# Stored data for newform 847.2.f.f, downloaded from the LMFDB on 25 April 2024.
{"label": "847.2.f.f", "space_label": "847.2.f", "level": 847, "weight": 2, "hecke_orbit": 6, "hecke_orbit_code": 22518341767791439, "dim": 4, "is_polredabs": true, "nf_label": "4.0.125.1", "trace_hash": 2094193807009584154, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [0, 1]], [3, [1, 1, 1, 1, 1]], [13, [256, -64, 16, -4, 1]]], "qexp_display": "q+\\zeta_{10}^{2}q^{3}+2\\zeta_{10}^{3}q^{4}-3\\zeta_{10}q^{5}+\\cdots", "char_order": 5, "char_parity": 1, "char_degree": 4, "char_conductor": 11, "char_orbit_label": "f", "char_is_real": false, "Nk2": 3388, "analytic_conductor": 6.763329051202448, "hecke_ring_index": 1, "level_radical": 77, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 10, "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": [847, 5, [122, 365], [5, 2]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 4, "level_primes": [7, 11], "conrey_indexes": [148, 323, 372, 729], "field_disc": 125, "field_disc_factorization": [[5, 3]], "field_poly": [1, -1, 1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.226", "prec": 17}, {"__RealLiteral__": 0, "data": "0.926", "prec": 17}, {"__RealLiteral__": 0, "data": "118.951", "prec": 24}, {"__RealLiteral__": 0, "data": "59.376", "prec": 20}, {"__RealLiteral__": 0, "data": "4961.854", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c5", "trace_display": [0, -1, -3, -1], "traces": [0, 4, 0, -1, 2, -3, 0, -1, 0, 2, 0, 0, -8, 4, 0, -3, -4, 6, 0, -2, 6, 4, 0, 12, 0, -4, 0, 5, 2, 6, 0, -5, 0, 0, 0, -3, -4, -11, 0, 4, 0, -6, 0, 32, 0, -24, 0, 0, -4, -1, 0, 6, -8, 6, 0, 0, 0, -2, 0, 9, 6, 10, 0, 2, 8, -48, 0, 20, -12, -3, 0, -9, 0, -2, 0, -4, -16, 0, 0, 10, -12, -1, 0, -12, 2, 18, 0, -24, 0, -12, 0, 4, 6, -5, 0, -6, 0, 1, 0, 0, -32, 12, 0, 4, 0, -3, 0, -6, -10, 80, 0, 44, -4, 3, 0, -9, -12, -8, 0, 6, 0, 0, 0, -6, 10, 3, 0, -2, 0, -8, 0, -24, 0, 8, 0, 15, 0, 3, 0, -14, 6, 0, 0, 0, -32, 18, 0, -1, 22, 6, 0, 10, 0, 48, 0, 60, -8, 13, 0, 6, 0, -3, 0, -20, -48, 0, 0, -6, 0, -3, 0, 4, 16, 0, 0, 16, 0, -36, 0, 15, -12, 7, 0, 10, 0, -33, 0, 0, 0, 5, 0, 27, 8, -14, 0, 12, 2, 72, 0, -64, 0, -5, 0, 6, -12, -18, 0, 6, -64, 0, 0, -14, -12, -9, 0, -24, 0, -5, 0, 8, 0, 96, 0, 19, 0, 8, 0, 12, 4, -5, 0, 0, 0, -6, 0, 0, -18, 10, 0, 12, -12, -112, 0, 