# Stored data for newform 930.2.bg.d, downloaded from the LMFDB on 25 April 2024.
{"label": "930.2.bg.d", "space_label": "930.2.bg", "level": 930, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13512997938922402, "dim": 16, "is_polredabs": true, "trace_hash": 543540533800982778, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[7, [841, 261, -2261, 386, 3906, -7042, 7726, -6337, 4307, -2623, 1556, -848, 401, -166, 54, -11, 1]]], "qexp_display": "q+\\beta _{4}q^{2}+(\\beta _{5}+\\beta _{7})q^{3}+(-1+\\beta _{1}+\\cdots)q^{4}+\\cdots", "char_order": 15, "char_parity": 1, "char_degree": 8, "char_conductor": 31, "char_orbit_label": "bg", "char_is_real": false, "Nk2": 3720, "analytic_conductor": 7.426087387979075, "hecke_ring_index": 1, "level_radical": 930, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.003", "prec": 17}, "analytic_rank_proved": true, "char_values": [930, 15, [311, 187, 871], [15, 15, 8]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3, 5, 31], "conrey_indexes": [121, 361, 391, 421, 541, 661, 691, 751], "field_disc": 8073145513916015625, "field_disc_factorization": [[3, 8], [5, 14], [449, 2]], "field_poly": [1, 0, 149, 0, 777, 0, 1472, 0, 1350, 0, 653, 0, 167, 0, 21, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.075", "prec": 17}, {"__RealLiteral__": 0, "data": "16.153", "prec": 20}, {"__RealLiteral__": 0, "data": "6.453", "prec": 17}, {"__RealLiteral__": 0, "data": "851.753", "prec": 24}, {"__RealLiteral__": 0, "data": "1378.312", "prec": 27}, {"__RealLiteral__": 0, "data": "82452.210", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c15", "trace_display": [-4, 2, 8, 11], "traces": [0, 16, -4, 2, -4, 8, -8, 11, -4, 2, -2, -4, 2, -20, -4, 4, -4, -12, 2, -7, -2, -4, 11, 11, 2, -8, 5, -4, -4, 23, -16, -17, 16, -2, -2, 7, -8, 17, -2, -5, -2, 8, -4, 32, 1, -2, 11, -7, 2, -1, 2, -12, 10, 54, -4, -11, 1, 18, -22, -38, 4, -28, -27, -2, -4, -10, -7, 1, -2, -13, 7, -11, 2, 53, 2, 2, -2, 44, 10, 48, -2, 2, 8, 56, 11, -24, -13, 1, -9, -43, -2, -50, -44, -22, -72, -14, 2, 17, 29, -9, 2, 72, -12, -61, 10, 4, -6, 47, -4, 31, 4, 2, -4, 37, -7, 13, -22, -5, 27, 54, 4, 26, -3, 4, 23, -16, 8, 9, -4, 7, -5, -8, -7, -61, 61, -2, 28, -51, 2, 17, -8, -14, 4, 5, 2, -11, -22, 12, -18, -11, -8, 33, -7, -26, 34, -4, -10, -46, -2, -18, 8, 6, 2, 9, -37, -1, -34, 37, -4, -6, 26, 14, 2, -49, -34, -4, 1, -28, -43, -58, 8, 44, 60, -36, 11, 34, 13, -58, -7, -4, -4, 1, -8, 38, 17, 5, -16, -31, 1, -96, 2, -2, -23, 18, 28, -23, -1, -13, -5, 112, -11, 19, 9, 52, -48, 4, 16, -6, -34, 19, -1, -85, 17, -15, 11, -4, -23, 99, -2, -33, -2, 38, 23, 18, 10, -11, 7, 48, -6, 20, 4, -78, -49, -8, 17, 16, -31, 90, 13, -2, 4, -84, -7, -44, 39, 12, -4, 84, -28, 1, 20, -34, 37, -10, -2, 36, 39, -31, 21, 16, -2, 49, -12, 10, 14, -7, -13, 