# Stored data for newform 357.2.a.b, downloaded from the LMFDB on 25 September 2025.
{"Nk2": 1428, "analytic_conductor": 2.8506593521597097, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, 1], [7, 1], [17, -1]], "atkin_lehner_string": "++-", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [357, 1, [239, 52, 190], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 1, "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[2, [0, 1]], [11, [-3, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503599660925285, "hecke_ring_generator_nbound": 1, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": true, "is_maximal": true, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": true, "label": "357.2.a.b", "level": 357, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": true, "level_primes": [3, 7, 17], "level_radical": 357, "minimal_twist": "357.2.a.b", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q-q^{3}-2q^{4}+q^{5}-q^{7}+q^{9}+3q^{11}+\\cdots", "related_objects": ["EllipticCurve/Q/357/b"], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "357.2.a", "trace_display": [0, -1, 1, -1], "trace_hash": 1784584962104518821, "trace_moments": [{"__RealLiteral__": 0, "data": "0.028", "prec": 17}, {"__RealLiteral__": 0, "data": "0.991", "prec": 17}, {"__RealLiteral__": 0, "data": "0.069", "prec": 17}, {"__RealLiteral__": 0, "data": "1.953", "prec": 17}, {"__RealLiteral__": 0, "data": "0.203", "prec": 17}, {"__RealLiteral__": 0, "data": "4.829", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.014", "prec": 17}, "traces": [0, 1, 0, -1, -2, 1, 0, -1, 0, 1, 0, 3, 2, 3, 0, -1, 4, 1, 0, 3, -2, 1, 0, 7, 0, -4, 0, -1, 2, -6, 0, 10, 0, -3, 0, -1, -2, 4, 0, -3, 0, -9, 0, 9, -6, 1, 0, 6, -4, 1, 0, -1, -6, -10, 0, 3, 0, -3, 0, -2, 2, 0, 0, -1, -8, 3, 0, -12, -2, -7, 0, -12, 0, 6, 0, 4, -6, -3, 0, 10, 4, 1, 0, 10, -2, 1, 0, 6, 0, -4, 0, -3, -14, -10, 0, 3, 0, 8, 0, 3, 8, 12, 0, 1, 0, 1, 0, -17, 2, 0, 0, -4, -4, 9, 0, 7, 12, 3, 0, -1, 0, -2, 0, 9, -20, -9, 0, -13, 0, -9, 0, 17, 6, -3, 0, -1, 0, 2, 0, 2, 2, -6, 0, 9, 4, -6, 0, -1, -8, -6, 0, -16, 0, 1, 0, 10, 6, 15, 0, 10, 0, -7, 0, 14, 18, -3, 0, 7, 0, -4, 0, 3, -18, -11, 0, 4, 12, 2, 0, -14, -2, 14, 0, 0, 0, 4, 0, 3, -12, 1, 0, -2, 