# Stored data for newform 845.2.a.b, downloaded from the LMFDB on 23 April 2024. {"label": "845.2.a.b", "space_label": "845.2.a", "level": 845, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503599660925773, "dim": 2, "is_polredabs": true, "nf_label": "2.2.5.1", "trace_hash": 311578052331102050, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [-1, 1, 1]]], "qexp_display": "q-\\beta q^{2}+(1-2\\beta )q^{3}+(-1+\\beta )q^{4}+\\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": 10, "field_poly_is_real_cyclotomic": true, "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": "0.025", "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": 5, "field_disc_factorization": [[5, 1]], "field_poly": [-1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.982", "prec": 17}, {"__RealLiteral__": 0, "data": "0.133", "prec": 17}, {"__RealLiteral__": 0, "data": "9.588", "prec": 17}, {"__RealLiteral__": 0, "data": "1.629", "prec": 17}, {"__RealLiteral__": 0, "data": "64.661", "prec": 20}], "related_objects": ["Genus2Curve/Q/714025/a"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[5, 1], [13, 1]], "trace_display": [-1, 0, -2, -4], "traces": [0, 2, -1, 0, -1, -2, 5, -4, 0, 4, 1, -4, -5, 0, -3, 0, -3, 2, -2, -4, 1, -10, 7, 12, -10, 2, 0, 0, 7, -6, -5, 0, 9, 10, -11, 4, -2, -6, -3, 0, 0, -6, -5, -8, -3, -4, -11, -8, 15, 4, -1, -20, 0, 12, -5, 4, 10, -10, -7, -12, 5, 2, 0, -8, 4, 0, -15, -8, 9, -10, 3, 8, 0, 12, 3, 0, 7, -2, 0, 0, 3, -22, -17, 0, 15, -2, -1, -20, -10, 18, 2, 0, -1, 0, 24, 4, 5, -2, 18, -8, -1, 10, 15, 8, 0, 10, -6, -16, 5, 4, -7, 0, -9, -6, -5, -12, 13, 0, 21, 16, 10, -4, 29, -40, 0, -2, -6, -4, -25, -10, 0, -24, 5, 18, 19, 0, 20, 6, 35, -20, -7, 40, 1, 0, -6, 6, -6, 40, 3, -18, 5, -16, 10, 4, 1, 0, 0, -36, 0, 0, -9, -14, 11, -16, 23, -10, -20, 12, 20, 0, 11, -8, 9, -2, -5, -4, 21, 30, -9, -12, 2, 12, 0, 60, 10, 6, 0, -24, -16, 10, 3, -32, -10, -2, 11, 0, -22, -6, 14, -16, 0, 30, -15, 32, 5, 6, 16, 24, 0, -2, 5, -4, -6, 10, 13, 8, 10, 0, -2, 0, 3, 0, -15, 12, -23, 4, 13, 8, 15, 4, 11, 0, 20, 4, 0, 8, -9, 0, 7, 16, -15, -30, -18, 0, -31, -4, 5, 0, 0, -40, 1, 36, 14, -34, -3, 20, 7, 26, -15, 12, 0, -12, 12, 12, 20, -12, 11, 0, -11, -22, 5, -16, -33, 0, -13, -4, -25, -2, -5, 0, -10, -4, -40, -8, -9, 10, 0, 52, 18, 8, 7, 20, -6, 42, -10, 12, 0, -10, 19, 0, -5, 26, 8, -20, -9, -2, -22, -32, 1, 40, 0, -48, 0, -28, 18, 8, 0, -12, 30, -8, -4, 10, -13, 16, 11, 0, -7, 0, 40, -24, 15, -20, 20, -12, 19, 8, -15, 20, 0, 20, -9, 0, -6, -20, 10, 10, -39, 48, 25, 22, -3, 0, -13, 30, -45, -8, -9, 30, 1, 0, 0, -20, -6, -40, 0, -12, -25, -20, -33, -12, -3, -24, 0, 38, 37, 0, -40, 0, 5, -44, -7, -10, -9, -4, 5, 2, 11, -16, -9, -36, 0, 32, -40, 0, 3, 0, -6, -38, 23, 40, -3, 18, -35, 0, 5, 22, 19, 12, -10, -14, 17, -20, -24, -6, -22, 0, 0, -30, 1, 4, -15, -12, -23, -16, 0, 2, 15, -64, 3, 0, 1, -32, -15, -38, 0, 20, -2, -14, 30, -32, 10, 8, 0, -16, 15, -18, -21, 20, 2, 10, -2, -28, -7, 0, 1, 0, 20, 30, -42, 20, 1, 30, -5, -40, -21, 0, -42, 0, 0, -14, -24, 0, -30, 6, 0, -4, -23, 24, 32, -24, -5, 0, 15, -40, 22, 2, -40, 