# Stored data for newform 147.2.a.a, downloaded from the LMFDB on 18 April 2024.
{"label": "147.2.a.a", "space_label": "147.2.a", "level": 147, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 33554579, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1951275430986965797, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [1, 1]], [5, [-2, 1]]], "qexp_display": "q-q^{2}-q^{3}-q^{4}+2q^{5}+q^{6}+3q^{8}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 588, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 1.1738009097128217, "hecke_ring_index": 1, "level_radical": 21, "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": [147, 1, [50, 52], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [3, 7], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.013", "prec": 17}, {"__RealLiteral__": 0, "data": "0.978", "prec": 17}, {"__RealLiteral__": 0, "data": "0.025", "prec": 17}, {"__RealLiteral__": 0, "data": "1.908", "prec": 17}, {"__RealLiteral__": 0, "data": "0.028", "prec": 17}, {"__RealLiteral__": 0, "data": "4.694", "prec": 17}], "related_objects": ["EllipticCurve/Q/147/a"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[3, 1], [7, -1]], "trace_display": [-1, -1, 2, 0], "traces": [0, 1, -1, -1, -1, 2, 1, 0, 3, 1, -2, 4, 1, 2, 0, -2, -1, 6, -1, -4, -2, 0, -4, 0, -3, -1, -2, -1, 0, -2, 2, 0, -5, -4, -6, 0, -1, 6, 4, -2, 6, -2, 0, -4, -4, 2, 0, 0, 1, 0, 1, -6, -2, 6, 1, 8, 0, 4, 2, -12, 2, 2, 0, 0, 7, 4, 4, 4, -6, 0, 0, 0, 3, 6, -6, 1, 4, 0, 2, -16, -2, 1, 2, 12, 0, 12, 4, 2, 12, 14, -2, 0, 0, 0, 0, -8, 5, -18, 0, 4, 1, -14, 6, -8, 6, 0, -6, 4, 1, -18, -8, -6, 0, -14, -4, 0, 2, 2, 12, 0, -6, 5, -2, 2, 0, -12, 0, 0, 3, 4, -4, -4, 4, 0, -4, -2, 18, -6, 0, -12, 0, 0, 0, 8, -1, -4, -6, 0, -6, 6, -1, 8, -12, 6, 0, 0, 2, 2, 16, -6, -10, 0, -1, 4, 2, -8, -12, 8, 0, -9, -12, -4, 4, 10, -2, 0, -4, 12, -14, -4, -2, 26, 0, -2, 0, 12, 0, 24, 0, 0, 8, -8, -7, 2, 18, -4, 0, 22, -4, -24, -3, -4, 14, 0, 6, -4, 8, 0, -2, -16, 0, 4, -6, 0, -4, -8, -3, 0, 18, -6, -8, 12, 6, -16, 0, -1, 14, 12, -4, 10, 0, 0, -6, -6, -2, 0, 12, 16, 0, 24, 2, -2, -5, -1, -2, 0, -2, -8, 0, -12, 12, 20, 0, 0, 0, -12, -17, -26, -4, 0, -4, -2, 4, 16, -12, 12, 0, -14, -4, -6, 2, -16, -6, 0, 6, -4, 0, 22, 12, 0, 0, -22, 0, 20, 0, 8, -8, 0, -5, 19, 4, 18, -6, -14, 0, -24, 18, -4, -6, 0, -1, 0, -8, 14, 4, 4, -6, -4, 0, 8, 0, 24, -6, -26, -2, 0, 16, -18, 6, -8, 14, -4, 0, -24, -1, -2, -4, 18, -6, 0, 8, -4, -12, 6, -8, 8, 0, -14, 9, 14, -12, 0, 4, 0, -12, 0, -10, -28, -2, 2, 0, -2, -20, -10, -12, 0, -14, 0, 4, 32, 6, -3, -26, -5, 0, 12, 2, 0, 0, -2, -12, 0, 0, -10, -24, 12, 0, -4, 0, 12, 8, 0, 8, 0, -3, 0, -2, -4, 18, 6, 4, 0, 0, 4, -22, -32, -4, 18, 24, 0, 1, -30, 4, 0, 14, 2, 0, 24, -18, 22, 4, 6, 8, 0, 0, 24, -10, 12, 16, 12, 0, 38, -4, 0, 18, -6, 0, 0, -4, -8, 8, -24, 