [605, 1, [122, 486], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [5, 11], "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": "0.987", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.007", "prec": 17}, {"__RealLiteral__": 0, "data": "0.028", "prec": 17}, {"__RealLiteral__": 0, "data": "5.115", "prec": 17}], "related_objects": ["EllipticCurve/Q/605/a"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[5, -1], [11, -1]], "trace_display": [-1, -3, 1, -3], "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_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "605.2.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], [-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]]}