# Stored data for newform 418.2.f.a, downloaded from the LMFDB on 18 April 2024. {"label": "418.2.f.a", "space_label": "418.2.f", "level": 418, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 343630938530, "dim": 4, "is_polredabs": true, "nf_label": "4.0.125.1", "trace_hash": 1727659593220674581, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[3, [16, 24, 16, 4, 1]]], "qexp_display": "q+(-1+\\zeta_{10}-\\zeta_{10}^{2}+\\zeta_{10}^{3})q^{2}+\\cdots", "char_order": 5, "char_parity": 1, "char_degree": 4, "char_conductor": 11, "char_orbit_label": "f", "char_is_real": false, "Nk2": 1672, "analytic_conductor": 3.33774680448952, "hecke_ring_index": 1, "level_radical": 418, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 10, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.005", "prec": 17}, "analytic_rank_proved": true, "char_values": [418, 5, [343, 287], [2, 5]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 11, 19], "conrey_indexes": [115, 191, 229, 267], "field_disc": 125, "field_disc_factorization": [[5, 3]], "field_poly": [1, -1, 1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.934", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "45.739", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "963.750", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c5", "trace_display": [-1, -4, -8, -7], "traces": [0, 4, -1, -4, -1, -8, 6, -7, -1, -13, 2, 1, -4, 4, -7, -2, -1, -3, 7, -1, -8, 32, 11, -10, 6, 1, 4, 20, 8, -16, -2, 0, 4, -26, 2, 19, 7, -4, -1, -24, 7, 14, -18, -26, -4, 66, -5, -10, -4, -12, -14, -2, 4, -14, -40, 3, -2, 6, -16, 22, 18, -3, 10, -11, -1, -8, 4, -28, -3, 10, 4, 0, -13, -18, -4, 54, 4, 32, 16, 12, 7, 19, -6, 2, 2, 1, 9, 56, 1, -12, -44, 28, 10, -20, 5, 7, -4, -28, 18, 23, 26, -16, -2, -22, 4, -84, -4, -12, 20, -32, -7, 24, 8, 22, -4, 5, 14, -28, 22, 9, -32, -41, -18, -4, 10, 3, 44, -6, -1, 26, 32, 42, 4, -2, 12, -60, 2, 22, 0, 4, 4, 0, -20, -44, 12, 22, -18, -18, 6, -2, -26, 18, -1, 26, -38, 20, -24, -3, 2, 64, -8, 25, 19, -38, -16, 72, 22, 2, 2, -3, -9, -13, 4, -4, -24, -58, -9, -72, 28, -44, 11, 22, -32, 18, 10, 18, 0, -2, 10, -100, 7, 17, 6, 24, 12, 8, -12, -8, -52, 102, -14, 28, 29, -22, 8, -38, -22, -5, -16, 1, 76, -26, -4, 20, 8, 57, 0, 40, -12, 88, -2, -8, -16, -40, -7, -122, 2, -10, -4, 15, 40, -2, 4, 10, -28, 25, -18, -52, -1, -10, 18, -96, 19, -44, -3, 24, 16, 4, 0, -22, 3, 11, -66, -10, -36, 34, -1, -18, -44, -18, -28, -8, -18, -64, -6, 48, 8, 12, 2, -28, 100, -10, 2, 72, 2, 44, -20, 26, 4, -30, 19, 