# Stored data for newform 930.2.n.f, downloaded from the LMFDB on 19 April 2024. {"label": "930.2.n.f", "space_label": "930.2.n", "level": 930, "weight": 2, "hecke_orbit": 6, "hecke_orbit_code": 22518891523605410, "dim": 12, "is_polredabs": true, "trace_hash": 342326997500928259, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[7, [104976, -303264, 392040, -212490, 106561, -26150, 7459, -875, 306, -25, 15, 1, 1]]], "qexp_display": "q+\\beta _{8}q^{2}-\\beta _{6}q^{3}+(-1-\\beta _{3}-\\beta _{6}+\\cdots)q^{4}+\\cdots", "char_order": 5, "char_parity": 1, "char_degree": 4, "char_conductor": 31, "char_orbit_label": "n", "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": "0.005", "prec": 17}, "analytic_rank_proved": true, "char_values": [930, 5, [311, 187, 871], [5, 5, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3, 5, 31], "conrey_indexes": [481, 721, 841, 901], "field_disc": 2375762921486328125, "field_disc_factorization": [[5, 9], [1102901, 2]], "field_poly": [121, -462, 1235, -1720, 1336, 50, 316, -25, 61, -15, 10, -3, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "13.034", "prec": 20}, {"__RealLiteral__": 0, "data": "5.819", "prec": 17}, {"__RealLiteral__": 0, "data": "657.748", "prec": 24}, {"__RealLiteral__": 0, "data": "1310.008", "prec": 27}, {"__RealLiteral__": 0, "data": "62928.477", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c5", "trace_display": [3, 3, 12, -1], "traces": [0, 12, 3, 3, -3, 12, 12, -1, 3, -3, 3, 14, 3, 4, 1, 3, -3, -7, 3, 12, -3, 1, -14, -6, -3, 12, 6, 3, -1, -23, 12, 34, -12, 11, -3, -1, 12, 22, 8, 1, 3, 15, -1, -17, -11, -3, 6, -2, 3, -8, 3, 7, 4, -21, -3, 14, -4, 8, -17, -15, 3, 16, 26, 4, -3, 4, 14, 24, 8, 6, 1, 23, 3, 56, 8, 3, -8, -8, 4, -9, -3, -3, 15, -24, 1, -7, -18, -12, 6, -27, 3, -3, 24, 11, -28, 12, -3, 38, -52, -6, -3, -49, -7, 2, 1, 1, -14, -42, 3, -19, -14, 8, -1, -8, 12, -6, 17, -1, -10, -42, -3, -21, -6, 0, -6, 12, 1, 25, 3, 2, 6, -36, -14, -29, 1, 3, -3, -55, -6, -16, -1, 12, 22, -49, -3, -23, -56, 18, -3, -94, 12, -31, -12, 3, 18, 34, 6, 25, -1, 21, -12, 20, 3, -21, -15, 11, 4, -17, -1, 55, -3, 12, 18, -58, -23, -1, -11, -10, 27, -59, 12, -40, -12, -6, 6, 22, 34, 2, -2, 1, 8, 16, -12, 19, -38, 1, -8, 60, 11, 5, 3, 1, -31, 24, -3, 15, 28, -6, -1, 31, -1, -98, 14, -23, -18, -17, 12, 145, 14, 24, -11, 52, 22, 36, 1, -3, 8, 19, 8, -25, 6, -17, 23, -70, 1, -2, -15, 9, -58, -51, 3, -3, 6, -12, -14, -8, 15, 76, -9, -56, 3, 51, -1, -14, 30, 7, -3, -6, -17, 101, 4, -23, 36, -47, -11, -21, 29, -28, -11, -50, -3, -58, -7, 18, -50, 14, 6, 103, 66, 9, -4, 21, -2, -33, -2, 8, -11, -64, 3, 26, -17, 47, -24, -94, -8, -15, 3, 11, -71, -19, 3, -41, 31, 49, -8, 16, 7, -26, -8, -52, 26, 16, 4, 78, 40, 4, 16, -73, -21, 1, -3, 42, -45, -4, -3, 4, -9, -26, -15, -62, 14, -95, -4, -3, -38, 24, -4, -47, 20, -17, 8, 35, 8, 133, 17, 6, -32, 32, -17, -99, 1, -4, -14, -1, -15, 23, 28, -58, 59, -41, 3, 63, -50, -24, 12, 56, 16, 80, -6, 15, 8, 246, 26, -102, 68, 3, 12, 26, 4, -2, -8, 10, 29, 41, -3, -8, -19, -17, -47, 57, 4, -56, 18, -49, -60, -9, 14, 110, 40, 29, -3, 34, 24, 45, 36, -3, -29, 27, 8, 22, 15, -30, -28, 67, 6, -24, -4, -49, 49, -118, 1, -92, 23, -12, -14, -7, 23, 132, 48, -76, -18, 34, 3, -76, -15, -12, -19, 89, 56, 136, 6, -18, -52, -39, 