# Stored data for newform 845.2.a.l, downloaded from the LMFDB on 23 April 2024.
{"label": "845.2.a.l", "space_label": "845.2.a", "level": 845, "weight": 2, "hecke_orbit": 12, "hecke_orbit_code": 49539595934630733, "dim": 4, "is_polredabs": true, "nf_label": "4.4.4752.1", "trace_hash": 1074877747157976136, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [1, -4, -3, 2, 1]]], "qexp_display": "q-\\beta _{1}q^{2}-\\beta _{3}q^{3}+(\\beta _{1}+\\beta _{2})q^{4}+q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 3380, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 6.747358970798192, "hecke_ring_index": 1, "level_radical": 65, "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": "0.016", "prec": 17}, "analytic_rank_proved": true, "char_values": [845, 1, [677, 171], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [5, 13], "conrey_indexes": [1], "field_disc": 4752, "field_disc_factorization": [[2, 4], [3, 3], [11, 1]], "field_poly": [1, 4, -3, -2, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.682", "prec": 17}, {"__RealLiteral__": 0, "data": "0.159", "prec": 17}, {"__RealLiteral__": 0, "data": "36.806", "prec": 20}, {"__RealLiteral__": 0, "data": "1.056", "prec": 17}, {"__RealLiteral__": 0, "data": "545.593", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[5, -1], [13, -1]], "trace_display": [-2, -2, 4, -10], "traces": [0, 4, -2, -2, 2, 4, 4, -10, -6, 4, -2, 0, -10, 0, 2, -2, 2, -2, -20, -16, 2, -4, 12, -10, 24, 4, 0, -2, -8, 8, 4, -8, -4, -18, 4, -10, 20, 2, 8, 0, -6, -8, -4, -2, -12, 4, -16, -8, -28, 12, -2, 4, 0, -12, 16, 0, 12, 14, -22, -12, -10, 28, 4, -4, 4, 0, 6, -30, 14, -16, 2, -4, -12, 8, -10, -2, -20, 18, 0, -8, 2, -8, 4, 12, 28, -2, 4, -22, -18, 12, -20, 0, 22, -8, -32, -16, -4, -2, 24, -24, 2, -4, 10, -52, 0, -4, 24, -34, -34, -20, 12, 32, 22, -26, -34, -10, 46, 0, -12, -16, 24, 16, -2, -2, 20, 4, 56, -6, 18, 4, 0, 0, 36, 46, 18, -2, -12, 18, 38, 28, -8, -20, 20, 0, 32, 8, -28, 36, 4, 4, 4, -20, 42, -8, -36, -8, 0, 8, 52, 12, -4, 40, 22, -18, 8, -18, 0, 2, -54, 0, 4, -16, 14, -22, 68, -10, 24, 6, -72, 36, 20, 24, 0, -26, -12, 2, 28, -18, 56, 20, 8, 16, 46, -58, 10, 0, 0, 22, 24, 36, -6, 24, 50, -26, -22, -8, 44, 32, 0, 0, -4, -24, -24, 74, 20, -2, 24, 8, 16, -16, -12, 0, -28, -34, 22, 4, -8, -30, 64, 40, -16, 36, -54, -32, 0, -8, 0, -8, -28, 32, -28, -36, -8, -8, -10, 12, 10, 0, -24, 36, -2, 24, -32, -6, 12, 4, -26, -42, 10, -32, 0, 44, 