# Stored data for newform 245.2.f.a, downloaded from the LMFDB on 20 April 2024. {"label": "245.2.f.a", "space_label": "245.2.f", "level": 245, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 343630938357, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 170491684341360304, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [1, 2, 2, -2, 1]], [3, [1, -2, 2, 2, 1]]], "qexp_display": "q+(1-\\zeta_{12}+\\zeta_{12}^{2})q^{2}+(-1+\\zeta_{12}+\\cdots)q^{3}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 35, "char_orbit_label": "f", "char_is_real": false, "Nk2": 980, "analytic_conductor": 1.9563348495213695, "hecke_ring_index": 2, "level_radical": 35, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 12, "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": "0.259", "prec": 17}, "analytic_rank_proved": true, "char_values": [245, 4, [197, 101], [3, 2]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [5, 7], "conrey_indexes": [48, 97], "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.002", "prec": 17}, {"__RealLiteral__": 0, "data": "3.716", "prec": 17}, {"__RealLiteral__": 0, "data": "0.475", "prec": 17}, {"__RealLiteral__": 0, "data": "48.798", "prec": 20}, {"__RealLiteral__": 0, "data": "14.083", "prec": 20}, {"__RealLiteral__": 0, "data": "930.703", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c4", "trace_display": [2, -2, 8, 0], "traces": [0, 4, 2, -2, 0, 8, 0, 0, -2, 0, 6, -4, 6, 8, 0, -6, 4, 4, -4, -4, 0, 0, 4, -10, -4, 12, 0, -2, 0, 0, -8, 0, 18, -4, -8, 0, -12, 0, -8, 0, -2, 0, 0, -6, 0, -4, -28, -12, -14, 0, 14, 8, 0, -20, -20, -8, 0, 8, 6, -12, 6, 0, 4, 0, 0, 24, 0, 14, -12, 28, 0, 12, 8, 24, 0, -14, 0, 0, 16, 0, 8, 8, 6, -2, 0, 4, -36, -6, 8, 32, -4, 0, -18, -4, 12, -8, 0, -4, 0, 0, 0, 0, 4, 10, -8, 0, -20, -6, -18, 0, 12, 0, 0, -24, 0, -10, 0, 8, 12, 0, -8, -28, -22, -6, 24, 8, 0, -12, 22, 36, 8, 0, 0, 0, 0, -2, 0, -4, 38, -12, 0, -12, 12, -8, 0, -12, 0, 0, 24, 0, -32, 0, -4, -16, 0, 16, 24, 28, 16, 20, 54, 0, 34, -12, 24, -12, 0, -2, 0, 0, -16, 0, -30, -4, -24, 0, 20, -12, 46, 0, -24, 0, 0, 22, 0, 0, 8, -16, 24, 0, -24, 60, 14, 16, -52, -8, 0, 8, 4, -72, 2, 0, 26, 0, 0, 12, 0, -8, 8, -8, 0, 20, 0, -12, 0, -6, 0, 0, -46, 0, 12, 16, -24, -24, 0, -16, -12, -28, -12, -32, -56, 0, 6, -12, -16, -12, 0, -16, 0, 0, -42, 0, -26, -28, -24, 0, 0, -8, -20, 0, 26, 0, 0, -8, 0, 16, 36, 8, 