# Stored data for newform 847.2.a.e, downloaded from the LMFDB on 18 April 2024.
{"label": "847.2.a.e", "space_label": "847.2.a", "level": 847, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014398543037263, "dim": 2, "is_polredabs": true, "nf_label": "2.2.13.1", "trace_hash": 1319981172891428852, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [-3, 1, 1]], [3, [-3, 1, 1]]], "qexp_display": "q-\\beta q^{2}-\\beta q^{3}+(1+\\beta )q^{4}+(-1+2\\beta )q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 3388, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 6.763329051202448, "hecke_ring_index": 1, "level_radical": 77, "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": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.012", "prec": 17}, "analytic_rank_proved": true, "char_values": [847, 1, [122, 365], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [7, 11], "conrey_indexes": [1], "field_disc": 13, "field_disc_factorization": [[13, 1]], "field_poly": [-3, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.889", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "8.652", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "55.076", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[7, -1], [11, -1]], "trace_display": [-1, -1, 0, 2], "traces": [0, 2, -1, -1, 3, 0, 7, 2, -6, 1, -13, 0, -8, -6, -1, -13, -3, -9, -7, 6, 13, -1, 0, -9, 3, 16, 16, -4, 3, -13, 13, 2, 7, 0, -2, 0, 8, 4, -3, 16, 0, -14, 7, -7, 0, 13, -2, 7, -5, 2, -8, -2, -22, -15, -11, 0, -6, -3, 0, 17, -26, 5, -1, 1, -4, -26, 0, -1, -7, -2, -13, -5, -3, 10, 24, -8, 9, 0, -34, 13, 13, -14, 7, -6, -8, 13, -3, 0, 0, 3, -13, -6, -7, -1, 16, 0, -10, 0, -1, 0, 24, 7, -25, -25, 18, -13, 27, -32, 7, 16, 0, 24, -3, -25, 21, 13, -13, -16, -2, -9, 39, 0, -9, 7, 3, 0, -7, -4, 27, -3, 52, 12, 0, 6, -32, 26, 27, 5, -25, -36, 13, 16, 9, 0, 5, 13, -5, -1, -20, -1, 56, -14, -18, 2, 0, 0, 50, 0, -13, 27, 13, -9, 20, -16, -21, 0, 3, -4, 3, 18, 52, 3, -4, -1, -39, 16, 0, -2, 57, -20, 26, -36, 16, -9, 27, -52, 7, 0, -9, -4, -39, -32, 41, -21, 13, 52, 3, 14, 0, 10, -48, -32, -10, -13, 23, 0, 19, 2, -4, 0, 13, -13, -42, 9, 3, 13, 12, 2, -8, -5, 0, 14, -12, 17, 7, 8, 6, 5, -24, 2, 52, 0, 39, -36, 34, -39, 19, -13, -2, -13, 13, -19, 0, 32, 14, 0, -49, -18, -6, 3, -39, 16, 8, 0, 2, 52, -25, 31, -18, 4, -78, 0, -6, 10, 0, -39, -3, 57, 31, 7, 13, 39, 20, 16, 43, 0, 23, -13, 31, 1, 0, -20, 5, -16, -14, -39, 0, -14, 10, 13, 78, 13, 15, 12, 7, -13, -12, 0, -19, 14, -64, -7, -19, -10, -9, 13, 25, -10, 0, 19, -13, 20, -48, 27, -26, 13, 26, 31, -72, 0, -78, 3, -2, -27, -34, -48, -31, -8, 42, 7, 0, 26, -9, -24, -24, 65, -5, -38, -87, 6, -39, 0, -21, 2, 21, 52, -6, -12, 39, 13, -8, -14, 0, 21, 53, -13, -54, -2, -3, 21, -39, -20, 44, 0, -22, 0, 24, 8, 20, -7, 0, -15, -8, 15, 0, -39, -21, 26, -11, -10, 39, 2, 55, 34, -33, 0, -35, 3, -13, 6, -130, 47, -6, -6, -20, 13, 0, 46, -57, -3, -24, -28, 29, -6, 17, -26, 0, 0, 6, -34, 91, 43, -44, 17, 25, 0, -34, 31, 0, -48, -26, -22, 39, -16, 45, -72, -24, 5, -35, 0, 39, -19, 19, -3, -1, 78, 24, -27, 35, -23, 0, 1, -46, 7, 36, -117, -28, -19, -4, 41, -56, 0, -31, -19, 30, -26, 9, -17, 12, 31, -39, -27, 0, -40, 26, -13, 18, 27, -50, -1, -26, -26, -51, 0, 52, 48, -7, -27, 78, 14, -52, 40, -23, -2, 0, -26, -29, 