# Stored data for newform 930.2.i.n, downloaded from the LMFDB on 12 February 2026.
{"Nk2": 3720, "analytic_conductor": 7.426087387979075, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 31, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 9, "char_orbit_label": "i", "char_order": 3, "char_parity": 1, "char_values": [930, 3, [311, 187, 871], [3, 3, 1]], "cm_discs": [], "conrey_index": 211, "dim": 6, "field_disc": -3636603, "field_disc_factorization": [[-1, 1], [3, 3], [367, 2]], "field_poly": [64, -16, 12, 4, 3, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[7, [144, 60, 73, 4, 21, 4, 1]], [11, [16641, -3741, 1486, -113, 54, -5, 1]], [13, [1024, 1280, 1664, -16, 44, 2, 1]]], "hecke_orbit": 14, "hecke_orbit_code": 58547344945185698, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 12, "hecke_ring_index_factorization": [[2, 2], [3, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 31, 3, 1, 3, 0]], "is_cm": false, "is_largest": true, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "930.2.i.n", "level": 930, "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": [2, 3, 5, 31], "level_radical": 930, "minimal_twist": "930.2.i.n", "nf_label": "6.0.3636603.4", "prim_orbit_index": 3, "qexp_display": "q-q^{2}-\\beta _{1}q^{3}+q^{4}+(-1-\\beta _{1})q^{5}+\\cdots", "related_objects": [], "relative_dim": 3, "rm_discs": [], "sato_tate_group": "1.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "930.2.i", "trace_display": [-6, 3, -3, -4], "trace_hash": 2079603321526398016, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.925", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "150.976", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "6994.459", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.006", "prec": 17}, "traces": [0, 6, -6, 3, 6, -3, -3, -4, -6, -3, 3, 5, 3, -2, 4, -6, 6, -11, 3, -2, -3, 4, -5, 14, -3, -3, 2, -6, -4, 24, 6, 8, -6, 10, 11, 8, -3, 17, 2, -4, 3, -12, -4, -3, 5, -3, -14, 6, 3, -5, 3, 11, -2, 2, 6, 5, 4, 2, -24, -12, -6, -16, -8, 8, 6, -2, -10, -17, -11, 7, -8, 10, 3, 6, -17, 3, -2, 4, 4, -3, -3, -3, 12, 0, 4, 22, 3, 12, -5, -56, 3, 88, 14, 1, -6, 4, -3, 40, 5, 5, -3, -6, -11, -18, 2, 4, -2, -4, -6, -4, -5, -17, -4, -13, -2, -7, 24, -2, 12, 6, 6, -50, 16, -24, 8, 6, -8, 6, -6, 3, 2, 17, 10, 30, 17, 3, 11, -1, -7, 40, 8, 3, -10, -14, -3, -12, -6, -10, 17, 44, -3, -38, 2, 22, -4, -7, -4, 16, 3, 4, 3, -30, 3, -6, -12, -5, 0, 6, -4, -45, -22, 4, -3, 0, -12, -4, 5, 12, 56, -5, -3, 0, -88, -8, -14, -34, -1, -54, 6, 4, -4, -4, 3, -48, -40, 2, -5, -16, -5, -12, 3, -34, 6, -28, 11, -12, 18, -7, -2, 108, -4, 26, 2, 20, 4, 6, 6, -34, 4, 12, 5, -68, 17, 26, 4, 6, 13, -8, 2, 26, 7, 2, -24, 58, 2, -3, -12, 3, -6, 30, -6, 56, 50, 3, -16, -5, 