8, -27, 39, -71, -1, 35, 3, 4, 17, -14, 6, -3, -8, -21, 0, -8, 24, -83, -8, 140, 12, 11, -120, 45, 4, 39, -28, -30, -10, -98, -9, 12, -37, 14, -4, 89, -3, -93, 3, -45, -21, 38, -3, -49, 14, 21, -52, -14, 15, -72, 69, -6, -11, -46, -24, 103, -3, 42, 134, 15, 1, -49, 4, -55, 25, -69, -7, 25, 3, 8, 11, 2, -18, -17, -101, -42, 1, -6, -12, -82, 49, 1, -68, 134, 6, 79, -14, 10, 116, 44, -27, -42, 11, -96, -10, -61, 3, -127, -37, -50, 7, -19, -3, 0, -55, -14, -14, 24, 24, 168, 12, 8, -16, 304, 11, -28, -1, 68, 104, 78, -28, -8, 33, -1, 22, 109, 12, -66, 11, 29, -11, -6, -3, 24, 94, 46, 17, -138, 38, -14, 64, -1, -71, -64, -52, -17, -10, 15, -8, 52, -6, -42, -24, -15, 19, 160, -3, -163, -109, -11, 14, -21, -49, 31, -12, -24, -6, -37, -7, 52, -54, 0, -17, -14, 2, 120, -6, -24, 54, 277, 1, 12, 132, -31, -40, 161, 1, 51, -1, 23, 73, 25, -14, 54, 54, -22, 3, -66, -42, 55, -55, 2, 14, -115, 3, 105, 6, 70, 24, -13, -19, -36, 0, -64, -43, -65, -14, -46, -80, 63, 24, -29, 8, -92, 38, 39, 1, 40, -1, -11, 47, 3, -70, 292, -8, 98, -3, 26, 40, -84, 12, -55, 152, -50, -2, 61, -6, -18, -58, 17, 23, -16, 17, -51, -51, -10, -1, 1, -1, -28, 14, 12, 36, 282, -10, -145, 22, 1, 2, 33, -42, -49, 96, 51, 126, 32, -3, -138, -63, -27, -30, -23, -21, 120, 3, -3, -56, -176, -6, 3, 50, 18, 6, -57, 0, 54, -3, 69, 104, 50, -6, -94, -23, -24, 67, 50, 12, -115, -12, -16, 19, -31, 1, -73, 2, 4, -12, 35, 25, -170, 21, 3, -41, -75, 3, -146, 18, 6, -46, 17, 2, 34, -18, -46, 58, -75, 6, -62, -104, -17, -18, 25, -36, -222, -15, -13, -1, 116, -14, -85, 25, 21, 5, 38, -29, 165, -12, -2, 6, 105, 1, 20, 0, -80, -31, 70, 3, -194, -106, 58, -27, -21, -3, -118, 3, -3, -15, 32, -55, 27, -2, 11, 3, -71, -6, -127, 4, 182, -6, -234, -16, -17, 36, 6, 8, 66, -1, 88, -158, -166, 72, 55, 12, -112, -21, -22, -3, 66, 22, -31, -132, 12, -18, -118, -49, -81, 18, 64, -24, 148, -3, -58, 56, -136, -30, -124, -23, 163, -26, 18, 6, -1, -56, -27, 99, 94, -11, -10, 18, -99, -63, -10, -36, -42, -3, -124, 27, 14, 21, 82, -94, -59, 1, -26, -130, -34, 12, 123, -4, 41, 18, -40, -31, -90, -6, 31, -12, -170, -12, 44, -19, -6, 0, -182, 3, -139, 6, 1, 83, -57, 18, 22, 60, 2, 23, 270, 34, -56, -70, 54, 90, 2, 6, -180, -39, 12, -2, 145, 25, 116, 10, 1, -77, -167, -1, 65, 8, 8, 37, 49, 21, 16, 94, -1, 6, 53, -12, 172, -182, 18, 27, 19, 20, -250, -24, -11, -38, 86, 3, -19, -51, 1, 6, 17, -21, 26, -8, 26, 44, -68, -15, 60, -128, -38, 31, -38, 11, 234, -34, -30, 66, 5, 4, 72, 72, 3, 3], "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, 4, 1, 5, 0]], "char_orbit_index": 14, "prim_orbit_index": 4, "minimal_twist": "930.2.n.f", "char_is_minimal": true, "conrey_index": 481, "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], [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, -1, 0, 0, 0, 0, 0], [-1, 0, 0, -1, 0, 0, -1, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, -1, 1, 1, 0, 0, 0, -1, 1, -1], [0, 0, 0, -1, 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, 0, 0], [1, 1, -1, -1, 0, 0, 1, -1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, -1, -1, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 1, -1, 0, 2, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, -1, 1, -1, -1, 0, -1, 1, 1, 0, 0, 1], [-1, 0, 0, -1, 0, 0, -1, 0, 1, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1], [-2, 1, -1, -1, 0, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, -1], [-1, 0, 0, -1, 0, 0, -1, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, -1, 0, 0, 1, 0, 0, 0, 0], [1, 0, 0, 1, 0, 0, 1, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [0, 0, 1, 3, 0, 0, 3, 1, -3, 0, 0, -1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -1, 0, 0, 1, 0, -2, 1, 1, 1, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, -2, 0, 0, -2, -1, 1, 0, 0, 0], [0, -3, 0, 0, -1, 0, -1, 1, 0, 0, -1, 0], [0, 1, -1, -1, 1, 1, 0, 0, 0, -1, 1, -1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, -4, 0, 4, 2, -1, -2, 1, 0, 0, 0], [0, -2, 2, 0, -1, -1, 0, 1, 1, 1, -1, 1], [0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, -1, -3, 1, 0, -2, -1, 1, -1, 1, 1], [0, 1, -1, -1, 1, 1, 0, 0, 0, -1, 1, -1], [0, 6, -3, 0, 4, 0, 2, -3, -1, -2, 2, -1], [-2, 0, 0, -2, -1, 0, -1, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, -1, -1, 1, 1, -2, -1, 0, -1, 1, 0], [1, -3, 0, 1, -2, 0, 3, 2, 0, 0, -1, 0], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 1, 1, 2, -1, 4, -2, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 2, 1, 0, 1, 1, 1, -1, -1, -1, 1, -1], [0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0], [-2, -1, 1, 2, 2, -1, 0, 0, 2, 2, 0, 1], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, -1, -1, 0, 0, 1, -1, 1, 0, 0, 0], [0, 0, -1, 0, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, -1, 1, 1, 0, 0, 0], [0, 1, 0, 2, 1, 1, 0, 0, -3, -1, 1, -1], [-1, -3, 1, 0, 0, -1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [3, 1, -3, 0, 4, 2, 1, -2, -1, 0, 1, -1], [1, -1, 1, -1, -1, 0, 0, 0, 3, 0, 1, 0], [0, 0, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0], [1, 1, -1, -1, 0, 0, 1, -1, 1, 0, 0, 0], [2, 0, 1, 0, -1, -1, 2, 4, -2, 0, 0, 0], [1, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0], [2, -1, 0, 2, -1, -1, 2, 1, -2, 0, -1, 0], [0, 0, 0, -1, -1, 0, 0, 0, 0, -1, 0, 0], [2, 1, -1, 0, -2, -1, 0, 0, -2, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [8, -2, 2, 4, -1, -1, 8, 1, -3, 1, -1, 1], [0, -2, -2, -1, -2, 0, -1, -2, 4, 0, 0, 2], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [-1, -1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0], [-2, 1, -2, -4, -2, 2, -1, 2, 0, -2, 2, 0], [0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0], [-1, 1, -1, 1, 1, 1, 0, 0, 1, 1, 0, -1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [1, -3, 1, 0, -2, -2, 1, 2, 1, 1, -2, 1], [0, 0, -2, 0, -1, 0, 1, -2, -4, -1, 1, 1], [0, 0, 0, -1, -1, 0, 0, 0, 0, -1, 0, 0], [0, 1, -1, 0, 2, 0, 0, 0, 0, -1, 0, 0], [-1, -1, -2, 0, -1, -1, -1, 2, -1, -1, -1, -1], [0, 0, 1, 0, -1, -1, 3, 1, -3, 0, 0, 0], [1, 0, 1, 0, -1, 0, 2, 1, -2, 0, 0, 0], [-2, -2, 1, 4, 0, 0, -2, -1, -1, 3, 0, 3], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 3, 2, 0, 0, 2, 3, -1, 0, 0, -1], [2, -1, 0, 0, -1, -1, 0, 1, 0, 0, -1, 1], [0, 0, 1, 2, 0, -1, -3, 0, 1, 1, -1, 1], [-3, 0, 1, 0, -1, 1, -1, -1, 1, 0, 0, 0], [0, -1, 1, -1, -1, 0, -1, 1, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, 3, -4, -6, 2, 2, 1, -3, 6, 0, 2, 0], [-4, 1, -2, 0, 3, 0, 0, 1, 0, 0, 1, -1], [-1, 0, -1, 0, 1, 0, -2, -1, 2, 0, 0, 0], [-1, 0, 0, -1, 0, 0, -1, 0, 1, 0, 0, 0]]}