25, -58, -11, 2, -56, -4, 4, -1, -18, -55, 22, 2, 38, -26, 49, -2, 38, 17, -31, -18, 1, 24, -50, 2, 71, 33, -6, 18, -14, 24, -189, 44, -68, -9, -104, 10, 12, 74, -1, -17, -84, -18, 43, -2, 47, -4, -113, 2, 10, 24, -53, 23, 8, 4, -10, 11, 36, 32, -1, 1, -38, 4, -19, -4, 82, -36, -65, -28, -11, 96, -49, -4, 15, 11, 10, -4, -25, 7, 41, 47, 27, 32, -88, -2, -21, -1, -39, 60, 22, 14, -22, 11, 8, 19, 26, 18, 90, -98, -2, 43, -100, 1, -5, -4, 54, 91, 30, 2, 22, 8, -4, -8, 124, 20, -47, -6, -48, 74, -9, 11, 71, 64, 47, 2, -12, -2, -85, -98, 4, 18, -122, -2, -64, 37, -13, -1, 136, 2, 34, -20, 54, -38, 94, 4, 96, 69, -14, -21, -12, 52, -43, -43, 100, -11, -60, -4, 76, -41, 2, 31, 73, -31, -10, 9, -6, -85, 126, 17, 1, 75, 24, -4, -92, -4, -21, -73, -9, 124, -40, -2, -3, -33, -2, -22, -17, -22, 22, -2, -8, -72, -47, 10, 34, -36, 28, -28, -157, -57, -7, -21, -6, -65, -120, 4, -135, 12, -4, -19, 46, 2, 44, 17, -42, -29, 42, 29, -106, 45, -18, 8, -34, -22, -66, 4, 12, -59, -83, -7, 6, -29, -6, -6, 12, 12, 37, -4, -2, 14, -29, 2, -7, 1, 73, 5, 88, 1, -60, -48, 8, 40, 127, 18, -67, 21, -4, 29, -20, 44, 34, -24, -53, 56, 62, -2, -130, 9, 2, -12, 83, 10, 72, 24, 29, -7, -1, 22, 69, -30, -17, 17, -104, 14, -130, -8, 34, 34, 61, 36, 23, 4, 11, 49, 50, 7, -77, -25, 13, 12, 2, 2, 31, 58, -27, 4, -1, 29, 37, -12, 5, -32, -19, -58, -68, 54, 27, 17, -2, -9, -54, 4, -23, 25, -10, 2, 210, -19, 21, 3, 7, -66, 95, -7, 18, 36, 5, 24, -98, -9, 2, -61, -61, 32, 166, 16, -44, 6, -193, -5, -8, -8, 19, 74, -37, 4, 131, 28, 69, 96, 3, 27, -50, -102, 4, -2, 58, -13, 143, 1, -7, -53, -140, 2, -2, -10, 7, -66, -144, 52, 29, -2, -12, -27, 79, -11, -14, 60, 5, -34, -14, -19, 28, 17, 75, 59, -18, -4, 149, -38, 2, -11, -54, -14, -213, 26, -38, -138, 116, 14, -24, 40, 57, 7, -255, -11, 71, 26, 38, 21, -44, 26, -34, 75, -69, -4, 166, 10, -152, 11, -43, 50, 27, 27, -4, -49, -26, -8, 38, -108, -20, -53, 20, 17, -23, -2, 76, 9, 17, -36, -34, -19, 267, -50, -4, -53, -17, 39, 148, 118, 6, 11, -207, -2, -14, -36, -60, -24, 64, -7, -22, -80, 56, 127, 21, 8, -30, 43, 1, 0, 24, -4, 212, 10, -77, -14, 62, -6, -29, -9, 2, -45, -5, 2, 13, 17, -18, -27, 7, -14, 13, -18, -37, -61, -119, -5, -33, -37, -22, -6, 7, 37, 84, -36, -25, 26, 23, -4, 240, -54, 36, 9, -253, 47, -11, -8, 4, -12, -41, -2, 12, 5, -42, -23, 27, 4, -30, 3, 13, -122, 42, -2, -17, 21, 10, -8, 213, 27, -27, 29, 1, 26, -69, -13, 226, -11, -5, 5, -32, -61, -61, -148, 23, -216, -63, 4, 5, 26, -22, -56, 48, -29, -82, -36, -87, 28, -33, -53, -35, 2, 7, 57, 78, -25, 60, -11, 49, 0, 137, -4, -26, -34, 24, 89, -148, -23, -245, -14, 9, -27, -11, -31, 65, 5, 38, -1, -139, -6, -24, 95, -32, -79, 172, -18, -68, -44, -7, -60, -46, -11, -26, -4, 5, -12, -41, 16, 78, -51, -52, -33, -44, -9, -69, -146, 4, 30, 189, -7, 53, 22, 3, 57, 131, 