12, -60, -30, -18, 4, 35, 34, 0, 8, 0, -26, 20, 8, 1, 50, -13, -4, 20, -10, 57, 0, 7, 22, -15, -24, 24, 10, -3, -8, 25, 56, 9, -80, 0, -12, -14, 24, 12, -10, -11, 0, -45, 36, 6, -24, -29, 0, 45, 16, -30, -10, 21, 32, -5, 20, 23, 0, -1, -4, 0, -16, 7, 4, 7, 32, -60, 0, 41, 0, 25, 2, 0, 0, 9, 50, 42, 48, 0, 6, -11, 44, -10, -2, 5, 56, 0, -50, 29, 12, 8, -20, -24, 20, -13, 40, -15, -24, 0, 0, -1, -16, -30, 0, -21, 0, 9, -20, 15, -16, -1, 30, 0, -48, -10, 70, 17, -16, 8, 4, 35, 12, -23, 70, -29, 0, 18, -62, -4, 40, 0, 54, 0, -24, 0, 10, 24, -36, 0, 2, 54, 0, 18, -6, 6, -8, 0, -50, 46, 4, -30, 0, 9, 16, 25, -18, -45, 48, 27, 10, 7, -44, 0, 54, 0, 0, 23, -42, 10, 24, -51, 24, -8, -92, -5, 38, 45, 0, 40, -18, 6, -16, -31, -30, -19, 56, -55, -46, -50, 0, 0, 60, -25, -16, -20, 10, 0, -56, 14, -6, -5, -80, -3, 0, -35, -28, 41, -4, -9, 20, 30, 74, -41, -80, 7, -20, 0, 12, -18, -40, -5, 0, 15, 14, -1, 0, 0, 0, 25, 0, 11, 80, -40, -24, 6, -56, 30, 0, -6, -6, 10, 40, 0, -14, 6, 12, -35, 52, 45, -40, 49, 46, -34, 12, -3, 0, -18, 36, 0, 18, 1, 0, -13, 22, -5, -48, 72, 10, 0, 16, -15, 22, 47, 80, -10, 58, -5, -8, 41, -4, -3, 0, -45, -6, -1, 20, -9, 58, -2, 0, -20, 30, 58, 52, 0, -6, -81, 20, 54, 36, -60, 8, 3, -10, 0, -8, -20, 0, -1, 0, -7, 54, 25, -88, 9, 36, -49, -24, 5, 14, 0, 20, 20, 30, -11, 8, -51, 30, -21, 16, 45, 26, -33, 0, -23, 6, 25, -4, -40, 10, 3, 0, -2, -6, 20, 80, 0, -76, -35, -12, 1, 0, 33, -48, -20, 0, 6, 80, 27, 0, 48, 48, -18, -30, -11, -36, -25, -12, -33, 8, -10, 36, 0, 8, -9, 110, -9, 24, -5, 2, 29, -40, 0, 0, 5, 0, 0, -4, -13, 4, -30, -22, 1, 40, -21, 30, 36, -32, 0, -30, 28, 4, 30, 18, 9, 44, 9, -24, -55, 12, 45, 0, -25, 0, -2, 12, 39, 60, -20, -12, -40, 0, -9, 20, 0, 96, -15, -40, -45, -60, 38, 48, -15, 80, -10, -40, -45, 0, 5, -6, 40, 16, -37, -22, 0, -48, 38, 0, 20, 24, 0, -12, -3, 80, 16, -12, -90, 4, 63, -10, -13, -56, 0, 0, -3, 80, -30, -14, -12, 32, -48, 10, -33, 8, 10, -62, 0, -32, 15, 2, -15, 56, 40, 30, -11, -28, 40, 70, -51, 0, 87, -42, -25, -36, 22, 8, -7, -24, 30, 6, 3, -40, 0, -38, -14, -80, 0, 70, -17, 16, 20, -2, 36, 0, 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": "65.2.e.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], [1, 0], [0, -1], [1, -2], [-1, 1], [-1, 0], [2, 1], [-3, 2], [-1, 2], [2, 0], [0, 1], [-1, -2], [-3, 1], [0, 0], [-2, 1], [-1, 2], [0, -3], [-1, 4], [0, -2], [-3, 2], [1, -1], [-7, 4], [2, 3], [5, 2], [-5, 0], [1, 0], [0, 0], [-1, 2], [5, -3], [-5, 4], [-2, -1], [0, 0], [5, -1], [3, 4], [-4, -3], [3, -2], [-2, 2], [-3, 0], [-2, 1], [0, 0], [1, -2], [-7, 8], [-4, 3], [-5, 2], [-1, -1], [-2, 0], [-2, -7], [0, -8], [6, 3], [6, -8], [0, -1], [-9, -2], [0, 0], [6, 0], [-2, -1], [1, 2], [7, -4], [-7, 4], [-4, 1], [-3, -6], [3, -1], [7, -12], [0, 0], [-6, 4], [1, 2], [0, 0], [-4, -7], [-1, -6], [5, -1], [1, -12], [2, -1], [5, -2], [-2, 4], [6, 0], [0, 3], [1, -2], [5, -3], [-1, 0], [0, 0], [0, 0], [0, 3], [-11, 0], [-8, -1], [-4, 8], [11, -7], [1, -4], [-2, 3], [-13, 6], [-3, -4], [9, 0], [0, 2], [0, 0], [-3, 5], [0, 0], [8, 8], [3, -2], [7, -9], [1, -4], [8, 2], [-2, -4], [-1, 1]]}