# Stored data for newform 847.2.a.n, downloaded from the LMFDB on 19 April 2024. {"label": "847.2.a.n", "space_label": "847.2.a", "level": 847, "weight": 2, "hecke_orbit": 14, "hecke_orbit_code": 58546795189371727, "dim": 6, "is_polredabs": true, "nf_label": "6.6.7674048.1", "trace_hash": 1758025164410343961, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [1, -8, -4, 12, 0, -4, 1]], [3, [4, 36, 25, -20, -11, 2, 1]]], "qexp_display": "q+(1-\\beta _{1})q^{2}+\\beta _{5}q^{3}+(1-\\beta _{1}+\\beta _{2}+\\cdots)q^{4}+\\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": "0.013", "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": 7674048, "field_disc_factorization": [[2, 6], [3, 3], [4441, 1]], "field_poly": [-2, -6, 7, 8, -5, -2, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.022", "prec": 17}, {"__RealLiteral__": 0, "data": "5.621", "prec": 17}, {"__RealLiteral__": 0, "data": "0.623", "prec": 17}, {"__RealLiteral__": 0, "data": "82.834", "prec": 20}, {"__RealLiteral__": 0, "data": "22.195", "prec": 20}, {"__RealLiteral__": 0, "data": "1788.680", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[7, -1], [11, 1]], "trace_display": [4, -2, -4, 6], "traces": [0, 6, 4, -2, 4, -4, -6, 6, 12, 8, -8, 0, -14, 4, 4, 2, 8, 22, 24, 6, 2, -2, 0, 2, -20, 4, 6, -2, 4, 12, 20, -2, 8, 0, 24, -4, 18, 14, -22, 20, 18, 26, -6, -4, 0, -36, 12, -16, -24, 6, -4, -4, 12, 4, -32, 0, 12, 20, -2, -4, 24, -8, 20, 8, 26, 24, 0, 6, 12, -14, -8, 22, 16, 14, 44, -20, -30, 0, 32, -28, -4, -6, -4, 22, -14, -24, -30, 22, 0, 0, -22, 4, 10, -50, -38, -24, -62, -4, 4, 0, -52, 34, -34, -14, 26, 2, -8, 0, -56, 20, 0, 12, 8, -16, -2, -64, 0, -12, -54, 22, -24, 0, -56, 0, 48, -24, 24, 0, 20, 10, 22, 36, 0, 6, -48, 8, 38, 38, -76, -46, 2, 8, -12, 0, 84, 18, 2, -2, 74, 36, -16, -36, 2, 66, 0, 48, 8, 24, -46, 12, -42, 2, -40, -12, -22, 0, -22, 28, -20, -24, -38, 8, -56, 2, 50, 4, 0, -32, 14, 32, 28, 22, 6, -48, 0, -26, -60, 0, -2, -2, 6, 28, -134, -4, -52, -56, 4, 32, 0, -78, -88, -30, 62, 12, -88, -32, -14, 76, 12, 0, 20, -16, -6, 56, 14, 44, -34, -2, 86, -36, 0, 18, -20, -20, 8, 40, -44, -18, -48, -54, -18, 0, 16, 68, -14, 26, -94, -30, 24, -12, -50, 12, 0, 2, -2, -4, -26, -20, 82, 40, -32, -22, 18, 0, 0, -14, 20, -44, 98, 14, -4, -32, -40, 48, 0, 60, -22, 14, -62, -28, -4, -6, 78, 20, 16, 0, -124, 36, -2, 2, 18, 48, -8, -26, -48, -72, 0, 26, 120, 18, 12, 54, -46, 82, -6, -26, 64, 0, 56, -64, 52, -4, 10, -44, 4, 104, 88, -2, 0, 54, -20, -14, -44, 2, 44, -36, 0, 26, 70, 0, -20, 44, 12, 10, -18, -64, 0, -12, 28, -16, 0, -40, -46, 46, 92, -16, -24, 60, 28, 2, 20, 0, 12, 6, -78, 40, -18, 48, 