# Stored data for newform 42.2.a.a, downloaded from the LMFDB on 25 April 2024.
{"label": "42.2.a.a", "space_label": "42.2.a", "level": 42, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 33554474, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1611795495172191507, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q+q^{2}-q^{3}+q^{4}-2q^{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": 168, "fricke_eigenval": -1, "atkin_lehner_string": "-++", "analytic_conductor": 0.3353716884893776, "hecke_ring_index": 1, "level_radical": 42, "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": "0.015", "prec": 17}, "analytic_rank_proved": true, "char_values": [42, 1, [29, 31], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3, 7], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.004", "prec": 17}, {"__RealLiteral__": 0, "data": "0.976", "prec": 17}, {"__RealLiteral__": 0, "data": "0.039", "prec": 17}, {"__RealLiteral__": 0, "data": "1.927", "prec": 17}, {"__RealLiteral__": 0, "data": "0.133", "prec": 17}, {"__RealLiteral__": 0, "data": "4.761", "prec": 17}], "related_objects": ["EllipticCurve/Q/42/a"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [3, 1], [7, 1]], "trace_display": [1, -1, -2, -1], "traces": [0, 1, 1, -1, 1, -2, -1, -1, 1, 1, -2, -4, -1, 6, -1, 2, 1, 2, 1, -4, -2, 1, -4, 8, -1, -1, 6, -1, -1, -2, 2, 0, 1, 4, 2, 2, 1, -10, -4, -6, -2, -6, 1, -4, -4, -2, 8, 0, -1, 1, -1, -2, 6, 6, -1, 8, -1, 4, -2, 4, 2, 6, 0, -1, 1, -12, 4, 4, 2, -8, 2, 8, 1, 10, -10, 1, -4, 4, -6, 0, -2, 1, -6, -4, 1, -4, -4, 2, -4, -6, -2, -6, 8, 0, 0, 8, -1, -14, 1, -4, -1, -2, -2, 8, 6, -2, 6, 12, -1, -2, 8, 10, -1, -14, 4, -16, -2, 6, 4, -2, 2, 5, 6, 6, 0, 12, -1, 0, 1, 4, -12, -20, 4, 4, 4, 2, 2, 10, -8, 4, 2, 0, 8, -24, 1, 4, 10, -1, -10, 6, 1, -8, -4, 2, 4, 0, -6, -10, 0, -6, -2, -8, 1, 20, -6, -8, -4, -8, 1, 23, -4, -4, -4, 22, 2, 1, -4, -4, -6, -12, -2, -18, -6, -6, 8, 20, 0, -8, 0, 1, 8, 0, -1, 2, -14, 12, 1, -10, -4, 8, -1, -4, -2, 2, -2, 12, 8, 8, 6, 16, -2, 20, 6, -8, 12, 8, -1, 0, -2, -10, 8, 12, 10, -16, -1, -1, -14, 12, 4, -2, -16, -4, -2, -22, 6, 0, 4, 0, -2, 0, 2, 2, 5, -1, 6, -2, 6, -24, 0, 4, 12, -12, -1, -32, 0, 4, 1, -30, 4, 10, -12, -2, -20, -24, 4, -12, 4, 6, 4, 22, 2, 0, 2, 6, 10, 4, -8, -10, 4, 0, 2, 26, 0, 4, 8, -8, -24, 6, 1, -13, 4, 14, 10, 30, -1, -8, -10, 4, 6, 48, 1, 4, -8, 2, -4, -12, 2, 28, 4, -8, 0, -8, -6, 10, -10, 2, 0, -18, -6, 8, -2, -12, -8, -8, 1, -6, 20, 2, -6, 0, -8, -4, -4, -10, -8, -8, 1, 18, 23, 14, -4, 0, -4, -1, -4, 16, 22, 12, 2, 22, 1, -6, -4, -30, -4, -16, -6, 2, -12, -8, -2, -3, -18, -5, -6, -20, -6, 32, 8, -6, 20, -6, 0, 22, -8, -12, 0, -12, 1, -20, 8, 0, 0, -16, -1, -8, 2, -4, -14, -26, 12, 16, 1, 20, -10, 0, -4, 6, 8, -4, -1, 18, -4, 0, -2, -2, 2, 40, -2, -22, 12, -10, 8, -4, 8, 8, 6, -4, 16, -36, -2, 6, 20, 0, 6, -2, -8, -6, 12, 24, 8, 0, -1, 2, 0, -4, -2, -32, -10, -24, 8, 1, 