# Stored data for newform 714.2.a.g, downloaded from the LMFDB on 25 April 2024.
{"label": "714.2.a.g", "space_label": "714.2.a", "level": 714, "weight": 2, "hecke_orbit": 7, "hecke_orbit_code": 27021597797778122, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 807725420999783501, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [-3, 1]], [11, [-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": 2856, "fricke_eigenval": -1, "atkin_lehner_string": "-+++", "analytic_conductor": 5.701318704319419, "hecke_ring_index": 1, "level_radical": 714, "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": [714, 1, [239, 409, 547], [1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3, 7, 17], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.015", "prec": 17}, {"__RealLiteral__": 0, "data": "1.016", "prec": 17}, {"__RealLiteral__": 0, "data": "0.091", "prec": 17}, {"__RealLiteral__": 0, "data": "1.981", "prec": 17}, {"__RealLiteral__": 0, "data": "0.363", "prec": 17}, {"__RealLiteral__": 0, "data": "4.815", "prec": 17}], "related_objects": ["EllipticCurve/Q/714/g"], "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], [17, 1]], "trace_display": [1, -1, 3, -1], "traces": [0, 1, 1, -1, 1, 3, -1, -1, 1, 1, 3, 1, -1, 1, -1, -3, 1, -1, 1, 6, 3, 1, 1, -2, -1, 4, 1, -1, -1, -2, -3, 0, 1, -1, -1, -3, 1, 5, 6, -1, 3, 4, 1, -9, 1, 3, -2, 0, -1, 1, 4, 1, 1, 11, -1, 3, -1, -6, -2, 4, -3, 6, 0, -1, 1, 3, -1, -11, -1, 2, -3, -12, 1, -5, 5, -4, 6, -1, -1, -15, 3, 1, 4, 1, 1, -3, -9, 2, 1, 9, 3, -1, -2, 0, 0, 18, -1, -9, 1, 1, 4, 8, 1, -7, 1, 3, 11, -8, -1, -2, 3, -5, -1, -9, -6, -6, -2, 1, 4, 1, -3, -10, 6, -4, 0, -3, -1, -10, 1, 9, 3, -10, -1, -6, -11, -3, -1, 0, 2, -1, -3, 0, -12, 1, 1, -6, -5, -1, 5, -9, -4, -8, 6, -1, -1, 0, -1, -10, -15, -11, 3, 2, 1, 10, 4, -3, 1, -3, 1, -12, -3, 6, -9, -18, 2, -4, 1, -4, 9, 18, 3, 12, -1, -6, -2, 15, 0, -1, 0, 1, 18, 15, -1, -8, -9, -3, 1, 20, 1, 8, 4, 11, 8, 2, 1, 12, -7, -2, 1, 6, 3, -10, 11, 12, -8, -27, -1, 0, -2, 5, 3, -1, -5, 24, -1, 4, -9, 12, -6, -17, -6, 1, -2, 3, 1, 0, 4, 15, 1, -15, -3, 22, -10, -1, 6, 3, -4, 6, 0, -1, -3, 23, -1, -2, -10, 3, 1, 15, 9, -5, 3, -2, -10, 31, -1, 33, -6, -9, -11, -18, -3, 15, -1, 1, 0, 4, 2, -30, -1, 0, -3, 26, 0, -21, -12, -18, 1, -4, 1, 1, -6, 9, -5, 0, -1, 12, 5, -1, -9, -2, -4, 9, -8, -8, 6, 18, -1, 28, -1, 7, 0, -3, -1, -30, -10, -3, -15, -18, -11, -2, 3, 8, 2, -6, 1, 4, 10, 2, 4, 0, -3, 1, 1, 5, -3, -33, 1, -22, -12, 9, -3, 0, 6, -1, -9, 6, -18, 27, 2, -13, -4, -1, 1, 5, -4, -36, 9, -1, 18, -8, 3, 17, 12, 10, -1, -15, -6, 12, -2, 4, 15, -11, 0, 32, -1, 3, 0, -2, 1, -10, 18, 10, 15, 24, -1, -3, -8, -9, -9, -6, -3, 2, 1, 10, 20, -45, 1, -4, 8, 6, 4, 18, 11, 0, 8, 3, 2, 5, 1, 38, 12, 0, -7, -4, -2, 3, 1, 1, 6, -26, 3, 6, -10, 0, 11, -4, 12, -6, -8, -1, -27, 40, -1, -28, 0, 6, -2, -12, 5, 16, 3, 1, -1, -4, -5, 