16, -15, -31, -13, 29, 56, 65, 48, 0, -3, -5, -21, -5, 39, -24, 5, -40, -3, 13, 0, -87, -6, 41, -13, 10, -22, -12, 17, -13, 15, 0, 24, -6, 78, -14, 39, 35, 18, -8, 86, -9, 0, 1, 117, 2, 9, 42, -48, 26, 3, -3, -49, 0, 13, 72, -52, 44, -25, 0, -34, 13, -38, 9, 0, -39, 6, 13, 91, 0, -67, 36, -7, 8, 13, 0, -3, -3, 11, 13, -5, -14, 15, 0, 39, 6, 0, 55, 7, -72, -41, -10, 52, -35, -65, -6, -13, 0, -30, -52, 33, -20, -8, 6, -104, -20, -32, -38, 0, 13, 18, -57, -46, -44, 24, -10, -3, 32, 5, 0, 31, -13, 21, 0, -39, 18, -23, -6, -73, 91, 0, 0, -94, 58, 13, 31, 3, 3, 2, -2, -20, 0, 26, -44, -13, 10, -39, 39, -22, 0, 99, -6, 0, -9, 39, -36, -99, 48, -7, 39, -6, 14, 42, 0, 128, -1, 15, 8, 56, 0, 21, 5, 16, 34, 0, -33, -52, -46, 18, 0, 12, 65, 20, -28, -26, 0, -10, -12, -7, -32, 105, -17, -81, 0, -39, 30, 0, 35, 24, -91, -1, 12, 17, 84, -13, 2, 5, 0, 19, -26, 0, 63, 0, 18, 24, 37, 20, 12, 0, -26, 9, 7, -55, 11, 39, 13, -9, -9, -25, 0, -17, 78, -95, -8, -13, -25, 10, -23, -80, -104, 0, 23, 18, 13, -65, 38, -33, 28, 74, -13, -25, 0, 49, 61, -52, 48, 27, -43, 3, 39, -53, -3, 0, -32, 39, -28, -30, 5, -78, 52, 7, -26, 44, 0, 0, -84, -14, 16, -87, -52, -95, -38, 32, 39, 0, 17, 14, 18, 18, 16, 0, 24, 36, -42, 182, 0, 35, 39, -3, 52, 42, 63, 34, 86, -91, -25, 0, -28, -49, 117, 67, -14, 21, -51, 56, -57, 40, 0, -61, 13, 16, -49, -21, -27, 104, 24, -13, -52, 0, 78, 29, -21, 30, -16, -91, 26, -28, 56, 75, 0, -2, 50, -23, 59, 39, 91, 90, -9, -139, 52, 0, -4, 76, 70, 39, 33, 50, -3, -52, 156, -5, 0, 3, -5, -16, -44, 33, 59, -9, 39, 96, 5, 0, -47, -26, 7, -36, 34, -1, 13, -109, 52, 3, 0, -39, -62, -48, -13, -6, 0, -40, -22, 70, 33, 0, 29, -7, 17, 60, -104, -88, -63, -72, -4, 39, 0, 45, 21, 16, 26, 27, -46, -92, -13, 64, 48, 0, -3, 75, -52, -23, 8, -25, 10, 52, -36, -15, 0, 54, -39, -10, 12, 56, -10, -39, -73, -6, 28, 0, 32, 59, -19, -39, -12, 13, 6, -54, 3, 84, 0, 48, -56, -32, -20, -13, -46, 26, 63, -32, 26, 0, 14, -65, -30, -24, -22, 27, -24, 72, -78, -91, 0, -85, 5, 65, -60, -72, -3, 4, 91, -25, -63, 0, -6, 13, -56, 61, -36, 31, 128, -1, 44, -17, 0, 13, 8, -8, -51, -21, 26, 39, 16, -66, 38, 0, -55, 7, -52, 9, 104, 24, -95, -17, -60, 0], "weight_parity": 1, "has_non_self_twist": 0, "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]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "847.2.a.e", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [0, -1], [0, -1], [1, 1], [-1, 2], [3, 1], [1, 0], [-3, 0], [0, 1], [-6, -1], [0, 0], [-3, -2], [-2, -2], [0, -1], [-6, -1], [-2, 1], [-5, 1], [-3, -1], [3, 0], [5, 3], [0, -1], [0, 0], [-5, 1], [0, 3], [8, 0], [6, 4], [-3, 2], [1, 1], [-7, 1], [3, 7], [1, 0], [3, 1], [0, 0], [-3, 4], [-1, 2], [3, 2], [4, -4], [0, -3], [6, 4], [3, -6], [-7, 0], [3, 1], [-4, 1], [0, 0], [6, 1], [-3, 4], [5, -3], [-3, 1], [1, 0], [0, -8], [-3, 4], [-8, -6], [-6, -3], [-6, 1], [0, 0], [-3, 0], [0, -3], [-3, 6], [9, -1], [-9, -8], [2, 1], [0, -1], [0, 1], [1, -6], [-10, -6], [0, 0], [-3, 5], [-2, -3], [-3, 4], [-6, -1], [-2, -1], [0, -3], [5, 0], [12, 0], [0, -8], [3, 3], [0, 0], [-12, -10], [6, 1], [8, -3], [-6, -2], [0, 7], [-3, 0], [-3, -2], [11, -9], [-3, 3], [-3, 6], [0, 0], [6, -9], [-3, -7], [-2, -2], [-2, -3], [0, -1], [9, -2], [-3, 6], [-3, -4], [1, -2], [0, -1], [0, 0], [8, 8]]}