12, -4, 10, 12, -16, -6, -1, 34, -1, 24, -14, 8, 12, 12, 4, 10, -2, -2, -16, 22, -4, -32, -2, 0, -22, 28, 6, -4, 0, 10, 4, 16, 0, 4, -2, 6, 0, -16, 2, -60, 2, 8, 5, 28, -1, 8, 6, -20, -2, 12, 6, -4, -24, 8, 0, -8, 4, -44, 12, 8, -12, 24, -1, 4, -32, -23, 0, 6, 4, -10, 1, 4, -30, -16, 4, 0, 10, -22, -12, -6, -2, 20, -20, -1, -24, 0, 4, 41, -12, 4, 4, -36, 6, -24, 4, 12, 22, -4, 2, 30, 0, 18, 2, 4, 6, -12, 10, 6, 4, 8, -8, 0, -10, -20, 4, -2, 0, -24, 2, 8, 26, 44, 0, 28, 4, -1, 8, -6, -8, 12, -24, 0, 6, -8, 1, 34, -13, -2, 4, 4, 14, -24, 10, -12, 30, -28, -1, 0, -8, 10, -10, 18, 4, 4, 6, -8, 48, 24, 1, 26, 4, 4, -8, -10, 2, 48, -4, -2, -12, 0, 2, -42, 28, -12, 4, -22, -8, -44, 0, -8, -8, 6, -6, -19, 10, -16, -10, -20, 2, 8, 0, -20, -18, 0, -6, 6, 8, 8, -2, 2, -12, -4, -8, -8, -8, 24, 1, -16, -6, 0, 20, -18, 2, 40, -6, 10, 0, -28, -8, -2, -4, -12, -4, -8, -10, -16, -8, 16, -8, -24, 1, 2, 18, 1, 23, -18, 14, 14, -4, -12, 0, 12, -4, -20, -1, 2, -4, 36, 16, -4, 22, 4, 12, -8, 2, -12, 22, 22, 1, -2, -6, 40, -4, 0, -30, 2, -4, -10, -16, 0, -6, 0, 2, 48, -12, 0, -8, 0, -2, -8, -3, -2, -18, 2, -5, -8, -6, 1, -20, -8, -6, 6, 32, 2, 8, -16, -6, -12, 20, 24, -6, 24, 0, -12, 22, -4, -8, -12, -12, 48, 0, 12, -12, 16, 1, 6, -20, 32, 8, -22, 0, 2, 0, -4, -16, 24, -1, -14, -8, 30, 2, -2, -4, 0, -14, -10, -26, 24, 12, -32, 16, 2, 1, 20, 20, -36, -10, 24, 0, 14, -4, 36, 6, 12, 8, 6, -4, 0, -1, -6, 18, -40, -4, 16, 0, -22, -2, 10, -2, -44, 2, 0, 40, -40, -2, 16, -22, -6, 12, 38, -10, -56, 8, -4, -4, -36, 8, -26, 8, 10, 6, 2, -4, 16, 16, 0, -36, 56, -2, -25, 6, -26, 20, -46, 0, -5, 6, -4, -2, -80, -8, 14, -6, 8, 12, 42, 24, 20, 8, -6, 0, -32, -1, -44, 2, 13, 0, 0, -4, 24, -2, -14, -32, -12, -10, -2, -24, -30, 8, 18, 1, 20, 12, 8, -4, -24, 10, 0, 12, -4, -16, 0, -6, 24, -1, -48, 34, 0, -1, 12, 24, -4, -14, 36, 8, 12, 12, -2, 12, 0, 4, 16, 10, 12, -2, 20, -2, 40, -16, -28, 22, 48, -4, 10, -32, 8, -2, 18, 0, -4, -22, 8, 28, 16, 6, -22, -4, -10, 0, -26, 10, -48, 4, -2, 16, 4, 0, 60, 4, 18, -2, 26, 6, 0, 0, -8, -16, -10, 2, -31, -60, 12, 2, -4, 8, 8, 5, 8, 28, -12, -1, -4, 8, 6, 6, 18, -20, 24, -2, -2, 12, -24, 6, 20, -4, 0, -24, -32, 8, -16, 0, 4, -8, -16, 4, 14, -44, 10, 12], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "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": "42.2.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], [-2], [-1], [-1], [1], [1], [-2], [-4], [-1], [6], [-1], [2], [1], [2], [1], [-4], [-2], [1], [-4], [8], [-1], [-1], [6], [-1], [-1], [-2], [2], [0], [1], [4], [2], [2], [1], [-10], [-4], [-6], [-2], [-6], [1], [-4], [-4], [-2], [8], [0], [-1], [1], [-1], [-2], [6], [6], [-1], [8], [-1], [4], [-2], [4], [2], [6], [0], [-1], [1], [-12], [4], [4], [2], [-8], [2], [8], [1], [10], [-10], [1], [-4], [4], [-6], [0], [-2], [1], [-6], [-4], [1], [-4], [-4], [2], [-4], [-6], [-2], [-6], [8], [0], [0], [8], [-1], [-14], [1], [-4], [-1]]}