42, 0, 0, -12, 12, 34, 4, -20, 0, -46, 30, 36, -40, 0, -20, 0, 0, -12, 0, -36, -36, 40, 0, 24, 0, -36, 0, 24, 0, 0, 12, 0, 6, 52, 24, -32, 0, -24, -24, -16, 30, -40, -6, 0, -48, -26, -28, 20, 0, 6, 0, 0, 4, 0, -8, -36, 100, 0, 12, -20, 40, 0, 16, 0, 0, 8, 0, 56, 36, 46, -18, 0, -4, 48, 18, 24, 76, 42, 0, 52, 10, 12, -36, 0, 4, 0, 0, 56, 0, -54, -18, -32, 0, -8, -12, -12, 0, 24, 0, 0, 60, 0, 24, -60, 26, 26, 0, 72, 64, -2, -46, 36, -24, 0, 12, -12, 8, -26, 0, 24, 0, 0, -12, 0, 36, 86, -4, 0, 4, -24, -48, 0, 16, 0, 0, -12, 0, -20, 24, -24, -60, 0, 12, 44, -2, -32, 12, 16, 0, -24, -4, -28, 6, 0, 6, 0, 0, -6, 0, 36, -4, -40, 0, -104, 28, 36, 0, -4, 0, 0, -54, 0, -72, 4, -38, 84, 0, -6, -84, 28, 24, -56, 8, 0, -16, -14, -24, 64, 0, -30, 0, 0, 4, 0, 12, 48, 20, 0, 4, -28, 20, 0, -54, 0, 0, 26, 0, -4, 0, 26, -24, 0, 24, -100, 24, -24, -52, -12, 0, 20, 52, 80, -24, 0, -64, 0, 0, -4, 0, 52, 2, -36, 0, 40, 6, -12, 0, 16, 0, 0, -22, 0, 0, -76, -32, 74, 0, -40, -20, -10, 24, -24, 12, 0, 10, 20, 8, 30, 0, 36, 0, 0, -16, 0, 12, -84, -24, 0, 16, 40, -4, 0, -40, 0, 0, -24, 0, -18, -44, -60, -30, 0, -54, 36, -52, -26, 24, 8, 0, -22, -60, -4, 28, 0, 10, 0, 0, 24, 0, 36, -16, -24, 0, -8, 36, 66, 0, -24, 0, 0, 0, 0, 20, 4, -24, -36, 0, 10, 4, -32, -42, -4, 0, 0, 56, 20, -48, 8, 0, 20, 0, 0, 36, 0, -48, 40, -4, 0, 36, 60, -56, 0, -12, 0, 0, 44, 0, -56, -92, -6, -24, 0, -22, -48, -24, -16, 60, -6, 0, 4, 14, 20, 48, 0, -40, 0, 0, -28, 0, 4, 72, 48, 0, 44, 4, -28, 0, -36, 0, 0, 12, 0, 22, 8, 42, -84, 0, 72, 8, 50, 26, 48, 32, 0, 48, -16, 100, -48, 0, 48, 0, 0, 0, 0, 72, 16, -16, 0, 0, 30, 78, 0, -16, 0, 0, -24, 0, 2, 0, 48, 36, 0, 16, -20, -16, 2, 0, -12, 0, -20, -66, -80, 114, 0, 108, 0, 0, -24, 0, 36, -22, 0, 0, -88, -40, 24, 0, -24, 0, 0, 0, 0, 36, -8, 14, -4, 0, -24, 96, -52, -64, 92, 20, 0, -18, 64, 36, -48, 0, 30, 0, 0, 0, 0, 42, 8, -8, 0, -108, -44, -12, 0, 24, 0, 0, -42, 0, -24, -72, 16, 24, 0, -88, 16, 36, 32, 24, 0, 0, 44, -52, 20, -4, 0, -48, 0, 0, -48, 0, -24, -54, 64, 0, -8, -12, 4, 0, 64, 0, 0, -28, 0, 48, 0, 20, 6, 0, 28, -72, 74, -84, -16, 16, 0, -20, -40, -84, 40, 0, -104, 0, 0, 126, 0, 22, -48, 12, 0, 16, 30, 14, 0, 102, 0, 0, 52, 0, -12, 8, 36, 34, 0, 48, -128, 52, 42, -16, -28, 0, -74, 12, -72, -20, 0, -32, 0, 0, -2, 0, 28, 28, -76, 0, 80, -82, -36, 0, -20, 0, 0, -20, 0, -24, 72, 24, 24, 0, -8, 60, 16, 8, -112, -90, 0, -16, 