# Stored data for newform 350.2.a.e, downloaded from the LMFDB on 24 April 2024.
{"label": "350.2.a.e", "space_label": "350.2.a", "level": 350, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014398543036766, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 872865726942017119, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [-1, 1]], [13, [-2, 1]]], "qexp_display": "q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 1400, "fricke_eigenval": -1, "atkin_lehner_string": "---", "analytic_conductor": 2.7947640707448134, "hecke_ring_index": 1, "level_radical": 70, "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": [350, 1, [127, 101], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 5, 7], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.021", "prec": 17}, {"__RealLiteral__": 0, "data": "0.956", "prec": 17}, {"__RealLiteral__": 0, "data": "0.087", "prec": 17}, {"__RealLiteral__": 0, "data": "1.909", "prec": 17}, {"__RealLiteral__": 0, "data": "0.298", "prec": 17}, {"__RealLiteral__": 0, "data": "4.796", "prec": 17}], "related_objects": ["EllipticCurve/Q/350/e"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [5, -1], [7, -1]], "trace_display": [1, 1, 0, 1], "traces": [0, 1, 1, 1, 1, 0, 1, 1, 1, -2, 0, 3, 1, 2, 1, 0, 1, 3, -2, -7, 0, 1, 3, 0, 1, 0, 2, -5, 1, -6, 0, -4, 1, 3, 3, 0, -2, 8, -7, 2, 0, -9, 1, 8, 3, 0, 0, -6, 1, 1, 0, 3, 2, -12, -5, 0, 1, -7, -6, 12, 0, -10, -4, -2, 1, 0, 3, -7, 3, 0, 0, 6, -2, 5, 8, 0, -7, 3, 2, 14, 0, 1, -9, -9, 1, 0, 8, -6, 3, -15, 0, 2, 0, -4, -6, 0, 1, -10, 1, -6, 0, 0, 3, 20, 2, 0, -12, 3, -5, 14, 0, 8, 1, -9, -7, 0, -6, -4, 12, 3, 0, -2, -10, -9, -4, 0, -2, 2, 1, 8, 0, 0, 3, -7, -7, 0, 3, 21, 0, -7, 0, -6, 6, 6, -2, 0, 5, 1, 8, 12, 0, 8, -7, -6, 3, 0, 2, 20, 14, -12, 0, 0, 1, 5, -9, 0, -9, 12, 1, -9, 0, 14, 8, -6, -6, 0, 3, 12, -15, 3, 0, 2, 2, -10, 0, 0, -4, 9, -6, -5, 0, -6, 1, 5, -10, 0, 1, -6, -6, 14, 0, -7, 0, -6, 3, 0, 20, 0, 2, -21, 0, 17, -12, 6, 3, 0, -5, -4, 14, 5, 0, 6, 8, 14, 1, 0, -9, 12, -7, 26, 0, 3, -6, 6, -4, 0, 12, 14, 3, -12, 0, -25, -2, 16, -10, 0, -9, -14, -4, -9, 0, 15, -2, 0, 2, 0, 1, -30, 8, 8, 0, 12, 0, 6, 3, 0, -7, -15, -7, -6, 0, 2, 3, 2, 21, 0, 0, 2, -7, 8, 0, -18, -6, -1, 6, 0, 6, -9, -2, -8, 0, -10, 5, -6, 1, 0, 8, -15, 12, 0, 0, 8, 8, 0, -7, 0, -6, -7, 3, 20, 0, -18, 2, -10, 20, 0, 14, -12, -12, -18, 0, 3, 0, -21, 1, 0, 5, 14, -9, -6, 0, -25, -9, -16, 12, 0, 1, -13, -9, -9, 0, -12, 14, 1, 8, 0, -6, -21, -6, 8, 0, -10, 3, 30, 12, 0, -15, 3, 3, -6, 0, 30, 2, -2, 2, 0, -10, 8, 0, 18, 0, -12, -4, -4, 9, 0, -6, -12, -5, 17, 0, 2, -6, -30, 1, 0, 5, -16, -10, -24, 0, 0, 1, 0, -6, 0, -6, 2, 14, -7, 0, -27, -7, -8, 0, 0, -6, 24, 3, -25, 0, 21, 20, 12, 0, 0, 2, -7, -21, -3, 0, 20, 17, 12, -12, 0, 6, -10, 3, 6, 0, -36, -5, 11, -4, 0, 14, 0, 