# Stored data for newform 430.2.a.e, downloaded from the LMFDB on 13 May 2024.
{"label": "430.2.a.e", "space_label": "430.2.a", "level": 430, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014398543036846, "dim": 2, "is_polredabs": true, "nf_label": "2.2.12.1", "trace_hash": 2198751904338326402, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [-2, -2, 1]], [7, [-11, -2, 1]]], "qexp_display": "q-q^{2}+(1+\\beta )q^{3}+q^{4}+q^{5}+(-1+\\cdots)q^{6}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 1720, "fricke_eigenval": -1, "atkin_lehner_string": "+-+", "analytic_conductor": 3.4335672869150566, "hecke_ring_index": 1, "level_radical": 430, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 12, "field_poly_is_real_cyclotomic": true, "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": "0.014", "prec": 17}, "analytic_rank_proved": true, "char_values": [430, 1, [87, 261], [1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [2, 5, 43], "conrey_indexes": [1], "field_disc": 12, "field_disc_factorization": [[2, 2], [3, 1]], "field_poly": [-3, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.013", "prec": 17}, {"__RealLiteral__": 0, "data": "2.002", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.673", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "65.247", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [5, -1], [43, 1]], "trace_display": [-2, 2, 2, 2], "traces": [0, 2, -2, 2, 2, 2, -2, 2, -2, 2, -2, 2, 2, 2, -2, 2, 2, 10, -2, -6, 2, -10, -2, 6, -2, 2, -2, 8, 2, 16, -2, -16, -2, -4, -10, 2, 2, -2, 6, 14, -2, -2, 10, -2, 2, 2, -6, 14, 2, 12, -2, 16, 2, -4, -8, 2, -2, 6, -16, -20, 2, 0, 16, -22, 2, 2, 4, 0, 10, -12, -2, -10, -2, 8, 2, 2, -6, 14, -14, -4, 2, 2, 2, 0, -10, 10, 2, 10, -2, -6, -2, -22, 6, -22, -14, -6, -2, -6, -12, -10, 2, -10, -16, -16, -2, -10, 4, 4, 8, -28, -2, -20, 2, 24, -6, 6, 16, 26, 20, -2, -2, -14, 0, -14, -16, 2, 22, -4, -2, -2, -2, 0, -4, -30, 0, 8, -10, -32, 12, -2, 2, 8, 10, -10, 2, 16, -8, -12, -2, 32, -2, -16, 6, 22, -14, -16, 14, 22, 4, -16, -2, 42, -2, 8, -2, -4, 0, 6, 10, 0, -10, 18, -2, -6, -10, 2, 2, -8, 6, -6, 2, 26, 22, -6, -6, -2, 22, 4, 14, 8, 6, 14, 2, -20, 6, 14, 12, 2, 10, 14, -2, 18, 10, 28, 16, -2, 16, -30, 2, -18, 10, -32, -4, -4, -4, -2, -8, -4, 28, 26, 2, 22, 20, -4, -2, 2, -24, 4, 6, 8, -6, -4, -16, 8, -26, 14, -20, -46, 2, 4, 2, 30, 14, -34, 0, 12, 14, 18, 16, 12, -2, 4, -22, 24, 4, 16, 2, -16, 2, 34, 2, 4, 0, -6, 4, -4, 30, 36, 0, 12, -8, -36, 10, -22, 32, 2, -12, -20, 2, -28, -2, 18, -8, 20, -10, 6, 10, 22, -2, 22, -16, -60, 8, -12, 12, -20, 2, 8, -32, -30, 2, -2, 16, -40, -6, 0, -22, -12, 14, 20, 16, -40, -14, 20, -22, -22, -4, -38, 16, 22, 2, 46, -42, -18, 2, 2, -8, -40, 2, 26, 4, -8, 0, -38, -6, 0, -10, 12, 0, 18, 10, -10, -18, 46, 2, -12, 6, 30, 10, 0, -2, 8, -2, 10, 8, -10, -6, -56, 6, -48, -2, 4, -26, -26, -22, 8, 6, -16, 6, -26, 2, 20, -22, 10, -4, 2, -14, 4, -8, 8, -6, -16, -14, 18, -2, 14, 20, -2, -6, -32, -14, 12, -12, 60, -2, -4, -10, -8, -14, 18, 2, -6, -18, -28, -10, 2, -28, 16, -16, 62, 2, -14, -16, -44, 30, 0, -2, 4, 18, 14, -10, -8, 32, 2, 4, 10, 4, 12, 4, -4, 2, 48, 8, 4, 4, 10, -28, -54, -26, 32, -2, -36, -22, -28, -20, -6, 4, 50, 2, 26, -2, 10, 24, -52, -4, -22, -6, 48, -8, 40, 6, -6, 4, 54, 16, -22, -8, -14, 