27, 24, 9, -1, -1, 4, 4, -9, 8, 12, -3, -6, -25, -17, 1, -6, 2, 1, 8, -2, 0, 3, -32, 1, 11, 0, 10, 4, -9, 15, 24, 1, 11, -15, -21, -3, 5, 22, -2, -10, -27, -1, 23, 6, -10, 3, 2, -4, 2, 6, 3, 0, 12, -1, 36, -3, 3, 23, -16, -1, 24, -2, 12, -10, 16, 3, 5, 1, -6, 15, -21, 9, 0, -5, 18, 3, -16, -2, 0, -10, 4, 31, 0, -1, -19, 33, 4, -6, 4, -9, -24, -11, -18, -18, 1, -3, 25, 15, -12, -1, -6, 1, -22, 0, 6, 4, -12, 2, 15, -30, -15, -1, -2, 0, -9, -3, 1, 26, -11, 0, -27, -21, -1, -12, -26, -18, 32, 1, -15, -4, -8, 1, 14, 1, 8, -6, -1, 9, 11, -5, 3, 0, -23, -1, 0, 12, -20, 5, 18, -1, 3, -9, -8, -2, 24, -4, 26, 9, -11, -8, -30, -8, -32, 6, -2, 18, 0, -1, 8, 28, -12, -1, 43, 7, -19, 0, 2, -3, -9, -1, -29, -30, -6, -10, -5, -3, 48, -15, 10, -18, -30, -11, 1, -2, -12, 3, 7, 8, 11, 2, 27, -6, 4, 1, 4, 4, 0, 10, 42, 2, -30, 4, -5, 0, -48, -3, -22, 1, 1, 1, -18, 5, 4, -3, -24, -33, 6, 1, -48, -22, -4, -12, 27, 9, 9, -3, -12, 0, -8, 6, 0, -1, 17, -9, 11, 6, 21, -18, -1, 27, -3, 2, -4, -13, -3, -4, -7, -1, 30, 1, 0, 5, -8, -4, 5, -36, -15, 9, 0, -1, 3, 18, 15, -8, -40, 3, 7, 17, -22, 12, -8, 10, 17, -1, 1, -15, 9, -6, -14, 12, -3, -2, -11, 4, -12, 15, -6, -11, -26, 0, -27, 32, 1, -1, 8, 3, -12, 0, -23, -2, -24, 1, 36, -10, 2, 18, 43, 10, 2, 15, -3, 24, 4, -1, -34, -3, -15, -8, -32, -9, 0, -9, 5, -6, 24, -3, -12, 2, 2, 1, -30, 10, -11, 20, -31, -45, 9, 1, 6, -4, -33, 8, -14, 6, 0, 4, 9, 18, -5, 11, 6, 0, 18, 8, 30, 3, -29, 2, -15, 5, 30, 1, -54, 38, -1, 12, -2, 0, 9, -7, -4, -4, -11, -2, -31, 3, 30, 1, -1, 1, -9, 6, 0, -26, 11, 3, -25, 6, -26, -10, -36, 0, 10, 11, 21, -4, -10, 12, -46, -6, 18, -8, 32, -1, 50, -27, 4, 40, -37, -1, -54, -28, -1, 0, -15, 6, -11, -2, -9, -12, 3, 5, 23, 16, 0, 3, -22, 1, -20, -1, -12, -4, 51, -5, 10, 27, 1, 24, 0, 9, 54, -1, 2, -1, 0, 4, -11, 4, -9, -9, 36, 8, -8, 12, 8, -3, 40, -6, 1, -25, -18, -17, 10, 1, 20, -6, -28, 2, -12, 1, 20, 8, -7, -2, 28, 0, 6, 3, 3, -32, -3, 1, -32, 11, 30, 0, 49, 10, -8, 4, 3, -9, 4, 15, -5, 24, 18, 1, 6, 11, 45, -15, 2, -21, 0, -3, -31, 5, -8, 22, -24, -2, -12, -10, 6, -27, 53, -1, 1, 23, -4, 6, 8, -10, 9, 3, -2, 2, 16, -4, 60, 2, 0, 6, 18, 3, 9, 0, -1, 12, 24, -1, 4, 36, -5, -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": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "714.2.a.g", "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], [1], [1], [3], [1], [-1], [1], [-1], [-3], [1], [-1], [1], [6], [3], [1], [1], [-2], [-1], [4], [1], [-1], [-1], [-2], [-3], [0], [1], [-1], [-1], [-3], [1], [5], [6], [-1], [3], [4], [1], [-9], [1], [3], [-2], [0], [-1], [1], [4], [1], [1], [11], [-1], [3], [-1], [-6], [-2], [4], [-3], [6], [0], [-1], [1], [3], [-1], [-11], [-1], [2], [-3], [-12], [1], [-5], [5], [-4], [6], [-1], [-1], [-15], [3], [1], [4], [1], [1], [-3], [-9], [2], [1], [9], [3], [-1], [-2], [0], [0], [18], [-1], [-9], [1], [1], [4]]}