# Stored data for newform 931.2.v.b, downloaded from the LMFDB on 19 April 2024. {"label": "931.2.v.b", "space_label": "931.2.v", "level": 931, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4505042769937315, "dim": 6, "is_polredabs": true, "nf_label": "6.0.19683.1", "trace_hash": 535483043845600526, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [9, -27, 36, -24, 9, -3, 1]], [3, [1, -3, 6, -8, 12, -6, 1]]], "qexp_display": "q+(1-\\zeta_{18}^{2}-\\zeta_{18}^{3}-\\zeta_{18}^{4})q^{2}+(1+\\cdots)q^{3}+\\cdots", "char_order": 9, "char_parity": 1, "char_degree": 6, "char_conductor": 133, "char_orbit_label": "v", "char_is_real": false, "Nk2": 3724, "analytic_conductor": 7.434072428181204, "hecke_ring_index": 1, "level_radical": 133, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 18, "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": "0.017", "prec": 17}, "analytic_rank_proved": true, "char_values": [931, 9, [248, 344], [3, 7]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [7, 19], "conrey_indexes": [177, 214, 263, 275, 422, 606], "field_disc": -19683, "field_disc_factorization": [[-1, 1], [3, 9]], "field_poly": [1, 0, 0, -1, 0, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.076", "prec": 17}, {"__RealLiteral__": 0, "data": "5.682", "prec": 17}, {"__RealLiteral__": 0, "data": "0.426", "prec": 17}, {"__RealLiteral__": 0, "data": "89.175", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2128.287", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c9", "trace_display": [3, 6, 3, 0], "traces": [0, 6, 3, 6, -9, 3, 3, 0, 6, 12, 0, 0, 3, -3, 0, 3, 9, -6, 3, 6, -6, 0, 0, -12, 6, -9, 15, 6, 0, -3, 0, -18, -18, 9, 0, 0, -24, 0, 12, 12, 9, 21, 0, -3, -9, 30, -18, -12, -3, 0, -15, 3, 6, -12, -6, 18, 0, 24, -18, -6, 3, -12, -12, 0, -12, 24, 18, 6, 30, -12, 0, -6, 15, -12, -30, -15, 36, 0, 15, 24, 12, -3, 9, 0, 0, 0, -48, -21, -18, 15, 18, 0, 42, -36, -9, -15, -9, 18, 0, 9, 27, 15, 18, -36, -51, 0, 9, 0, 18, 0, 9, -27, 0, -18, 48, 0, 42, -33, -27, 0, 0, 15, -3, 12, 33, -12, 0, 45, -42, -27, 27, -15, 0, 0, 24, 21, -18, -12, 0, 15, 0, -21, -18, -18, 36, -9, 24, 0, -3, 30, -15, 30, -21, -24, 0, -21, -18, 33, -21, -3, 9, 0, -33, 0, -78, 9, 90, -48, 0, -39, -9, 21, 45, 48, -27, 0, -18, -42, 36, 27, -33, 54, 0, 21, 18, 6, -30, -18, 6, 0, -27, -27, -39, 24, -30, 24, 0, 18, 0, 24, 24, -24, 0, 0, -6, 0, -3, -48, -9, -27, 0, -39, 6, 30, 27, -21, 33, 0, -48, 0, -18, 6, -39, 6, 0, -51, -36, 18, -6, -9, -18, 0, 63, 12, -3, -18, -6, 9, 0, 9, -15, 24, 39, -42, 33, 0, -18, 42, 3, 81, -54, -12, 0, 0, -21, 0, -27, -3, -3, 0, 24, -75, -99, -15, -45, 18, 0, 60, -30, -69, -9, 36, -51, 0, 9, 9, 6, -15, -12, -78, 0, -21, -9, 27, 12, -6, 0, 0, -36, 