26, -36, -14, 52, 20, -2, 46, -6, -2, -28, -4, 36, -2, -38, -30, -12, -14, -6, 34, -18, 0, 32, -12, 48, -14, 74, -18, -10, -16, -22, -12, -2, 2, 36, -4, 48, 22, -10, -24, 24, -4, 52, -16, -28, -2, -24, 16, -16, -2, 20, -34, 30, -2, 22, -4, -10, 0, -10, 6, -86, -4, 26, 4, 4, -30, -26, -36, 4, 0, -54, -12, 36, 8, -24, 36, 32, -10, -28, 22, 16, -32, -12, -2, -60, 12, 80, 20, -20, -2, -10, 28, -2, 2, -20, -18, -24, 8, 24, -20, 26, 10, -26, -6, -22, -10, -4, -22, 6, 2, 4, -22, 16, 16, -24, 60, 8, -8, 26, 12, 42, -12, 36, 20, -22, -2, 36, -8, -2, 32, -52, 30, -36, -2, 64, 2, 36, -16, -14, 40, 8, 6, -74, 0, 2, 22, 34, 12, -14, -14, 16, -20, -22, -16, 24, 40, -90, 14, 2, -20, 12, 22, -28, 22, -22, 4, -8, 38, -4, -16, -36, -22, 2, -2, 8, -46, 12, 42, -2, 18, -30, -2, -32, -2, 86, 8, 30, 40, 0, -2, 44, -26, -2, -4, -18, 8, 88, 0, -30, 38, 66, 6, -52, 0, 6, 10, 0, -12, 8, 0, -56, -18, 102, -10, -8, 10, 36, 18, -32, -46, 92, -2, -28, 12, 20, -6, -22, -30, -2, -10, -22, 0, 56, 2, 42, -8, -30, 2, 8, -10, 50, -8, -62, 10, -88, 6, -30, 56, -10, -6, 58, 48, 48, 2, -88, -4, 24, 26, 16, 26, -80, 22, -46, -8, -10, -6, 22, 16, -12, -6, -18, 26, -38, -2, -6, -20, 62, 22, 32, -10, 24, 4, -80, -2, 10, 14, 28, -4, -16, 8, -64, -8, -12, 6, -24, 16, -4, 14, 22, -18, 4, 2, -66, -14, -70, -20, -10, 2, -16, 6, 28, 32, -18, 14, -16, -12, 64, 12, 22, -60, -52, 2, 6, 4, 36, 10, -12, 8, -16, 14, 6, -18, 64, -2, 78, 6, -10, 18, 42, 28, 24, 10, -50, -2, -46, 28, -42, -16, 8, 16, 6, -62, -22, -2, 40, 14, 16, 16, -4, 44, 44, -30, -28, 0, -56, 2, 36, -4, 6, -18, -64, -14, -18, 10, 76, 8, 18, -32, 0, -2, 10, -4, 50, -10, 48, -4, 4, -12, 18, -4, 2, 4, -22, -2, 22, -48, -36, -8, -6, -4, 82, -4, 38, -10, 36, 28, -114, 54, 2, 26, 52, -32, -84, 2, 18, 36, 20, 22, -8, 28, 14, 20, 20, 6, 14, -4, -54, -50, -6, -2, -12, -26, -122, 2, -32, -10, 10, -24, 26, 52, -72, 4, -70, 22, 46, 6, -12, -48, -6, 8, -120, -40, -56, -6, 42, 6, 2, -4, -2, -54, 56, -16, -64, 22, -84, 8, -58, 14, 4, -26, 24, 36, 44, 14, 6, -52, 30, -20, 8, 2, -48, -46, 44, 6, -62, 2, -20, 28, 14, 4, -32, -36, -68, 2, 72, 38, 88, 30, -20, 12, 2, 14, 24, 6, -74, -34, -14, 18, 14, 0, 18, -32, -48, 12, -52, -48, -10, 14, 2, -74, -64, 18, -6, 10, 8, 16, 52, 22, 14, 12, 76, 2, -8, -2], "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": "430.2.a.e", "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, 0], [1, 0], [-1, 0], [1, 1], [1, 0], [1, 0], [-1, -1], [1, -2], [-1, 0], [1, 2], [-1, 0], [1, -1], [1, 1], [1, 2], [-1, 2], [1, 1], [1, 0], [5, 1], [-1, -2], [-3, 2], [1, 0], [-5, -1], [-1, 1], [3, -3], [-1, -1], [1, 0], [-1, -2], [4, 0], [1, -2], [8, -1], [-1, -1], [-8, -1], [-1, 0], [-2, 0], [-5, -1], [1, -2], [1, 2], [-1, -3], [3, -2], [7, 3], [-1, 0], [-1, -2], [5, 1], [-1, 0], [1, -1], [1, 2], [-3, 3], [7, -1], [1, 1], [6, -4], [-1, 0], [8, 6], [1, 2], [-2, -2], [-4, 0], [1, -1], [-1, 2], [3, -1], [-8, 1], [-10, 2], [1, 1], [0, -1], [8, 1], [-11, 0], [1, 0], [1, 2], [2, 0], [0, 3], [5, 1], [-6, 0], [-1, 2], [-5, 1], [-1, -2], [4, 3], [1, 3], [1, 1], [-3, 2], [7, -3], [-7, -3], [-2, -7], [1, 0], [1, -2], [1, 2], [0, 2], [-5, -1], [5, 1], [1, 0], [5, 7], [-1, 1], [-3, 7], [-1, -2], [-11, 0], [3, -3], [-11, -9], [-7, 1], [-3, 2], [-1, -1], [-3, -9], [-6, 4], [-5, 1], [1, 0]]}