54, -6, -4, -8, 0, -52, 36, -18, -44, -4, 100, -32, 16, 22, -20, 0, 12, -8, -40, 24, 72, 40, 28, 4, -76, -44, 0, 70, 46, 50, -32, 44, 44, 36, -4, -38, -122, 0, 100, -92, -62, 10, -44, 20, 12, 92, -42, 36, 0, -44, -44, 20, -56, -30, -8, 16, 136, 30, -2, 0, -104, -52, -44, -124, -58, -4, 80, 16, -54, 8, 0, -68, 24, -18, -22, -58, 12, 56, 74, -8, -36, 0, -12, 16, -34, 0, 20, -36, 136, 78, -26, -50, 0, 8, 8, -2, -84, 8, 54, 14, 26, 32, -20, 0, -56, 64, 18, 24, 2, 56, -32, 4, 50, 30, 0, -36, -52, 34, 34, 40, 12, 6, 60, -28, -142, 0, 2, -8, 12, -68, -48, -10, 44, 44, -64, -14, 0, 26, 88, 0, 134, 78, -8, -32, -72, 20, -36, 0, 118, 22, 122, 30, 14, -140, 8, -36, 16, -64, 0, 22, 52, -30, 82, 14, 44, 64, -58, 10, 224, 0, 44, -176, -34, 30, -12, -8, -56, -20, 56, 16, 0, 36, 10, -82, -30, -10, 44, -42, -40, -130, 154, 0, 10, 68, 62, 60, 60, 44, 32, 40, 84, -118, 0, 8, -70, -28, 20, 24, -46, 100, 82, 20, -4, 0, 10, 0, -58, -58, -14, -6, -28, 92, -40, -68, 0, 94, -4, 36, 80, -28, 24, -106, 4, 22, 60, 0, -38, 36, 84, -58, -14, -124, -68, -56, 58, 92, 0, -24, 0, -2, -68, 0, 192, 28, -30, -56, -28, 0, -110, -48, 32, 22, 14, -20, 66, -108, 94, -36, 0, -22, 132, -32, -98, -20, -16, 0, -68, 62, 50, 0, 0, 32, -22, -56, -6, 90, -36, -52, 110, 4, 0, 6, -8, 30, 100, -46, 10, 16, -24, 16, 44, 0, -136, -50, -50, 56, -36, 20, 28, 40, -38, 0, 0, 32, 4, 80, -46, -24, 92, -72, 88, 56, -50, 0, -62, 28, 36, 60, 2, -96, -20, -4, 80, 24, 0, -14, -98, 6, 4, 40, -180, 68, 48, -48, 32, 0, 26, -44, 34, 104, -12, -28, -52, -60, -64, -4, 0, -86, 30, 34, 234, -22, -2, -124, -80, -76, -34, 0, 170, 102, -90, -30, -38, -14, -92, -76, -70, -52, 0, -22, 26, -112, -98, -34, -72, 64, -20, 2, 196, 0, 86, -140, 38, -28, -8, 4, -228, -48, -130, -80, 0, 0, 40, 104, 26, -102, 84, -86, -56, -82, 36, 0, -20, 28, -68, 20, 6, -192, 0, -116, 22, -104, 0, -38, 180, 34, -136, -12, 2, 12, 0, 104, 56, 0, 88, 2, 8, -24, 128, -68, -76, -40, 44, -16, 0, -8, -52, -38, -96, 74, -2, -116, -44, 42, 84, 0, 76, -64, -16, -46, 144, -8, 24, 28, 0, -40, 0, 38, -92, -66, -26, -12, 32, 48, -150, 72, -140, 0, -54, 84, 46, -16, -6, -70, -92, 22, 62, -40, 0, -40, -4, -50, -24, -86, -20, -20, -40, -2, -4, 0, -64, -132, -52, 56, 50, -66, -56, -64, -148, 146, 0, 52, -34, 0, 48, 116, -82, -44, -14, 54, 48, 0, -14, -88, 158, -48, 10, -24, 24, 20, 10, -52, 0, -90, 24, 58, 30, 162, 28, 16, -152, 0, -44, 0, 86, 116, 10, -2, 20, 32, 48, -38, -156, 2, 0, 10, -80, -86, -44, -116, 76, 54, 22, 0, 140, 0, -6, -90, -110, 36, -124, 60, -22, 36, 12, 48, 0, -144, -124, -48, -116, -14, 30, 6, -4, 82, 18, 0, 58, -2, -48, -108, -18, -62, -56, 50, -270, 8, 0, 108, 88, -28, 