122, -36, -12, 0, 42, 0, 0, -48, 0, 38, -44, 76, 0, 48, 80, -88, 0, 40, 0, 0, 60, 0, -36, 28, -70, 0, 0, 138, 52, -84, -12, -84, -24, 0, 56, -38, 48, -36, 0, -12, 0, 0, -16, 0, -50, 48, -28, 0, 60, 32, -16, 0, 22, 0, 0, 4, 0, 8, -60, -68, 24, 0, 0, 104, 16, 54, -76, 16, 0, 12, 40, 140, -16, 0, -96, 0, 0, 72, 0, -128, 6, 60, 0, -12, -62, -36, 0, -56, 0, 0, -96, 0, 120, 72, -12, 64, 0, 14, 12, 48, -60, -144, 16, 0, -30, 2, -8, -104, 0, -12, 0, 0, -32, 0, -64, -24, 28, 0, -76, -76, -58, 0, 24, 0, 0, 24, 0, 4, 16, -60, -72, 0, -144, -24, -96, 100, 72, 18], "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, 1, 35, 6, 1, 4, 0]], "char_orbit_index": 6, "prim_orbit_index": 6, "minimal_twist": "35.2.k.a", "char_is_minimal": true, "conrey_index": 48, "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], [1, -1, 1, 0], [-1, 1, -1, 0], [1, -1, 0, 1], [2, 0, -1, 0], [-1, 1, -2, -1], [0, 0, 0, 0], [-1, 0, 1, -1], [1, -1, -1, 1], [2, -2, 2, -1], [-1, -1, 1, -1], [1, 0, -1, -1], [2, 0, 2, 0], [0, 0, 0, 0], [-2, 2, -2, 1], [1, -2, 2, -2], [2, 0, -2, 2], [-1, 0, 1, 0], [-1, 1, -1, 1], [2, -3, 1, 1], [0, 0, 0, 0], [1, 0, 1, 0], [-1, 0, 1, 3], [-1, 0, 0, 0], [3, 0, -4, 0], [2, -2, 2, 2], [1, 0, -1, 3], [0, 0, 0, 0], [0, 0, -3, 0], [-4, 3, -5, -1], [-2, 2, 4, -2], [5, -1, 5, 0], [-1, 0, -1, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [-3, -1, 1, -1], [-2, 4, -2, 0], [-3, 2, -3, 0], [-2, 2, -2, -2], [-2, 1, 2, -2], [-2, 2, 3, -2], [0, 0, 0, 0], [1, 0, -1, 5], [-1, 1, 3, -1], [1, -3, -1, 1], [-7, 4, -4, 4], [-5, 0, 5, -4], [-5, 3, -5, 0], [0, 0, 0, 0], [3, -3, 3, -4], [2, 0, 0, 0], [2, 0, -2, 4], [-5, 0, 5, 0], [-5, 2, -2, 2], [-3, -1, 3, -3], [0, 0, 0, 0], [3, -2, 3, 0], [0, 0, 0, -3], [-3, -3, 3, -3], [0, 1, -4, -2], [2, -2, 5, 2], [2, 0, -2, 2], [0, 0, 0, 0], [1, -1, 4, 1], [6, 0, 2, 0], [-1, 1, -1, -1], [1, 5, 1, 0], [-2, -2, -2, 0], [7, -4, 4, -4], [0, 0, 0, 0], [3, -1, 1, -1], [1, 2, 1, 0], [4, 4, 4, 0], [-2, 2, -6, -2], [-3, 3, -3, 4], [-1, 1, -3, -1], [0, 0, 0, 0], [2, 0, -2, -4], [-1, 1, -5, -1], [0, -2, 3, -6], [2, -5, 5, -5], [2, 0, -2, 1], [-2, 3, -2, 0], [0, 0, 0, 0], [4, -2, -4, 4], [-9, 4, -4, 4], [0, 0, 0, 3], [3, 0, -3, 2], [8, -5, 5, -5], [-1, 0, 3, 0], [0, 0, 0, 0], [-7, 5, -7, 0], [-2, 0, 2, -2], [3, 1, -1, 1], [-1, 1, -1, 3], [-5, 5, -6, -5], [3, 0, -3, 8], [0, 0, 0, 0], [-2, 2, 4, -2], [3, -7, 4, -1]]}