1, 14, 0, 4, 18, 0, 6, 24, 24, 0, -12, 36, 6, 28, 16, -6, 0, -30, 1, -8, 14, -8, -12, 0, 12, 10, -10, -6, 0, 10, 0, 16, 2, 0, 6, -36, -2, 0, 0, -2, -36, -16, -16, 4, 0, 6, -24, 16, 10, 12, 2, 0, -5, -36, 1, -8, 6, -4, 0, 20, -2, -12, 8, 8, 0, 0, 12, 4, 12, -8, -20, -24, 0, -28, 0, 9, 0, 10, 12, 0, 11, 4, 26, -16, -4, 0, 0, -10, 12, -18, 2, 20, 4, 0, -16, 0, 4, -23, -12, -12, 0, -4, 14, 8, 12, 4, 6, 0, 2, -34, 16, -26, -30, -36, 0, 4, 6, 2, 4, 8, 0, 0, -22, -12, 12, -2, 0, -8, 0, -24, 22, -4, 0, -28, -20, 0, 0, 10, -8, -4, -8, 8, 0, 0, 7, -34, -19, -2, 4, 0, -18, 24, 18, 4, 14, -28, 0, 0, 24, -22, -6, 6, 4, 0, -6, 24, 0, 48, 3, 6, 0, 4, -8, 10, -14, 16, 20, 0, -4, 0, -6, -26, 4, 4, 0, -6, -8, 20, 0, 0, -24, 0, 2, -19, 26, 16, -2, 36, 0, -40, -48, -4, 18, 0, 6, 0, 8, 0, 6, 18, 4, -20, 0, 8, 24, 40, 3, -48, 2, 0, -4, -18, -18, -8, 2, 6, 0, 12, 8, -22, 4, -12, 36, 0, -6, 0, -8, 16, -8, 8, 0, 34, 14, 1, 9, 18, -14, 0, 36, -12, 0, -12, 4, -12, 0, -10, 4, 12, 0, -20, -10, 0, 28, -24, 6, -12, -2, 6, 0, 30, 2, -24, 28, 0, 10, 0, -12, 6, 0, -16, 42, 0, 0, 16, 4, -24, -32, 48, -2, 0, 3, 2, -26, 2, 5, 40, 0, 1, -12, -24, 2, 18, 0, 0, 0, 16, 2, 36, -12, 8, 0, 0, 0, 12, 10, 12, -24, 0, -12, -32, 0, -20, 4, 16, 0, -10, -12, 0, -24, -18, 0, 0, 8, 12, 0, -24, 17, -2, 0, 26, -2, -14, 4, 0, -54, 0, -6, 8, 4, 0, 0, 2, 0, 4, -4, 44, -22, -16, 32, 0, 12, 4, -18, -12, 24, 26, 0, 0, 5, 14, 30, 24, 4, 0, 0, 6, -42, 42, -2, -44, 0, 16, -24, 8, 6, 16, -22, 0, 4, 38, -6, 24, -24, 4, 0, -12, 0, -14, -24, -22, 14, 0, -12, 16, 16, 0, -12, 8, 0, -25, -38, 22, -4, -18, 0, 0, -6, -20, 6, 0, 0, 10, 0, -8, 12, 14, 8, -44, 8, 0, 24, -24, 5, 20, -14, -19, 0, -64, -4, 8, -54, -18, 0, 0, 6, 46, -24, 14, -8, 6, 0, -28, -12, 24, -36, -8, -18, 0, -28, 4, 16, 0, 6, -8, 0, 0, 30, 0, 1, 36, 8, 0, -42, 52, 8, -4, -12, -14, 0, -24, -4, 48, -10, -4, -10, 0, 6, 8, 0, 4, -10, 0, 0, -6, -16, -8, 10, -26, 0, 0, 6, -24, 36, 48, 6, -42, 0, 26, 0, -38, 2, 0, 12, 0, 16, 44, -16, 12, -4, 18, 0, 26, -6, -16, -24, 8, -16, 0, -14, -31, -12, 4, 2, 4, 0, 40, 15, 24, 36, -12, 1, 0, 8, 2, -2, -30, 4, 56, 0, -18, -20, -24, 6, 44, 12, 0, 8, 0, -8, -16, 0, 4, 0, -48, 12, 26, -4, -6, -36], "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": "21.2.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], [0], [3], [1], [-2], [4], [1], [2], [0], [-2], [-1], [6], [-1], [-4], [-2], [0], [-4], [0], [-3], [-1], [-2], [-1], [0], [-2], [2], [0], [-5], [-4], [-6], [0], [-1], [6], [4], [-2], [6], [-2], [0], [-4], [-4], [2], [0], [0], [1], [0], [1], [-6], [-2], [6], [1], [8], [0], [4], [2], [-12], [2], [2], [0], [0], [7], [4], [4], [4], [-6], [0], [0], [0], [3], [6], [-6], [1], [4], [0], [2], [-16], [-2], [1], [2], [12], [0], [12], [4], [2], [12], [14], [-2], [0], [0], [0], [0], [-8], [5], [-18], [0], [4], [1]]}