4, -10, -1, 0, -32, 16, -52, -13, 18, 22, 88, 22, 24, -18, -24, -4, 80, -32, 20, -26, 43, 8, 6, -1, -39, -19, -24, -3, 72, 30, -38, 16, 39, 32, -88, 2, 14, -56, 56, 2, -8, 25, 2, -41, 56, 37, 32, -6, 40, -58, -24, 2, -12, -28, 66, -18, 10, -3, -52, 16, -60, 12, -5, 4, -40, -4, -19, -4, -35, 67, 160, 1, -6, 28, -40, -22, -34, 46, 42, 11, -1, 32, 46, 8, 56, 18, 9, -5, 2, -2, -58, -20, -56, -2, -108, 5, 64, 60, -30, -8, 36, 17, 38, -4, -119, -56, 97, 12, 52, -72, 0, 3, -42, 22, -44, 53, 26, -28, 2, 1, 22, -52, -40, 29, -148, 88, 24, -12, -24, -38, -2, 18, 24, -10, 46, 4, -84, -9, -30, -84, -10, 14, 5, -14, 13, 20, -21, 8, -16, -28, 6, 0, 46, -30, -132, 28, 10, -52, -16, -32, 114, 12, -33, 4, 74, 30, 32, -7, -24, 138, 46, -48, -68, -10, -16, 6, -18, 0, -20, 5, -2, 78, 54, 14, -20, -25, -30, 52, 44, 25, -122, -8, -4, 48, -14, -1, 68, 25, -13, -2, 16, 14, -20, 19, 136, 66, 22, 12, 78, -51, -45, 16, 12, -16, -11, -20, -30, -22, -27, -27, 48, 16, 4, 44, 122, -35, -12, -6, -16, -16, -56, -1, 0, -18, 24, 36, -35, 32, 24, -28, -20, 62, 46, -3, 58, 16, 0, 24, -22, -82, 6, -7, 24, -68, 24, 2, -96, 52, -33, -80, -19, -10, -32, -3, 24, -8, -58, 22, 6, -51, 4, 0, 44, 6, -68, -21, -39, -30, -36, -46, 32, -16, -44, -10, -94, 14, 148, 10, 22, 18, -46, -4, 48, -12, 35, 7, -78, 13, 56, 22, 29, -112, 94, -8, 176, 24, -48, 42, 0, -34, 8, 6, -42, 0, -38, -2, -102, -40, -46, 54, 72, 43, 116, -52, 122, -64, 12, -1, -88, 21, -20, 6, -52, -4, 48, 7, -80, -28, 20, -40, 40, 7, -4, 16, -56, 14, -6, -58, 8, -88, 28, 12, 76, -6, -78, 64, -72, -74, -20, -8, -60, -8, -39, -5, 28, 2, 72, 44, -72, -104, 40, 37, -24, -8, -99, 14, -34, 5, 64, 62, -24, 16, 8, -13, 19, 38, 70, -28, -40, -44, 48, 32, 44, 10, -60, -3, 34, 48, -36, -9, 160, 0, -12, -13, 26, 25, -60, 9, 16, -40, -46, 16, -154, -34, -93, -4, -8, 0, 10, -38, -24, -80, -4, 11, -20, 74, 68, 8, -64, 30, -54, -22, 30, 36, 28, -4, -80, 42, 63, -44, -24, -1, 96, 22, -64, -84, -2, -32, -13, 6, 22, -12, 19, 9, 156, -10, -2, 32, 78, -2, 16, 82, -20, 20, -66, 24, 6, 3, 56, 102, -20, -10, -76, -56, -96, 60, -58, -40, 20, 2, 26, 36, 76, 12, -77, -32, -88, 6, 14, 76, 128, 24, 58, -48, 30, -28, -32, 52, -6, 128, 50, 10, -160, 3, -84, 78, -34, -18, 64, 66, -36, -17, 72, -29, -48, -23, -34, -18, 5, 1, 164, -68, 88, 48, 50, -40, -52, -16, -42, 47, 20, -22, -140, -26, 226, 8, 4, -44, -176, 12, -44, -2, 28, 8, -114, -116, 48, -10, 30, -29, -116, 4, 9, 76, -64, 1, 160, 55, 100, 46, 13, -30, 16, 14, -24, -30, 73, 36, -54, 13, 10, -20, -11, 39, 11, 8, 