64, -20, -3, 0, 8, 0, -12, 0, 9, 16, 0, 0, 18, -16, 6, 0, -11, -24, -12, 0, -120, 0, -72, 0, 3, 10, -30, 0, 16, 24, 4, 0, 0, -24, -8, 0, 10, 0, -12, 0, -32, 18, 24, 0, 24, 0, -19, 0, 1, 4, 30, 0, 27, 0, 0, 0, 12, 8, -8, 0, 12, -8, 30, 0, 80, 0, -16, 0, 0, 0, 19, 0, 6, -20, -9, 0, 0, -96, -6, 0, 12, 2, 16, 0, -20, 0, 0, 0, -4, 24, 22, 0, -15, -4, -14, 0, 3, 144, 0, 0, -1, 0, -9, 0, 18, -12, 10, 0, 80, 0, -12, 0, -27, -6, 6, 0, -24, 0, 15, 0, 0, 32, -6, 0, -17, -12, 12, 0, 6, 10, -16, 0, -12, 0, -24, 0, -11, 12, -2, 0, -21, 0, 0, 0, 16, -2, -33, 0, 18, 0, 6, 0, -120, 0, 8, 0, -2, -16, 6, 0, 20, -24, -3, 0, 0, 0, -14, 0, 3, -8, 9, 0, -36, 0, 56, 0, 96, 6, 10, 0, 0, 0, 24, 0, 10, -48, 0, 0, -12, 20, -11, 0, 18, 40, -6, 0, 104, 0, -8, 0, -9, 22, 9, 0, 6, 8, 9, 0, 0, 24, 10, 0, 12, 0, -8, 0, -30, 18, -24, 0, 20, 24, -15, 0, -15, 16, -5, 0, 13, 0, 0, 0, -8, -12, -12, 0, 12, 0, 44, 0, 12, 0, -12, 0, -11, 0, -20, 0, 30, 12, -36, 0, 0, 80, -9, 0, 4, -6, -6, 0, 0, 0, -144, 0, 12, 4, -21, 0, -2, 0, 10, 0, 12, -64, 0, 0, 0, 0, -3, 0, 16, -12, -4, 0, -120, 0, -56, 0, -18, 4, 24, 0, -18, 0, 15, 0, 0, 120, 16, 0, 7, 0, -60, 0, -8, -6, 80, 0, -48, 0, 10, 0, -33, 28, -30, 0, 32, 48, 0, 0, -36, 0, 9, 0, -1, 0, 18, 0, -16, 0, -108, 0, -12, -16, -11, 0, -14, -36, -12, 0, 0, 0, -24, 0, -12, 2, -10, 0, -18, -44, 24, 0, -72, -12, 16, 0, 0, 0, -8, 0, 10, 80, 0, 0, -14, 0, 6, 0, 0, 24, 16, 0, 72, 0, -120, 0, 19, 30, 15, 0, 3, 16, 29, 0, 0, 104, 66, 0, -11, 0, -14, 0, -6, -12, -16, 0, -72, 0, -15, 0, 49, 6, -24, 0, 33, 0, 0, 0, -5, 40, -39, 0, 18, -24, 4, 0, 120, 0, -196, 0, -24, 0, -6, 0, 18, 12, 19, 0, 0, 0, 28, 0, 20, 6, 18, 0, 1, 0, -48, 0, 48, -8, 9, 0, -5, -32, -24, 0, -35, 0, 0, 0, -42, 0, 36, 0, -6, 8, 0, 0, 88, 0, 0, 0, 12, -18, 1, 0, -20, 0, -15, 0, 0, 120, 12, 0, 39, 24, 4, 0, 28, -14, -96, 0, 68, 0, -13, 0, 48, -20, 4, 0, -3, 0, 0, 0, 34, 66, 8, 0, -24, 0, 18, 0, -96, 0, 24, 0, 31, 0, 9, 0, 30, -10, -38, 0, 0, 0, -48, 0, -20, -54, -36, 0, -36, -16, -160, 0, -24, 28, 6, 0, -20, 0, -11, 0, -12, 96, 0, 0, -30, -4, 39, 0, -50, 36, 30, 0, -12, 0, 160, 0, 18, -32, 21, 0, 0, 0, -6, 0, 0, -40, -9, 0, -30, 0, -30, 0, -2, -12, -64, 0, 240, 24, -16, 0, -8, 36, -18, 0, -23, 0, 0, 0, -36, -12, 25, 0, -8, -32, 6, 0, 72, 0, -100, 0, 15, 0, -7, 0, -12, 28, -9, 0, 0, -96, -32, 0, -33, 18, 10, 0, 12, 0, -48, 