100, -170, 38, 56, -56, 138, -80, 0, -46, 38, 162, 54, 154, 8, -138, -72, -76, -88, 0, 158, 48, -144, 132, -46, -64, 96, 74, -70, 130, 0, 2, 60, -96, -62, -38, -80, 6, 8, -76, -168, 0, 10, 110, 92, -12, -36, 208, -60, -40, -128, 110], "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.m", "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [1, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [1, -1, 1, 0, 0, 0], [-1, 1, 1, 0, -1, 0], [-1, 1, 0, 1, -1, 1], [1, 0, 0, 0, 0, 0], [2, 0, 2, -1, 0, 0], [2, -2, -1, -1, 1, 0], [-1, 0, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0], [-3, 2, -1, 3, -2, 0], [1, 0, 1, 0, -1, 1], [1, -1, 0, 0, 0, 0], [0, -1, -1, 2, 0, -2], [2, -2, 1, -3, 1, 0], [4, -1, -1, -1, 0, 0], [4, -1, 1, -1, 1, -1], [1, 1, 0, -1, 2, 1], [1, -1, -1, 0, 1, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0], [1, -2, -1, -1, 3, 0], [-4, 2, -4, 4, -1, 0], [0, 0, -4, 0, 0, -2], [2, -1, 2, 1, -1, 2], [-1, 2, -1, -1, 0, 0], [1, -1, 1, 0, 0, 0], [2, 1, 1, 1, -1, 1], [3, -1, -2, 1, 0, -2], [-1, 0, 1, -1, -2, -2], [2, -3, 1, -3, 3, -1], [0, 0, 0, 0, 0, 0], [5, -3, 1, 0, 1, 0], [-1, 1, 1, 0, -1, 0], [3, -2, 4, -2, 0, -2], [4, -3, 2, 1, 1, 2], [-4, 0, -2, -2, 0, -1], [4, -2, -2, 2, 0, 0], [2, 1, -3, 1, -1, -2], [4, 1, -1, -1, 1, 0], [-1, 1, 0, 1, -1, 1], [-2, 3, -1, 2, -3, -1], [0, 0, 0, 0, 0, 0], [-6, 1, 4, 1, -1, 1], [1, 0, -1, -3, 1, -3], [-3, 2, 3, -1, 2, 1], [-5, 4, -7, 3, 0, 1], [1, 0, 0, 0, 0, 0], [-2, 2, -4, 2, 2, -2], [1, 0, -1, -1, 1, 5], [3, -2, 1, 2, -1, 1], [0, 2, 1, 1, -3, 0], [-6, 2, -2, 0, 1, 0], [0, 0, 0, 0, 0, 0], [2, 0, 2, -1, 0, 0], [4, -1, -3, -4, 3, 1], [1, -2, 0, 2, -2, 2], [-3, 4, -3, 3, 0, -3], [5, -1, 0, -3, 1, 2], [-4, 6, 4, -2, -1, -2], [4, -2, 4, -2, 3, 0], [2, -2, -1, -1, 1, 0], [3, 0, 2, -2, 2, -4], [3, 0, -3, 2, -1, -3], [0, 0, 0, 0, 0, 0], [-1, 4, -1, 1, 1, -2], [3, -4, 5, 0, 0, -1], [-3, 4, -1, -3, 0, 2], [-1, 0, 1, 0, 0, 1], [4, 1, -1, 0, 0, 2], [5, -7, 6, -6, 2, 0], [1, 1, -4, -1, -2, -3], [9, -4, 3, 0, -3, 1], [-2, 0, 6, -6, 2, 4], [-7, 3, 0, 1, -1, -3], [0, 0, 0, 0, 0, 0], [6, -2, -2, 4, -2, 0], [-6, 3, 3, 2, 1, -1], [-2, 1, -2, 3, -1, -3], [-2, 3, 2, -1, 1, 0], [0, -3, -2, -1, 1, -1], [3, 3, 0, 3, -2, 1], [-3, 2, -1, 3, -2, 0], [-6, 5, 5, 1, -5, -1], [-5, 2, -3, 5, -1, 2], [5, -3, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0], [0, -1, -4, -1, -3, -1], [-4, 3, 3, -1, -2, 2], [1, 0, 1, 0, -1, 1], [0, 1, 3, -4, 0, -4], [-10, 3, -1, 6, -2, -2], [-7, 1, 0, -5, 0, -1], [-5, 0, 1, 3, -1, -3], [-13, 9, -6, 3, -2, 1], [-1, 3, 1, -2, 1, 2], [1, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-10, 4, -2, 2, 0, 0]]}