24, -128, -8, 0, -6, -15, 8, 3, -6, 11, 6, -27, -3, 2, -2, -12, -17, -18, -10, 2, -30, -28, -17, -15, -3, -16, -11, 44, 1, -10, 7, -78, -40, -7, -8, 4, -3, 6, 10, 2, 14, 132, 3, -10, 12, 20, 6, -18, 10, 24, -17, -5, -44, -46, 3, 8, 38, -3, -2, 8, -22, 2, 4, -36, 7, 52, 4, 0, -16, -4, -3, 2, -4, 86, -3, 4, 30, -40, -3, 4, 6, -2, 12, -66, 5, 42, 0, -34, -6, -17, 4, -60, 45, -26, 22, 95, -4, 64, 3, -14, 0, -14, 12, -72, 4, 2, -5, 13, -12, 10, -56, 12, 5, -34, 3, -67, 0, 50, 88, 6, 8, 72, 14, -12, 34, -64, 1, -46, 54, 3, -6, -32, -4, -6, 4, -6, 4, 21, -3, -2, 48, 6, 40, -29, -2, -5, 5, -17, 16, 6, 5, 59, 12, 60, -3, 28, 34, 54, -6, 6, 28, 74, -11, 3, 12, -2, -18, -78, 7, 0, 2, 20, -108, -58, 4, 20, -26, -3, -2, -11, -20, -22, -4, 14, -6, -24, -6, 64, 34, -24, -4, 28, -12, -49, -5, -5, 68, 26, -17, 28, -26, -44, -4, -68, -6, -72, -13, -19, 8, -44, -2, 88, -26, 11, -7, 62, -2, -56, 24, -8, -58, 120, -2, 4, 3, 8, 12, 122, -3, -2, 6, 2, -30, 4, 6, 60, -56, 30, -50, -20, -3, 28, 16, -3, 5, -19, -24, -32, 128, -10, 8, 56, 0, 58, 6, -6, 15, 10, -8, 3, -3, 45, 6, 21, -11, -16, -6, 2, 27, -18, 3, -21, -2, 0, 2, 48, 12, -2, 17, -8, 18, 29, 10, -64, -2, 24, 30, -108, 28, 8, 17, 5, 15, 57, 3, -44, 16, 0, 11, 2, -44, -45, -1, 8, 10, 82, -7, 8, 78, -17, 40, -44, 7, -44, 8, -27, -4, -10, 3, -13, -6, -4, -10, -42, -2, -24, -14, -8, -132, -7, -3, -64, 10, 48, -12, 76, -20, 80, -6, 4, 18, -220, -10, 122, -24, -32, 17, 56, 5, 6, 44, -24, 46, 10, -3, 43, -8, -17, -38, 100, 3, 12, 2, 28, -8, -126, 22, -2, -2, 12, -4, -61, 36, -200, -7, -14, -52, -4, -4, -3, 0, 54, 16, 83, 4, 39, 3, -26, -2, -12, 4, -110, -86, 10, 3, -66, -4, 60, -30, 3, 40, 4, 3, 12, -4, -20, -6, -124, 2, -34, -12, 6, 66, 22, -5, -44, -42, -34, 0, 30, 34, 80, 6, -26, 17, 44, -4, -24, 60, 3, -45, 36, 26, 68, -22, -16, -95, 184, 4, -1, -64, -26, -3, 60, 14, 60, 0, -2, 14, -20, -12, -12, 72, 29, -4, -79, -2, 44, 5, -6, -13, -20, 12, -64, -10, 6, 56, 22, -12, 28, -5, 60, 34, -58, -3, 172, 67, -56, 0, -12, -50, -64, -88, 6, -6, -23, -8, 5, -72, 5, -14, 37, 12, 68, -34, -64, 64, -122, -1, -88, 46, 0, -54, -26, -3, 13, 6, 15, 32, 19, 4, -19, 6, 6, -4, -10, 6, -30, -4, -11, -21, 264, 3, -36, 2, -54, -48, -92, -6, -1, -40, 4, 29, 0, 2, -34, 5, -24, -5, -8, 17, 65, -16, -9, -6, -72, -5, -60, -59, -2, -12, -10, -60, 51, 3, 28, -28, -10, -34, 60, -54, -30, 6, 22, -6, -68, -28, -8, -74, 3, 11, -92, -3, -44, -12, -42, 2, 30, 18, -5, 78, 40, -7, -16, 0, -39, -2, -70, -20, -12, 108, -8, 58, 56, -4, 78, -20, 2, 26, 90, 3, 16, 2, 3, 11, 19, 20, -12, 22, -2, 4, -17, -14, 22, 6, 66, 24, -11, 6, 0, -64, -20, -34, 122, 24, 30, 4, -20, -28, -4, 12, 55, 49, 18, 5, -98, 5, -166, -68, 12, -26, 53, 17, -30, -28, -10, 26, 96, 44, 10, 4, -92, 68, 176, 6, 44, 72, 