28, -66, 13, 96, -17, 130, -17, 17, 2, -61, 23, 220, 17, 68, 18, 27, 63, -29, 5, 84, 34, 172, 4, 85, 53, -12, 32, -8, 133, 28, 28, -110, -2, -19, -6, -30, 54, -1, -15, 19, -75, -34, -16, 67, 0, -9, 17, 46, 6, 21, -39, -114, -29, -101, 2, -173, -31, 10, -3, -107, 33, 247, 1, -53, -8, -54, 29, -74, 54, -22, -90, 47, 2, -200, -17, 80, -9, -9, 23, -58, 49, -18, 4], "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, 31, 7, 1, 15, 0]], "char_orbit_index": 33, "prim_orbit_index": 7, "minimal_twist": "930.2.bg.d", "char_is_minimal": true, "conrey_index": 121, "id": null, "nf_label": 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 1, 0, 0, 1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, -1, 0, 0, 1, -1, 0, 1, 1, 0, 1, 0, 1, 0], [0, -1, -1, 0, -1, 0, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 1, -1, 0, 0, 0, 0, 1, 2, 0, 0, -1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [-2, -2, -1, 3, -1, -1, 2, -2, -2, 0, -2, 0, -1, 2, -2, 1], [1, -1, 0, 1, 1, -1, 1, -1, -1, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 3, 1, -2, -1, 3, -3, 2, 4, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, -1, 3, -1, -1, 1, -3, -5, -1, -4, 2, -1, 1, -3, 1], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -1, 1, -1, 0, 2, -1, -2, 0, 0, 0, 0, 1, 0, 1], [-3, 1, 0, 0, 1, 1, -2, 2, 3, -2, -3, 0, -1, 0, -3, -1], [3, 1, 2, 0, 3, 0, -1, 3, 3, 1, 3, -2, 2, 0, 1, -1], [1, -1, 0, 0, 0, -1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 0, 0, -1, -1, -2, 0, 2, 0, 0, 0, -2, -2, -1, 0], [-1, 1, 1, 0, 0, 1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [-3, 2, 1, 1, -1, 1, -2, 1, 0, -1, -1, 1, -1, 0, -1, 1], [0, 3, 2, -1, 1, 4, -5, 5, 4, 2, 2, 1, -1, -1, 1, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -1, -1, -2, 3, 3, -1, -1, 2, 3, 1, 0, 1, 1, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 2, 1, 1, 1, 1, -2, 1, 1, -3, -2, 0, 0, 0, -2, 1], [6, -5, -2, -2, 0, -2, 6, -3, -1, 2, 2, -2, 2, 0, 2, -2], [1, 0, 0, 0, 0, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -4, -4, -1, -1, -1, 7, -4, -3, 2, 3, -1, 3, -1, -2, -5], [-4, 4, 0, 1, 0, 3, -5, 4, 5, -1, -1, 1, -2, -2, -2, -1], [-1, 1, 1, 0, 0, 0, 0, -1, 1, 0, -2, 2, 0, -1, -2, 0], [0, 0, -1, 0, -1, 0, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0], [-3, 3, 4, -1, 1, 1, -5, 2, 3, -1, 0, 1, 0, 0, -1, 0], [-1, 0, 0, 1, 0, -1, -1, 0, 0, 0, -1, 0, -1, 0, -1, 0], [2, 1, -1, -3, 1, 0, -1, 2, 1, 0, 3, -3, 0, 0, 3, 0], [2, 1, 1, -4, 1, 2, -2, 2, 3, 1, 3, 1, 1, -3, 2, -2], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 1, 1, 1, 0, 2, -1, 0, -1, -2, -3, 0, -2, 2, -1, 2], [6, -1, 2, -2, 3, 5, -1, 2, 3, 5, 7, -2, 3, -3, 3, -3], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 1, 1, -2, 1, 1, -1, 5, 2, 1, 1, 1, 1, -2, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [1, -1, -1, -2, -1, 