18, -36, -15, -36, -9, 0, -45, 84, 0, -45, 12, 6, 0, 69, -21, -81, -3, 9, -54, 0, -27, -27, 54, 3, 9, -21, 0, -54, -3, 9, 9, 30, 0, 0, 30, -15, -3, 24, -15, 27, 0, 9, 90, 9, -42, 18, 24, 0, 6, 0, -90, 45, -27, 84, 0, 111, 0, 162, -24, 15, 0, 0, -21, 0, 45, -72, 72, -3, 0, 45, 12, 27, 60, 60, 15, 0, 24, 69, 60, -48, 102, -27, 0, -6, -42, 9, -12, -9, 3, 0, 90, 75, 24, -81, 3, -60, 0, 69, -30, -33, 51, 27, 18, 0, -33, -72, 15, 18, 69, -120, 0, -12, 3, -48, -12, -12, 12, 0, 9, -36, -90, 27, -3, 105, 0, -54, -18, 9, 3, 27, 18, 0, 18, 6, -12, -63, 12, 54, 0, -54, 18, -90, 15, -9, -3, 0, -9, -33, 24, -12, -21, 18, 0, -18, 114, 30, 0, -57, -24, 0, -45, -69, 45, -9, 30, -9, 0, -84, 0, 141, 3, 36, 39, 0, 45, -12, -39, 9, 126, 51, 0, -18, 9, 90, -27, 33, 27, 0, -48, -9, 51, 9, -21, 51, 0, -63, 33, -33, -6, -60, 45, 0, -51, 12, 27, 42, -9, -30, 0, 117, -30, 96, -30, -90, 51, 0, -9, 18, -3, -99, -66, 18, 0, 150, 78, 0, -39, 45, -27, 0, 120, 9, 54, -90, -120, 84, 0, -135, 24, -45, 0, 18, 12, 0, 6, 72, 0, -24, 54, -108, 0, 30, 6, 15, 42, 9, 15, 0, 24, 114, 48, 18, 87, 0, 0, -111, -12, 24, 33, -21, 39, 0, 0, 72, -54, -3, -27, 6, 0, -18, 36, 27, 0, 27, -90, 0, -12, -105, -42, -15, 18, 63, 0, -48, -45, -96, -12, -36, -24, 0, 9, -18, -72, 24, -12, 27, 0, -51, -24, -18, -93, 42, 81, 0, -132, -108, 12, -63, 18, -18, 0, -9, 3, 84, 18, -21, 9, 0, 105, 6, -54, 60, -48, 63, 0, 63, -72, -111, 9, -63, -21, 0, 60, 66, -9, -162, 60, -21, 0, 45, -6, -63, 30, 0, -3, 0, -48, 54, 9, 69, 81, -30, 0, 51, -81, -12, 18, 111, -12, 0, 132, 9, 27, 51, -3, -252, 0, -120, -36, 24, 18, 0, -36, 0, 0, -21, -63, 42, 0, -108, 0, 27, 18, -9, -36, 57, -126, 0, 117, -93, -51, 18, -24, -114, 0, 9, -66, 90, -45, -138, 75, 0, -69, -12, -9, 0, -36, 9, 0, 21, 51, 36, 69, -72, 30, 0, -45, 45, 9, 108, 111, 30, 0, 75, 48, -108, -57, -33, -39, 0, 60, 72, -3, -9, -150, 33, 0, 18, -90, 27, 33, -21, 75, 0, 48, 3, 54, 24, 126, 27, 0, 9, 60, -30, -12, -9, 69, 0, -57, 6, 18, 36, 9, -21, 0, -45, -18, 144, 60, 48, -3, 0, -3, -45, -39, -75, 24, 129, 0, 90, -78, -3, 0, 72, -75, 0, 24, 27, -36, 36, -78, -63, 0, -9, 51, 6, 0, 24, 54, 0, 0, 9, 114, 81, 0, -18, 0, -42, -105, 81, -81, 0, 27, 0, -51, -9, -3, 12, -12, -66, 0, -117, -21, 9, 27, -60, 27, 0, 6, 132, -126, 81, -96, -84, 0, -12, -81, -9, -27, 27, 12, 0, -63, 24, -66, 54, -36, 27, 0, -30, 30, 45, -60, 12, 141, 0, 57, -81, -33, 27, -21, 42, 0, -36, -36, -45, 18, -102, -42, 0, -90, 0, -156, 93, -36, 90, 0, -36, 15, -156, -9, -9, -99, 0, -48, -84, -27, 54, -39, 75, 0, 36, 45, 63, -57, -81, -117, 0, -42, 207, 57, 90, 0, -18, 0, 81, -30, -21, 63, 36, -57, 0, -216, -39, -27, 96, -3, 6, 0, 72, -9, 36, -51, -45, -30, 0, -57, 87, -105, -36, -15, -36, 0, 84, 99, 81, -18, -33, 