# Stored data for newform 79.2.a.a, downloaded from the LMFDB on 19 April 2024.
{"label": "79.2.a.a", "space_label": "79.2.a", "level": 79, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 33554511, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1030334534842869988, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [1, 1]]], "qexp_display": "q-q^{2}-q^{3}-q^{4}-3q^{5}+q^{6}-q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 316, "fricke_eigenval": 1, "atkin_lehner_string": "+", "analytic_conductor": 0.6308181759681151, "hecke_ring_index": 1, "level_radical": 79, "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": "0.016", "prec": 17}, "analytic_rank_proved": true, "char_values": [79, 1, [3], [1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [79], "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": "0.952", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.873", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.680", "prec": 17}], "related_objects": ["EllipticCurve/Q/79/a"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[79, 1]], "trace_display": [-1, -1, -3, -1], "traces": [0, 1, -1, -1, -1, -3, 1, -1, 3, -2, 3, -2, 1, 3, 1, 3, -1, -6, 2, 4, 3, 1, 2, 2, -3, 4, -3, 5, 1, -6, -3, -10, -5, 2, 6, 3, 2, -2, -4, -3, -9, -10, -1, 4, 2, 6, -2, 7, 1, -6, -4, 6, -3, 8, -5, 6, -3, -4, 6, -3, -3, -4, 10, 2, 7, -9, -2, 8, 6, -2, -3, 15, -6, 2, 2, -4, -4, 2, 3, -1, 3, 1, 10, -6, -1, 18, -4, 6, -6, -7, -6, -3, -2, 10, -7, -12, 5, -19, 6, 4, -4, 11, -6, -9, 9, -3, -8, -11, -5, 10, -6, 2, 1, 0, 4, -6, 6, -6, 3, 6, 9, -7, 4, 10, 10, 3, -2, -11, 3, -4, 9, 6, -2, -4, -8, -15, -18, 12, 2, -21, -3, -7, -15, -6, 2, 18, -2, 6, 2, -6, 4, 6, 12, 12, -2, 30, 3, -18, 1, -8, 15, -2, -1, 4, 10, -6, 6, 18, 3, -4, -18, -8, -4, -8, -6, -4, 2, 3, 7, -16, -6, 22, 3, 4, 6, 6, -10, 12, -7, -5, 12, -15, -7, 14, 19, 9, 6, -6, -4, 11, 12, -8, -11, 6, -6, 30, 9, -4, -3, -8, 3, -12, -8, -15, 11, -12, 15, 10, -10, -2, -6, -18, -2, -26, 5, -8, 0, -8, 4, 16, 6, -2, -18, -18, 6, -21, 3, 1, -6, 12, -3, -15, 7, -16, 4, 18, -10, 12, -30, 6, -3, -5, -2, -4, 11, -18, -17, -2, 4, 2, 9, 12, -6, 26, 6, -24, 4, 7, -8, -19, 15, 0, 6, 3, -12, -8, 2, 11, 21, 20, 9, 23, 7, 24, -15, 12, 6, 10, 10, 19, -18, 19, -2, -12, -6, 9, -6, -10, 6, 6, 4, -4, -6, -11, -4, 12, -12, 12, -2, 9, -30, 4, -9, -26, 18, -6, 1, 31, 8, 12, -21, 11, 2, -24, -1, 12, -4, -10, -30, -7, 6, 20, 6, 4, -18, -24, -1, 31, 4, 0, -18, 20, 8, 13, 12, 6, 8, -14, -6, 12, 4, 15, 10, -4, -3, -45, 7, -6, 16, -35, 18, -3, -22, 7, 3, -6, -4, -2, -2, 20, -6, -8, -10, -2, -12, -3, 21, -18, 5, -23, 12, 11, 15, 2, -3, -6, -14, -8, 19, -9, -9, -12, -18, -6, 6, 3, -4, -1, -11, 4, -4, 10, 8, -30, -11, -3, -6, 4, 18, 0, -30, -12, 9, 3, 4, 18, -15, 21, 8, 9, 3, -13, 12, -14, 24, -24, 15, 4, 11, 6, 12, 20, -5, -3, -10, -18, -10, 8, 2, -20, 18, 12, 18, -4, -2, 21, 26, 6, -7, -22, 8, 20, 0, -6, 8, 9, -12, 7, -16, -30, 6, -10, 2, -19, 6, -30, 18, 6, 6, -8, 21, 