1, 3, -2, 0, 0, 2, 0, 2, 0, 2, 0], [2, 0, -1, -3, 0, 1, 2, 1, 1, 0, 2, 0, 2, -1, 0, -1], [13, -5, -4, -2, 0, -5, 8, -8, -2, 6, 4, -3, 3, 1, 5, -1], [0, -1, -1, 0, -1, 0, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0], [-3, 2, -1, 0, -2, 4, -2, 3, 2, 0, 0, 3, -1, -2, -3, -1], [0, -1, -2, 0, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, -1, -1], [-2, 1, -1, 0, -2, 2, -2, 0, 0, 0, -1, 2, -1, -1, -3, 0], [1, -4, -1, 0, 2, -1, 2, -3, 0, 1, 2, -3, 2, 1, 1, 0], [-1, 1, -3, -2, 1, -2, 1, -3, 2, 1, 3, -2, 2, -3, -1, 0], [0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-10, -1, 4, 6, 0, -3, 0, -4, -2, -6, -6, 0, -3, 6, -3, 6], [3, -4, -1, 1, 0, -5, 4, -4, -2, 2, 1, -4, 1, 1, 1, -1], [0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -2, -2, 3, -2, 0, 2, -2, -2, -1, -3, 1, -1, 0, -3, -1], [-3, 2, 0, -1, -1, 4, -2, 3, 2, -1, -2, 3, -1, -1, -2, -2], [4, -7, -4, -1, -4, -6, 9, -7, -4, 1, 3, -4, 4, 4, 0, 0], [1, 1, 2, 0, 0, -4, 0, -2, -3, 0, 0, 0, 0, 0, 2, 2], [-5, 3, 1, 1, 2, 1, -3, 3, 3, -2, -2, -2, 0, 2, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0], [-7, 5, 7, 1, -2, 2, -1, 7, 0, -4, -2, -2, -2, 3, 1, 5], [0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [-2, 2, 1, 0, -1, 3, -2, 5, 0, -2, -1, 0, -2, 2, 0, 3], [-5, 6, 3, -1, 2, 2, -3, 6, 2, -3, -1, -3, -2, 2, 2, 2], [0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -2, 0, -2, -1, 2, 1, 2, 0, -1, 2, -1, 1, 1, 0, 0], [13, -8, -6, -2, -5, -6, 8, -6, -5, 5, 7, -3, 2, -2, 3, -2], [1, 0, -1, 0, -1, 1, 0, 0, 0, -1, -1, 1, 0, -2, -1, -2], [-2, 5, 1, -5, -4, 6, -7, 5, 4, -2, 1, 2, 2, -2, 0, -4], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [4, -2, -3, -1, 0, 1, 5, -3, 0, 1, 1, -1, 1, 0, 1, -2], [18, -11, 0, 1, 3, -8, 10, -10, -7, 6, 6, -6, 6, 1, 6, 1], [0, 1, 0, -1, 0, 1, -1, 1, 2, 0, 1, 0, 0, -1, 0, 0], [-2, 0, 1, 0, -2, -1, 1, -1, -1, 0, 0, 0, 0, 2, 0, 0], [3, 0, 2, -3, 4, 1, 0, 2, 2, 3, 3, 0, 3, 0, 3, 0], [3, -1, 2, -1, 3, 3, -1, 2, 4, 2, 3, -1, 3, -1, 2, -1], [2, -2, 0, 0, 0, -1, 4, -2, -3, 0, 1, -2, 3, 3, 2, 0], [2, -9, -4, 9, 0, -4, 10, -11, -12, 0, -5, 0, 1, 5, -1, 3], [0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [-5, -4, -6, 2, -5, -5, 4, -4, -5, -2, 0, -2, -2, 2, -2, 2], [1, 0, -1, -2, 0, 1, 0, 0, 2, 3, 3, 1, 1, -3, 1, -2], [4, -4, 1, -2, 0, -2, 4, -3, -2, 2, 4, -1, 4, 0, 3, 1], [-12, 2, 1, 2, -2, 1, 0, -1, -1, -4, -4, -2, -1, 4, -1, 4], [-1, -1, -2, 1, 2, 0, 0, -1, 0, -1, -3, 1, 0, -1, -3, -2], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [4, -5, -8, 5, -6, -1, 10, -7, -13, -1, -8, 5, 1, 3, -6, -4], [0, -1, 0, 1, 0, 0, -3, -1, -2, -1, -1, 0, 1, 1, 0, 0], [-7, 3, 0, 0, -1, 2, -4, 3, 2, -3, -2, 1, -3, 0, -2, 1], [1, -1, 0, 0, 0, -1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0]]}