5, -4, 0, -2, 6, 21, 8, 0, 14, 12, 1, -15, 0, -27, -9, 8, 12, 0, -7, 17, 26, -15, 0, 18, 3, 8, -6, 0, 6, 36, -4, -7, 0, 20, 12, 24, 14, 0, 3, 24, -12, 18, 0, 16, -25, 0, -2, 0, 16, -34, -10, 5, 0, -12, -9, -18, -14, 0, -4, 6, -9, -28, 0, 12, 15, -6, -2, 0, 0, -9, 2, 42, 0, 5, 1, 35, -30, 0, 8, -18, 8, -6, 0, 39, 12, -7, 0, 0, 6, -12, 3, -23, 0, -24, -7, -18, -15, 0, -7, 3, -6, 3, 0, 38, 2, 2, 3, 0, 2, 35, 21, 20, 0, 42, 0, 14, 2, 0, -7, 36, 8, 16, 0, 9, -18, 12, -6, 0, -1, 1, 6, -27, 0, -4, 6, -6, -9, 0, -2, -7, -8, 5, 0, -9, -10, -36, 5, 0, -6, 39, 1, 28, 0, -6, 8, -27, -15, 0, 12, 14, 0, 24, 0, -7, 8, 14, 8, 0, 0, 44, -7, -6, 0, -12, -6, 2, -7, 0, 3, -18, 20, -28, 0, 0, -18, -15, 2, 0, -10, -21, 20, 24, 0, 32, 14, 17, -12, 0, -12, 2, -18, -12, 0, -30, 3, -40, 0, 0, -21, -24, 1, 36, 0, -4, 5, 36, 14, 0, -9, -10, -6, 9, 0, -10, -25, 6, -9, 0, -16, 0, 12, 14, 0, -30, 1, 2, -13, 0, -9, 0, -9, -10, 0, 12, -12, 3, 14, 0, 1, 26, 8, -24, 0, -19, -6, -6, -21, 0, -6, -27, 8, 6, 0, 0, -10, -56, 3, 0, 30, 0, 12, -28, 0, -28, -15, 0, 3, 0, 3, -12, -6, 0, 0, 20, 30, -25, 2, 0, -2, -34, 2, 13, 0, 24, -10, -40, 8, 0, 0, -21, 18, 20, 0, -14, -12, -24, -4, 0, -4, 18, 9, 3, 0, -46, -6, 15, -12, 0, -5, -34, 17, 0, 0, -9, 2, 14, -6, 0, -30, 24, 1, 23, 0, -30, 5, -12, -16, 0, -10, 8, -24, 63, 0, 18, 0, 30, 1, 0, 0, -4, -6, 6, 0, -9, -6, -20, 2, 0, 14, -30, -7, -18, 0, 30, -27, 15, -7, 0, -8, -6, 0, 6, 0, 44, -6, 2, 24, 0, 3, -56, -25, -4, 0, 24, 21, 26, 20, 0, 12, 9, 0, -4, 0, 2, 2, 3, -7, 0, -21, 20, -3, -6, 0, 7, 20, -18, 17, 0, 12, -2, -12, -1, 0, 0, 6, -10, -10, 0, 3, 15, 6, -31, 0, -9, -36, -12, -5, 0, 11, -8, -4, 42, 0, -14, 14, 20, 0, 0, 5, 32, -4, -6, 0, -6, -2, 47, 6, 0, 21, 6, 8, 2, 0, 3, 14, 42, 12, 0, 1, 0, -15, 24, 0, -36, -27, 8, -9, 0, 8, -4, 12, 0, 0, 36, -7, -27, 17, 0, 26, 0, -15, -34, 0, -7, 18, 12, 3, 0, 8, -40, -6, -18, 0, -7, 6, -18, 36, 0, -4, 29, -7, -10, 0, 24, 20, 0, 12, 0, 24, 12, 14, 10, 0, -12, 3, 57, 24, 0, -12, -18, 18, 21, 0, -15, 16, -6, -25, 0, 0, -34, -2, -21, 0, 9, 16, -7, -34, 0, -10, -3, 5, -45, 0, -28, -12, 12, -9, 0, -18, -6, -14, 0, 0, 20, -4, -25, 6, 0, -9, 62, -28, -40, 0], "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": "350.2.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], [0], [1], [1], [1], [-2], [0], [3], [1], [2], [1], [0], [1], [3], [-2], [-7], [0], [1], [3], [0], [1], [0], [2], [-5], [1], [-6], [0], [-4], [1], [3], [3], [0], [-2], [8], [-7], [2], [0], [-9], [1], [8], [3], [0], [0], [-6], [1], [1], [0], [3], [2], [-12], [-5], [0], [1], [-7], [-6], [12], [0], [-10], [-4], [-2], [1], [0], [3], [-7], [3], [0], [0], [6], [-2], [5], [8], [0], [-7], [3], [2], [14], [0], [1], [-9], [-9], [1], [0], [8], [-6], [3], [-15], [0], [2], [0], [-4], [-6], [0], [1], [-10], [1], [-6], [0]]}