0, -16, -30, 57, 52, -54, 16, 20, 28, 46, -88, -20, -72, 88, -48, 28, 76, -5, 126, 8, 18, -46, 96, 38, -32, -96, 19, -8, 164, 42, -66, 4, -42, -156, -164, 20, 5, 32, 38, 8, 0, 6, 100, -122, 28, 46, -228, 2, 86, 52, 2, 40, -23, -16, -54, -4, -57, 22, -6, 0, -66, 40, -88, -25, 24, 68, 80, -72, -56, 44, -6, -16, 51, -40, 3, -25, 48, -30, 29, -48, -15, 44, -14, -5, -18, 58, -80, -18, 520, -69, -82, -52, 72, 1, -44, 9, 100, 68, 111, -30, 4, 102, -41, -2, -49, -24, 24, 34, -88, -30, -182, -1, -12, -104, 4, -44, 93, -38, 104, 12, -40, -152, 22, 54, 4, -45, -44, -4, 56, 2, -40, 4, 50, 154, 16, 0, 24, 40, -209, 18, 65, -27, -80, 48], "weight_parity": 1, "has_non_self_twist": 1, "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], [1, 1, 11, 3, 1, 5, 0]], "char_orbit_index": 6, "prim_orbit_index": 3, "minimal_twist": "418.2.f.a", "char_is_minimal": true, "conrey_index": 115, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [-1, 1, -1, 1], [0, -2, 0, -2], [0, 0, 0, -1], [-3, 1, -3, 0], [2, 0, 2, 0], [-3, 3, 0, 2], [0, 0, 1, 0], [-5, 1, -1, 5], [2, 0, 3, -3], [2, -4, 1, -2], [-2, 0, -2, 2], [4, -4, 4, -4], [0, -3, 1, -3], [-4, 4, 0, 10], [0, -1, 0, 0], [-1, 0, -1, 0], [4, -4, 0, -5], [0, 0, 1, 0], [-2, -1, 1, 2], [10, 0, 4, -4], [2, 1, 0, 2], [-1, 0, 3, -3], [2, 0, 0, -2], [0, 3, 5, 3], [0, 0, 0, 4], [4, 8, 4, 0], [3, -1, 3, 0], [-6, 6, 0, 2], [0, -4, -6, -4], [4, -6, 6, -4], [1, 0, 0, 0], [-10, 4, -4, 6], [1, 0, 1, -1], [13, -10, 10, -13], [0, 4, 1, 4], [-2, 2, 0, 2], [0, -1, 0, 0], [-8, 0, -8, 0], [3, -3, 0, -2], [0, 4, -6, 4], [-10, 6, -6, 10], [-7, 0, -1, 1], [-3, 2, -4, 2], [22, 0, 11, -11], [1, -4, 4, -1], [0, -3, 4, -3], [-2, 2, 0, 2], [-3, -3, -3, 0], [-3, -5, -3, 0], [-2, 2, 0, 4], [0, 0, -4, 0], [-10, 8, -8, 10], [-12, 0, -4, 4], [-7, 9, -8, 14], [-2, 0, -3, 3], [2, 0, 0, -2], [0, -6, 4, -6], [8, -8, 0, -2], [4, 6, 4, 0], [-3, 6, -3, 0], [2, -2, 0, 4], [0, -11, -11, -11], [-1, 1, -1, 1], [-8, 0, -12, 12], [6, -6, 4, -10], [-8, 0, -2, 2], [-1, 0, 0, 1], [0, 2, -6, 2], [-3, 3, 0, 13], [-2, 6, -2, 0], [-4, -1, -4, 0], [-8, 8, 0, 6], [0, -2, 0, -2], [22, -6, 6, -22], [1, 0, 0, 0], [6, 8, -1, -1], [8, 0, 8, -8], [8, -6, 6, -8], [0, 3, -1, 3], [12, -12, 0, -17], [-4, 6, -4, 0], [3, -7, 3, 0], [4, -4, 0, -10], [0, 2, 3, 2], [7, -6, 6, -7], [16, 0, 4, -4], [1, 1, 1, -3], [-8, 0, -10, 10], [-22, 11, -11, 22], [0, 12, -4, 12], [3, -3, 0, 1], [-8, 4, -8, 0], [3, -4, 3, 0], [3, -3, 0, -2], [0, -2, 0, -2], [-12, 4, -4, 12], [6, 0, 3, -3], [6, 9, 12, 2], [8, 0, 3, -3]]}