12, 6, -48, -12, 4, 6, -12, 40, 16, -28, -28, 0, -66, 0, -50, -34, -62, -8, 12, 24, 76, -26, -20, 14, 0, 14, -16, -28, -22, -44, -8, -54, -36, -12, 36, 42, 40, 0, -10, -16, 40, 14, -8, 28, -20, -20, -6, 20, 4, 8, 0, 44, -4, -4, -40, 4, -36, -24, 4, 20, 52, -10, 26, 0, 78, -8, -6, 20, 6, -20, -36, 20, -34, -30, 52, 12, 0, 64, 14, 0, 104, -26, -12, -16, 56, -14, -122, 8, 2, 0, 30, -6, -6, -4, 48, 14, -42, -40, -12, 0, 24, 40, 0, 8, 16, 6, 52, -8, -10, 24, -28, -38, -6, -2, -36, 0, -28, -48, -20, -36, -26, 34, -48, 18, 50, -8, 20, -16, 0, -4, 0, -36, 10, -8, -12, -26, -102, -8, 2, 52, -36, 0, -86, -8, 34, -78, -6, -12, 4, -96, -20, 42, -4, 12, 0, -74, -42, 84, 28, -40, 18, 64, 24, -2, -94, -46, -2, 0, 4, -24, -4, 10, -28, -22, -64, 34, 8, -4, -18, -48, 0, -48, -20, 12, 14, 46, -58, 12, -20, 0, 2, 76, 6, 0, -108, -10, -8, -32, 22, -16, -42, 16, 34, -8, 4, 12, 0, 60, -32, 44, 30, -18, -32, -16, -8, -48, 32, 36, -4, 0, 84, 58, -88, -2, -8, 18, -42, 60, 24, 40, -4, 26, 0, -24, -4, -62, -72, -88, 2, -76, -18, 14, -12, -4, -30, 0, 6, 60, 10, 28, 70, 26, -36, -52, -22, -48, 34, 32, 0, -80, -124, -10, 24, -4, -12, 40, 18, -4, 24, 24, 50, 0, 42, -34, 48, -6, 46, -48, -34, 20, -76, 72, -16, -20, 0, -16, 48, 4, 12, -56, 30, 20, 44, 32, 62, -18, -8, 0, 22, 60, 24, -6, -136, -26, 64, -10, 78, 0, -34, 16, 0, 82, -16, -10, -20, 16, 56, 20, 46, -36, 64, 24, 12, 0, 66, 58, 12, 8, -12, -8, -50, 16, -18, -16, -64, -6, 0, -8, 24, -52, -28, -36, -64, 16, -100, 22, 22, 52, -2, 0, 8, 34, 16, -2, 60, -10, -40, -32, 20, -28, 20, -18, 0, 4, -40, 30, 40, 20, 56, 52, -12, 42, -44, -6, 84, 0, 24, -40, 18, -12, -22, -50, -28, 4, -22, -82, -54, -24, 0, 56, -24, 70, -56, 0, -4, 56, 80, 12, 36, -32, -104, 0, 60, 46, -16, 34, 52, 104, 18, 60, 10, 74, -48, -2, 0, -48, -62, 20, -12, 72, -36, 46, -116, 18, -122, 16, -28, 0, 38, 20, -134, 72, 52, 28, 144, 22, 44, 76, -8, 0, 0, -2, -72, -20, -18, 34, 0, 20, 20, -104, 18, 32, -22, 0, -42, 68, -64, 84, 32, 112, 0, -18, -36, 8, -128, -8, 0, -56, -28, 40, -10, 12, 12, 36, 4, -18, 16, -132, 4, 0, -60, 10, -24, 4, 4, 0, 48, 64, 4, -40, 56, 18, 0, -20, 40, 86, 0, 84, 42, -52, 42, 116, -34, -8, -14, 0, 46, 112, -36, 0, 4, -6, -20, -8, -72, -74, -16, 20, 0, -108, -46, -70, -132, 8, 60, -22, 20, 0, 52, 20, 0, 0, -74, 12, 66, -34, 58, 28, -4, 144, 28, 12, 72, 40, 0, -26, 54, 0, 22, -32, -76, 38, 48, -18, 26, -10, 108, 0, 8, -12, 144, -18, 48, -18, 60, 28, 88, 56, 0, -28, 0, 84, 