8, 18, 0, -3, -2, -3, 0, -12, 0, 12, 0, 6, 2, -9, 0, 7, 12, 9, 0, 26, 20, 12, 0, 9, 0, -10, 0, -6, -6, 3, 0, -5, 0, -4, 0, 17, 6, -26, 0, 3, 0, 3, 0, 6, 4, -10, 0, 0, -4, -28, 0, -1, 0, 1, 0, 9, 0, -10, 0, -24, 2, 21, 0, -1, 16, -12, 0, -4, -6, -6, 0, -16, 0, -10, 0, 4, 24, -21, 0, -9, 4, 3, 0, -12, 14, -18, 0, 10, 0, -16, 0, -22, 24, -3, 0, 9, 0, 1, 0, -8, -12, 4, 0, -2, 0, -3, 0, 21, -8, -9, 0, -12, 12, 0, 0, -20, 6, -1, 0, 0, 0, 20, 0, -1, -20, 30, 0, -18, -8, 17, 0, 3, -2, -12, 0, 0, 0, -6, 0, 3, -20, 4, 0, -12, 4, 2, 0, -9, -2, 30, 0, -1, 0, -7, 0, -12, -12, 17, 0, -3, 0, -18, 0, -12, 8, 1, 0, -32, 0, -10, 0, 2, 6, 6, 0, -4, 28, -9, 0, 10, 20, 10, 0, 9, 0, -18, 0, 4, -6, 13, 0, -16, 0, -3, 0, 9, -16, -24, 0, 7, 0, -17, 0, 10, -6, 0, 0, 3, -16, -25, 0, 30, -24, 1, 0, 12, 0, -23, 0, -2, -2, 2, 0, 10, 0, -2, 0, 12, -2, -1, 0, 6, 0, -4, 0, 0, 34, -9, 0, 8, -4, 11, 0, 6, 0, 21, 0, 16, 0, 1, 0, -14, 8, -4, 0, 6, 8, -26, 0, -27, -18, 16, 0, -3, 0, 13, 0, -1, -14, 6, 0, 8, -24, -10, 0, 38, -6, 12, 0, -15, 0, 27, 0, -12, 2, -10, 0, -41, 0, 12, 0, 7, 4, 8, 0, 2, 0, -14, 0, 34, -18, -6, 0, 3, 40, 12, 0, 26, 18, -7, 0, 21, 0, 12, 0, 4, 26, 20, 0, -6, 0, -3, 0, 1, 18, 18, 0, 11, 0, -17, 0, 20, -34, -4, 0, 10, -12, 26, 0, -2, 6, -27, 0, -17, 0, 14, 0, 3, 2, -4, 0, -14, 0, 0, 0, 16, -4, 0, 0, -18, 0, -10, 0, -4, -4, 18, 0, 27, -4, -3, 0, 18, 12, 9, 0, -1, 0, -24, 0, 32, -18, 2, 0, -28, -8, 21, 0, -18, 12, -10, 0, -30, 0, 3, 0, 40, 2, 30, 0, 3, 16, -46, 0, -1, 12, 12, 0, 30, 0, 14, 0, -12, 32, -2, 0, -30, 0, -6, 0, 18, -2, 11, 0, 9, 0, 22, 0, 10, -20, -7, 0, 4, -12, 11, 0, -9, -30, 4, 0, -13, 0, -26, 0, -13, -20, 3, 0, -12, 0, -15, 0, -24, 14, -9, 0, -18, 0, -6, 0, 10, -28, -27, 0, 17, -36, 6, 0, 6, 6, -11, 0, -3, 0, -3, 0, -42, -14, 5, 0, 0, 0, 30, 0, 4, 8, 39, 0, -8, 0, -17, 0, -27, -6, 2, 0, 26, 36, -30, 0, 0, 22, -3, 0, 2, 0, -9, 0, -3, -8, -16, 0, 12, -24, -6, 0, -12, -4, -22, 0, 10, 0, 70, 0, 9, 28, 0, 0, 25, 4, -1, 0, 28, -28, 24, 0, -32, 0, 1, 0, 9, 0, -14, 0, -1, 0, -36, 0, -25, -8, -9, 0, -16, 0, -6, 0, 10, -6, 17, 0, 10, 24, 24, 0, -16, -2, 21, 0, -21, 0, 14, 0, 0, 4, 1, 0, -6, -16, 29, 0, 12, -36, 4, 0, -40, 0, 4, 0, -27, 6, -36, 0, 6, 4, 15, 0, 44, 6, 16, 0, -9, 0, 0, 0, 10, 24, -48, 0, 