18, -9, -8, -1, 16, -6, -16, -12, 0, -15, -6, 15, 2, 7, 57, 16, 18, -12, -4, -18, 13, -10, 36, -12, -12, 10, -15, -6, 10, -3, -18, 5, -13, 6, -33, 4, 4, 11, -20, 18, -2, 11, 20, 2, 27, 4, -14, -2, 8, -27, 0, -12, -6, -6, 4, -26, 60, -2, -19, 24, 6, 4, -30, -7, 33, 24, 16, 19, 12, 15, -29, 0, -22, 30, -30, -3, -18, -12, 8, 8, -24, -6, 1, -11, -6, 21, -11, -20, 12, -3, -12, -23, 18, 7, 0, -24, -1, 45, -30, -12, 26, 6, 15, -10, 8, -14, -16, -19, -14, -18, 6, -19, -16, 6, 18, 12, 25, -6, -40, -9, 6, 2, 27, 10, -18, 6, -11, -6, 12, -12, -44, 4, -16, -6, 21, 11, 13, -20, -6, -12, 21, -12, 6, -12, -30, 6, 37, -9, 37, -30, 10, -4, 7, 3, -29, 26, 8, 18, 12, 6, -7, -3, 12, -31, 33, 8, -18, -12, -30, -9, -9, -11, 16, 2, 12, 24, -32, 3, 6, -12, -10, -4, -7, 10, -18, 10, -4, 7, 15, 6, 14, -20, 18, -18, 12, -4, -12, -18, 26, 24, 8, -5, -30, -31, 20, 4, -15, 0, 19, 54, 8, -20, 24, 8, -36, -13, -16, -4, 24, -6, -23, 8, -4, 14, 63, 18, 60, -12, 18, 4, 2, -15, -8, -14, 21, 4, -11, -3, 38, 45, 2, -21, -20, 6, 18, 16, -12, 35, 6, -6, 9, 3, 15, -22, -24, -7, 30, -9, 13, 6, -24, -4, 34, 2, -18, -10, -16, -20, -13, -6, -12, 8, 20, 30, 18, 2, 12, -12, 11, 3, 10, -7, 5, 18, -18, 5, -9, 23, 4, -36, -10, -11, -10, 15, -36, -2, -9, 17, -36, 6, 2, -14, -6, 8, -40, -57, -2, 9, -40, -9, -30, 12, -30, 6, 54, 6, -26, 6, -26, -3, 0, 12, -12, 1, 24, -11, -10, -4, -42, -20, 14, -10, -4, 8, 6, 30, 19, 33, -9, 3, 50, -6, 0, -4, -12, -6, 16, 0, 6, -30, 2, 12, -48, -27, 8, -3, -1, 4, -4, -18, -11, 21, 36, -21, -54, 8, -50, -9, 12, -9, 7, 13, -23, 12, 12, 14, 7, -8, -24, 24, -4, 15, -4, -4, 24, -33, 41, -6, 45, 12, -10, -20, 14, -25, 24, 3, -19, -10, 2, 18, 24, 30, 38, -8, -3, 2, -30, 20, 12, -6, -32, -12, -49, 18, -9, 4, 38, 6, 11, -21, -2, 26, 28, -6, 48, -3, -6, 22, 60, 8, -48, -20, 4, 0, -66, 6, -32, 8, -22, -9, -48, 4, 12, -7, -12, -16, -6, 30, 56, -18, -12, 10, 45, 2, -8, 19, 18, 30, 12, 30, -24, 18, -4, -6, -36, -18, 28, 8, 26, 21, -6, -18, -20, 3, 15, 8, 0, -1, 6, -16, -31, 18, 9, 16, 45, -12, -12, 0, -12, 21, 69, 6, 22, 15, -42, -2, -32, -21, 24, -57, -18, 16, 21, -18, -12, 4, -6, 4, 14, -18, -20, -13, -40, 30, 18, -36, 7, -12, 8, 12, -57, 50, -20, 15, -33, -6, 2, -10, -10, 9], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": true, "level_is_prime_power": true, "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": "79.2.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], [-1], [-1], [-3], [1], [-1], [3], [-2], [3], [-2], [1], [3], [1], [3], [-1], [-6], [2], [4], [3], [1], [2], [2], [-3], [4], [-3], [5], [1], [-6], [-3], [-10], [-5], [2], [6], [3], [2], [-2], [-4], [-3], [-9], [-10], [-1], [4], [2], [6], [-2], [7], [1], [-6], [-4], [6], [-3], [8], [-5], [6], [-3], [-4], [6], [-3], [-3], [-4], [10], [2], [7], [-9], [-2], [8], [6], [-2], [-3], [15], [-6], [2], [2], [-4], [-4], [2], [3], [-1], [3], [1], [10], [-6], [-1], [18], [-4], [6], [-6], [-7], [-6], [-3], [-2], [10], [-7], [-12], [5], [-19], [6], [4], [-4]]}