136, 2, 42, -32, -30, 108, -54, -16, -16, -48, -30, 0, -80, 8, -36, 88, 4, -20, 64, -12, -10, -16, 36, -20, 0, 8, 14, 32, -24, -36, 32, -22, -104, -4, -20, 108, 68, 0, 60, -20, 106, -10, -20, 26, -34, 36, 24, 36, -48, 8, 0, 6, 0, -94, 42, 36, -72, 24, -80, 8, -110, 36, -78, 0, 0, 32, 20, 12, -30, 14, 96, 24, -140, -46, -60, -100, 0, 128, 118, -36, -22, -26, 32, 0, -2, 4, -12, -32, -28, 0, -42, 2, 40, -88, -32, 16, 28, -72, -88, 20, 84, -18, 0, -88, -30, -148, 56, 44, -4, 26, 24, 20, -6, -18, 140, 0, 8, -44, 66, 90, 96, 16, -80, 54, 0, 60, 46, -60, 0, -40, -144, -58, -86, -92, 120, -4, 10, -48, 80, -10, 102, 0, 38, -14, -84, -132, 0, -32, 82, -8, -36, 22, -4, 80, 0, -4, 24, 16, -4, -74, -56, 36, 60, -42, -4, -40, -6], "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": "65.2.m.a", "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], [1, 0, 0, 0], [0, -1, 0, 0], [0, 0, 0, -1], [0, 1, 1, 0], [1, 0, 0, 0], [0, 1, 1, 1], [-3, 0, -1, 1], [-1, 0, -1, -1], [0, 2, 0, 0], [0, -1, 0, 0], [0, -2, -1, 2], [-1, -3, -2, 0], [0, 0, 0, 0], [-1, 3, -1, 0], [0, 0, 0, -1], [-1, 1, -1, 2], [0, 0, 2, -1], [-4, -2, -2, 0], [-4, 0, -1, 0], [0, 1, 1, 0], [-2, 0, 1, 2], [3, 1, 0, -1], [-4, 2, 0, 1], [4, 4, 1, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, -2, -2, 1], [-1, -1, -1, -1], [1, 2, 2, 0], [0, 1, 1, 1], [-2, 0, 2, 0], [-1, -1, -1, 1], [-5, 0, 3, 1], [2, -1, 1, -1], [-3, 0, -1, 1], [2, 4, 2, 2], [1, 2, 1, -3], [-1, 5, 0, 1], [0, 0, 0, 0], [-1, 0, -1, -1], [-2, 0, 1, 0], [1, -1, -2, -3], [0, 0, 2, -1], [-2, 1, 2, -3], [0, 2, 0, 0], [-4, 1, -3, -1], [-4, 4, 2, 0], [-5, -3, 0, -1], [6, -2, 4, -4], [0, -1, 0, 0], [1, -2, -2, 2], [0, 0, 0, 0], [-2, -2, 0, 0], [2, 3, 1, 1], [0, -2, -1, 2], [3, -2, 4, 2], [1, 2, 1, 3], [-2, -5, -2, -2], [-4, 2, -1, 0], [-1, -3, -2, 0], [7, -2, -2, 2], [2, 0, 0, -2], [2, -6, 2, 0], [3, 0, 2, -4], [0, 0, 0, 0], [3, 1, -1, -4], [-7, 0, 1, -1], [3, -1, -2, 2], [-3, -4, -2, 2], [-1, 3, -1, 0], [2, 0, 3, -6], [2, -6, -2, -4], [0, 2, -4, 2], [-3, -1, 1, 2], [0, 0, 0, -1], [-2, -5, -4, -1], [4, 4, -2, -3], [0, 0, 0, 0], [0, -6, 0, 2], [-1, 1, -1, 2], [-1, -2, 4, 0], [1, 1, 0, -1], [4, 0, -2, -2], [4, 5, 2, 1], [0, 0, 2, -1], [2, -1, 1, -1], [-2, -6, -4, -1], [-6, 0, 2, 3], [0, 8, -1, -2], [-4, -2, -2, 0], [0, 0, 0, 0], [3, 3, 0, 2], [-2, -4, -2, 4], [-6, -2, -4, -2], [-4, 0, -1, 0], [-2, 1, 2, 1], [-1, -2, 1, 3], [8, -4, 6, 0], [-6, -2, 0, 2], [0, 1, 1, 0]]}