6, 0, -4, 0, 18, -24, -7, 0, 21, 0, 27, 0, -54, -12, 9, 0, 14, -4, 27, 0, -3, 18, -43, 0, -52, 0, 12, 0, 13, -14, -26, 0, 18, -24, 1, 0, 7, -18, -10, 0, -35, 0, 7, 0, 16, -52, -4, 0, 2, -40, 22, 0, 28, -24, 14, 0, 3, 0, 18, 0, 4, -18, -9, 0, 56, 0, -11, 0, -1, 20, 30, 0, -36, 0, 8, 0, 9, 12, -22, 0, -4, 12, 6, 0, 11, -6, 2, 0, 13, 0, 13, 0, 3, 10, 18, 0, -14, 0, -21, 0, -60, 8, -10, 0, 9, 0, 14, 0, -30, -34, 12, 0, 19, -12, 30, 0, 0, 52, -17, 0, -37, 0, 20, 0, -36, -6, -16, 0, 1, 0, -51, 0, 3, -6, 0, 0, 3, 0, -22, 0, -20, -12, -18, 0, -63, -8, 1, 0, 52, 20, 18, 0, -30, 0, 0, 0, -2, 0, 18, 0, -2, 8, 69, 0, -17, 56, 18, 0, -23, 0, -3, 0, 54, 2, -2, 0, 12, 0, -18, 0, -12, -2, 0, 0, 21, 0, -3, 0, 6, -18, 63, 0, 52, 0, -3, 0, -12, 20, -18, 0, -4, 0], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0], 1, 0, -1, -2, 1, 0, -1, 0, 1, 0, 3, 2, 3, 0, -1, 4, 1, 0, 3, -2, 1, 0, 7, 0, -4, 0, -1, 2, -6, 0, 10, 0, -3, 0, -1, -2, 4, 0, -3, 0, -9, 0, 9, -6, 1, 0, 6, -4, 1, 0, -1, -6, -10, 0, 3, 0, -3, 0, -2, 2, 0, 0, -1, -8, 3, 0, -12, -2, -7, 0, -12, 0, 6, 0, 4, -6, -3, 0, 10, 4, 1, 0, 10, -2, 1, 0, 6, 0, -4, 0, -3, -14, -10, 0, 3, 0, 8, 0, 3, 8, 12, 0, 1, 0, 1, 0, -17, 2, 0, 0, -4, -4, 9, 0, 7, 12, 3, 0, -1, 0, -2, 0, 9, -20, -9, 0, -13, 0, -9, 0, 17, 6, -3, 0, -1, 0, 2, 0, 2, 2, -6, 0, 9, 4, -6, 0, -1, -8, -6, 0, -16, 0, 1, 0, 10, 6, 15, 0, 10, 0, -7, 0, 14, 18, -3, 0, 7, 0, -4, 0, 3, -18, -11, 0, 4, 12, 2, 0, -14, -2, 14, 0, 0, 0, 4, 0, 3, -12, 1, 0, -2, 8, 18, 0, -3, -2, -3, 0, -12, 0, 12, 0, 6, 2, -9, 0, 7, 12, 9, 0, 26, 20, 12, 0, 9, 0, -10, 0, -6, -6, 3, 0, -5, 0, -4, 0, 17, 6, -26, 0, 3, 0, 3, 0, 6, 4, -10, 0, 0, -4, -28, 0, -1, 0, 1, 0, 9, 0, -10, 0, -24, 2, 21, 0, -1, 16, -12, 0, -4, -6, -6, 0, -16, 0, -10, 0, 4, 24, -21, 0, -9, 4, 3, 0, -12, 14, -18, 0, 10, 0, -16, 0, -22, 24, -3, 0, 9, 0, 1, 0, -8, -12, 4, 0, -2, 0, -3, 0, 21, -8, -9, 0, -12, 12, 0, 0, -20, 6, -1, 0, 0, 0, 20, 0, -1, -20, 30, 0, -18, -8, 17, 0, 3, -2, -12, 0, 0, 0, -6, 0, 3, -20, 4, 0, -12, 4, 2, 0, -9, -2, 30, 0, -1, 0, -7, 0, -12, -12, 17, 0, -3, 0, -18, 0, -12, 8, 1, 0, -32, 0, -10, 0, 2, 6, 6, 0, -4, 28, -9, 0, 10, 20, 10, 0, 9, 0, -18, 0, 4, -6, 13, 0, -16, 0, -3, 0, 9, -16, -24, 0, 7, 0, -17, 0, 10, -6, 0, 0, 