16, 13, 0, 19, 224, -8, 3, 44, -58, 2, -158, -88, 16, 26, 52, -11, 7, 7, -2, -62, -76, 2, 17, 56, -18, -24, -276, 8, -304, 58, 26, -120, 27, 2, 50, -4, 0, -3, -59, -8, -78, -12, -8, -122, -90, 3, 4, 2, -2, -6, 208, -2, -4, 30, 172, -4, -156, -6, 120, -60, 8, 56, 96, -30, -20, 50, -80, 20, 69, 3, -18, -28, 2, -16, -172, 3, -64, -5, 2, 19, 36, 24, -16, 32, 66, -128, 5, 10, 72, -8, 84, -56, -12, 0, -36, -58, -17, -6], "weight": 2, "weight_parity": 1, "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, 0, 0], [1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [-1, -1, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 1, 0, 0, -1, 0], [-1, 0, 0, 0, 0, 0], [-1, -1, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0], [2, 2, 0, -1, 0, 1], [0, -1, 0, 0, 0, 0], [0, 0, -2, 0, 0, 0], [0, -1, 0, 0, 1, 0], [-1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 4, 0, 0, 1, 0], [1, 1, 0, 0, 0, 0], [0, 1, 0, 1, 2, 0], [-1, -1, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0], [-2, -2, 0, 1, 0, -1], [2, 0, 1, 0, 1, 0], [0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 1, 0, 0, -1, 0], [4, 0, 1, 0, 1, 1], [1, 0, 0, 0, 0, 0], [1, -1, 1, 0, 0, 1], [-1, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 1], [0, -4, 0, 0, -1, 0], [1, 0, 1, 0, 1, 0], [-1, -1, 0, 0, 0, 0], [0, -6, 0, 0, -1, 0], [0, -1, 0, -1, -2, 0], [0, 0, -2, 0, -2, 0], [1, 1, 0, 0, 0, 0], [-3, -3, -2, -1, 0, 1], [-1, -1, -1, 0, 0, 0], [0, 1, 0, 1, 1, 0], [2, 2, 0, -1, 0, 1], [0, 1, 0, 0, 0, 0], [-2, 0, -1, 0, -1, 0], [0, 0, 3, 0, 3, 0], [0, -1, 0, 0, 0, 0], [-1, -1, -3, 1, 0, -1], [0, -1, 0, 0, 0, 0], [4, 4, -1, 0, 0, 0], [0, 0, -2, 0, 0, 0], [0, 0, 1, 1, 0, -1], [1, 0, 0, 0, 0, 0], [0, -2, 0, 1, 0, 0], [0, -1, 0, 0, 1, 0], [1, 1, -2, 1, 0, -1], [-4, 0, -1, 0, -1, -1], [0, 3, 0, 0, -3, 0], [-1, 0, 0, 0, 0, 0], [-3, 0, 2, 0, 2, 1], [-1, 1, -1, 0, 0, -1], [1, 0, 1, 0, 1, 0], [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, -2, 0], [-2, 0, 0, 0, 0, -1], [-6, -6, 1, 0, 0, 0], [0, 4, 0, 0, 1, 0], [0, -2, 0, 0, 1, 0], [-1, 0, -1, 0, -1, 0], [4, 4, -2, 0, 0, 0], [1, 1, 0, 0, 0, 0], [2, 2, 0, 0, 0, 0], [0, 6, 0, 0, 1, 0], [1, 1, 0, 0, 0, 0], [0, 1, 0, 1, 2, 0], [2, 0, -5, 0, -5, -1], [0, 0, 2, 0, 2, 0], [0, 1, 0, 1, 1, 0], [-1, -1, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [3, 3, 2, 1, 0, -1], [1, 1, -1, -2, 0, 2], [1, 1, 1, 0, 0, 0], [4, 0, -1, 0, -1, 0], [0, -1, 0, -1, -1, 0], [0, -4, 0, 1, 1, 0], [-2, -2, 0, 1, 0, -1], [-10, 0, 2, 0, 2, 0], [0, -1, 0, 0, 0, 0], [14, 0, 4, 0, 4, 2], [2, 0, 1, 0, 1, 0], [-1, -2, 1, 1, 1, 0], [0, 0, -3, 0, -3, 0], [1, 0, -2, 0, -2, -1], [0, 1, 0, 0, 0, 0], [8, 0, -5, 0, -5, -1], [1, 1, 3, -1, 0, 1], [0, -2, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0]]}