15, 0, -102, 9, 24, 24, -36, 84, 0, -9, -51, 45, -60, 66, -174, 0, 3, 9, 117, 27, 54, 72, 0, 3, -48, 30, 27, -111, -57, 0, 24, -39, 21, -18, -96, 111, 0, -21, -63, -126, 9, 69, 27, 0, 54, -72, -195, 45, -90, 81, 0, -156, -42, 9, 42, 9, 144, 0, 60, -90, 24, -39, -90, 117], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 133, 21, 1, 9, 0]], "char_orbit_index": 22, "prim_orbit_index": 21, "minimal_twist": "19.2.e.a", "char_is_minimal": false, "conrey_index": 177, "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, -1, -1, -1, 0], [1, 0, -1, 0, -1, 1], [-2, -2, -1, 1, 1, 1], [1, 1, 0, -1, 0, 1], [0, 0, -2, 1, -1, 2], [0, 0, 0, 0, 0, 0], [0, -1, 3, 2, 3, -1], [1, 1, 0, 2, -3, 0], [1, 1, 0, -2, -2, 0], [0, -1, 2, 0, -1, -1], [0, 0, 1, 1, 1, 0], [-2, -2, 0, 3, -1, 0], [0, 0, 0, 0, 0, 0], [1, 0, 0, -1, -1, 1], [3, 1, 3, -3, -1, -3], [-1, -2, -1, 0, 0, 0], [0, 0, -4, 1, -4, 0], [2, -4, -2, -2, 2, 1], [-1, -3, -3, 0, 2, 1], [0, 0, 0, 0, 0, 0], [0, -3, 0, 0, 0, 0], [-2, 0, -2, 0, -2, 0], [3, -2, 4, -4, 2, -3], [-2, 1, -2, 1, -2, 0], [0, 0, 1, 5, 1, 0], [0, 0, -3, 2, -3, 0], [0, 0, 0, 0, 0, 0], [-1, 1, -5, 1, -1, 0], [0, -1, -1, 0, -1, 2], [-3, -1, -1, 0, 3, -2], [-3, 0, 0, 0, -3, 0], [2, -3, 1, -1, 0, 1], [-2, -2, 0, 4, 4, 3], [0, 0, 0, 0, 0, 0], [-5, -3, -2, 2, 3, 5], [0, 3, -1, 0, -2, -2], [1, -3, -1, 2, 5, 6], [0, 1, -2, 4, -2, 1], [1, 0, -1, 1, 6, 2], [4, 4, 3, -1, 0, 1], [0, 0, 0, 0, 0, 0], [2, 0, -2, -5, 0, -3], [-2, 1, 0, 1, 1, 3], [5, -1, -1, 0, 1, 0], [-6, -2, -2, 6, 4, 4], [-1, -1, 2, -2, 3, -2], [2, -5, 2, -5, 2, 0], [0, 0, 0, 0, 0, 0], [-5, 0, -2, 5, 2, 2], [0, -1, 0, 1, 1, 1], [3, 6, 4, -4, -6, -3], [-3, -3, 2, 2, 1, -2], [-4, -1, -6, 6, 1, 4], [3, -3, 0, 0, 3, -3], [0, 0, 0, 0, 0, 0], [5, -4, 0, -2, 1, 5], [-6, 1, -5, 6, 4, 4], [0, 7, -2, -2, 0, 2], [0, 0, 0, 1, 2, 1], [0, -4, 3, -4, 0, 0], [-3, 0, 3, 2, 7, -1], [0, 0, 0, 0, 0, 0], [-4, 3, 0, 4, -3, -3], [4, -5, -5, 0, 5, 0], [3, -3, 0, 0, 0, 3], [-2, -4, 0, 6, 6, -6], [5, 7, 7, 0, -3, -4], [-4, 2, -2, 4, 0, 0], [0, 0, 0, 0, 0, 0], [-2, 0, 2, 2, -10, 0], [3, -1, 13, -1, 3, 0], [-4, 0, 4, 4, 0, 0], [-5, -1, -5, 0, 0, 0], [-5, 4, -3, 5, -1, -1], [5, 6, 9, 2, -3, -7], [0, 0, 0, 0, 0, 0], [1, 4, -3, 3, -4, -1], [7, -3, 6, -6, 3, -7], [3, 3, 4, -2, -1, -4], [0, 5, 1, -1, -5, 0], [7, 4, 0, -11, -11, -6], [0, -9, 3, 0, 6, 6], [0, 0, 0, 0, 0, 0], [1, -2, -3, -2, 1, 0], [-8, -8, -7, 0, 8, 7], [-7, 7, -6, 7, -1, -1], [-3, 6, 6, 0, -3, -3], [3, -2, 0, -1, -1, 5], [5, 0, -5, -4, -3, 1], [0, 0, 0, 0, 0, 0], [6, 8, 8, 2, 0, -2], [-5, 0, 5, -2, 8, -7], [0, -2, 4, -3, 4, -2], [1, 1, -3, -7, 0, 4], [-3, 0, 0, 3, 0, 0], [2, 5, -2, 2, -5, -2], [0, 0, 0, 0, 0, 0], [4, 1, 0, -5, -5, 6], [4, 5, 5, 1, 0, -1]]}