3, -16, -25, 0, 30, -24, 1, 0, 12, 0, -23, 0, -2, -2, 2, 0, 10, 0, -2, 0, 12, -2, -1, 0, 6, 0, -4, 0, 0, 34, -9, 0, 8, -4, 11, 0, 6, 0, 21, 0, 16, 0, 1, 0, -14, 8, -4, 0, 6, 8, -26, 0, -27, -18, 16, 0, -3, 0, 13, 0, -1, -14, 6, 0, 8, -24, -10, 0, 38, -6, 12, 0, -15, 0, 27, 0, -12, 2, -10, 0, -41, 0, 12, 0, 7, 4, 8, 0, 2, 0, -14, 0, 34, -18, -6, 0, 3, 40, 12, 0, 26, 18, -7, 0, 21, 0, 12, 0, 4, 26, 20, 0, -6, 0, -3, 0, 1, 18, 18, 0, 11, 0, -17, 0, 20, -34, -4, 0, 10, -12, 26, 0, -2, 6, -27, 0, -17, 0, 14, 0, 3, 2, -4, 0, -14, 0, 0, 0, 16, -4, 0, 0, -18, 0, -10, 0, -4, -4, 18, 0, 27, -4, -3, 0, 18, 12, 9, 0, -1, 0, -24, 0, 32, -18, 2, 0, -28, -8, 21, 0, -18, 12, -10, 0, -30, 0, 3, 0, 40, 2, 30, 0, 3, 16, -46, 0, -1, 12, 12, 0, 30, 0, 14, 0, -12, 32, -2, 0, -30, 0, -6, 0, 18, -2, 11, 0, 9, 0, 22, 0, 10, -20, -7, 0, 4, -12, 11, 0, -9, -30, 4, 0, -13, 0, -26, 0, -13, -20, 3, 0, -12, 0, -15, 0, -24, 14, -9, 0, -18, 0, -6, 0, 10, -28, -27, 0, 17, -36, 6, 0, 6, 6, -11, 0, -3, 0, -3, 0, -42, -14, 5, 0, 0, 0, 30, 0, 4, 8, 39, 0, -8, 0, -17, 0, -27, -6, 2, 0, 26, 36, -30, 0, 0, 22, -3, 0, 2, 0, -9, 0, -3, -8, -16, 0, 12, -24, -6, 0, -12, -4, -22, 0, 10, 0, 70, 0, 9, 28, 0, 0, 25, 4, -1, 0, 28, -28, 24, 0, -32, 0, 1, 0, 9, 0, -14, 0, -1, 0, -36, 0, -25, -8, -9, 0, -16, 0, -6, 0, 10, -6, 17, 0, 10, 24, 24, 0, -16, -2, 21, 0, -21, 0, 14, 0, 0, 4, 1, 0, -6, -16, 29, 0, 12, -36, 4, 0, -40, 0, 4, 0, -27, 6, -36, 0, 6, 4, 15, 0, 44, 6, 16, 0, -9, 0, 0, 0, 10, 24, -48, 0, 6, 0, -4, 0, 18, -24, -7, 0, 21, 0, 27, 0, -54, -12, 9, 0, 14, -4, 27, 0, -3, 18, -43, 0, -52, 0, 12, 0, 13, -14, -26, 0, 18, -24, 1, 0, 7, -18, -10, 0, -35, 0, 7, 0, 16, -52, -4, 0, 2, -40, 22, 0, 28, -24, 14, 0, 3, 0, 18, 0, 4, -18, -9, 0, 56, 0, -11, 0, -1, 20, 30, 0, -36, 0, 8, 0, 9, 12, -22, 0, -4, 12, 6, 0, 11, -6, 2, 0, 13, 0, 13, 0, 3, 10, 18, 0, -14, 0, -21, 0, -60, 8, -10, 0, 9, 0, 14, 0, -30, -34, 12, 0, 19, -12, 30, 0, 0, 52, -17, 0, -37, 0, 20, 0, -36, -6, -16, 0, 1, 0, -51, 0, 3, -6, 0, 0, 3, 0, -22, 0, -20, -12, -18, 0, -63, -8, 1, 0, 52, 20, 18, 0, -30, 0, 0, 0, -2, 0, 18, 0, -2, 8, 69, 0, -17, 56, 18, 0, -23, 0, -3, 0, 54, 2, -2, 0, 12, 0, -18, 0, -12, -2, 0, 0, 21, 0, -3, 0, 6, -18, 63, 0, 52, 0, -3, 0, -12, 20, -18, 0, -4, 0]}