0, -52, 48, -6, 0, 12, 0, 0, 0, -19, -40, 0, 0, 20, 0, -2, 0, 3, 4, 22, 0, -120, 0, -36, 0, -20, 48, 27, 0, 42, 0, -2, 0, 0, 152, 0, 0, 45, 0, 12, 0, 30, -16, 144, 0, 32, 0, 21, 0, -8, -24, -24, 0, -48, 32, 0, 0, 30, 10, 6, 0, 16, 0, -20, 0, -144, 0, 176, 0, -8, 0, -18, 0, -2, 12, 0, 0, 0, 0, -20, 0, 19, 0, -18, 0, -18, 36, -60, 0, -108, -20, 8, 0, -9, 0, 36, 0, 81, 96, 0, 0, 3, 24, 6, 0, 12, -56, -42, 0, 56, 0, -48, 0, 39, 32, -14, 0, 16, 40, -9, 0, 0, -24, 40, 0, -33, 0, -54, 0, 0, -16, 96, 0, -64, 0, 1, 0, 48, 24, 28, 0, 55, 0], "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, 3, 11, 3, 1, 5, 0]], "char_orbit_index": 6, "prim_orbit_index": 3, "minimal_twist": "77.2.a.b", "char_is_minimal": false, "conrey_index": 148, "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], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 2], [0, -3, 0, 0], [0, 0, 0, 0], [0, 0, 0, -1], [0, 0, 0, 0], [2, -2, 2, -2], [0, 0, 0, 0], [0, 0, 0, 0], [-2, 0, 0, 0], [4, -4, 4, -4], [0, 0, 0, 0], [0, 0, 0, -3], [0, -4, 0, 0], [0, 6, 0, 0], [0, 0, 0, 0], [0, 0, 2, 0], [6, -6, 6, -6], [1, 0, 0, 0], [0, 0, 0, 0], [3, 0, 0, 0], [0, 0, 0, 0], [0, 0, 4, 0], [0, 0, 0, 0], [0, 5, 0, 0], [0, 2, 0, 0], [0, 0, 0, 6], [0, 0, 0, 0], [-5, 5, -5, 5], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-3, 3, -3, 3], [0, 0, 4, 0], [0, 0, 0, -11], [0, 0, 0, 0], [0, 4, 0, 0], [0, 0, 0, 0], [0, 0, 6, 0], [0, 0, 0, 0], [8, 0, 0, 0], [0, 0, 0, 0], [-6, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -4], [0, -1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 6], [0, 0, 8, 0], [6, -6, 6, -6], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-2, 2, -2, 2], [0, 0, 0, 0], [0, 0, 0, 9], [0, 6, 0, 0], [0, 10, 0, 0], [0, 0, 0, 0], [0, 0, -2, 0], [8, -8, 8, -8], [-12, 0, 0, 0], [0, 0, 0, 0], [5, 0, 0, 0], [-12, 12, -12, 12], [0, 0, 3, 0], [0, 0, 0, 0], [0, -9, 0, 0], [0, 0, 0, 0], [0, 0, 0, -2], [0, 0, 0, 0], [-4, 4, -4, 4], [-4, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [10, -10, 10, -10], [0, 0, 12, 0], [0, 0, 0, -1], [0, 0, 0, 0], [0, -12, 0, 0], [0, 0, 0, 2], [0, 0, -18, 0], [0, 0, 0, 0], [-6, 0, 0, 0], [0, 0, 0, 0], [-3, 0, 0, 0], [0, 0, 0, 0], [0, 0, -4, 0], [0, 0, 0, 6], [0, -5, 0, 0], [0, 0, 0, 0], [0, 0, 0, -6], [0, 0, 0, 0], [1, -1, 1, -1], [0, 0, 0, 0], [0, 0, 0, 0], [-8, 0, 0, 0]]}