# Stored data for newform 260.2.bg.a, downloaded from the LMFDB on 24 April 2024.
{"label": "260.2.bg.a", "space_label": "260.2.bg", "level": 260, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 2199056810244, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 732050562994206508, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [0, 1]], [17, [1, -4, 53, -14, 1]]], "qexp_display": "q+(-1+\\zeta_{12}+\\zeta_{12}^{2})q^{2}+(-2\\zeta_{12}+\\cdots)q^{4}+\\cdots", "char_order": 12, "char_parity": 1, "char_degree": 4, "char_conductor": 260, "char_orbit_label": "bg", "char_is_real": false, "Nk2": 1040, "analytic_conductor": 2.07611045255329, "hecke_ring_index": 1, "level_radical": 130, "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": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.567", "prec": 17}, "analytic_rank_proved": true, "char_values": [260, 12, [131, 157, 41], [6, 9, 10]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 4, "level_primes": [2, 5, 13], "conrey_indexes": [23, 43, 127, 147], "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.728", "prec": 17}, {"__RealLiteral__": 0, "data": "0.815", "prec": 17}, {"__RealLiteral__": 0, "data": "72.785", "prec": 20}, {"__RealLiteral__": 0, "data": "46.906", "prec": 20}, {"__RealLiteral__": 0, "data": "2106.742", "prec": 27}], "related_objects": [], "self_twist_discs": [-4], "cm_discs": [-4], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.1.d12", "trace_display": [-2, 0, 4, 0], "traces": [0, 4, -2, 0, 0, 4, 0, 0, -8, 0, -12, 0, 0, -4, 0, 0, 8, 14, -12, 0, 4, 0, 0, 0, 0, -6, 2, 0, 0, 30, 0, 0, 8, 0, -20, 0, 12, -8, 0, 0, -4, 24, 0, 0, 0, 6, 0, 0, 0, 0, -14, 0, -24, -10, 0, 0, 0, 0, -26, 0, 0, -12, 0, 0, 0, -28, 0, 0, 28, 0, 0, 0, 12, -22, 30, 0, 0, 0, 0, 0, 32, 18, -14, 0, 0, 22, 0, 0, 0, -20, -6, 0, 0, 0, 0, 0, 0, -26, 14, 0, 32, 2, 0, 0, 20, 0, 54, 0, 0, -80, 0, 0, 0, -12, 0, 0, -16, -36, 0, 0, 0, 22, 24, 0, 0, -8, 0, 0, -16, 0, 6, 0, 0, 0, 0, 0, -36, 38, 0, 0, 0, 0, 0, 0, 0, -8, 22, 0, 28, -20, 0, 0, 0, 42, 0, 0, 0, -10, 0, 0, -24, 0, 18, 0, -40, 0, 0, 0, 0, 10, -38, 0, 0, 30, 0, 0, 0, 0, -20, 0, 48, -36, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -56, -26, 0, 0, -4, 0, 62, 0, 0, -20, 0, 0, 16, 0, 0, 0, -64, 0, 0, 0, 0, 0, 40, 0, 0, -50, 0, 0, 0, 48, 0, 0, 0, 120, 0, 0, -52, -20, 30, 0, 0, 0, 0, 0, 0, -24, -44, 0, -60, -28, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, -32, 66, 0, 0, -16, -24, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 90, -94, 0, -8, 26, 0, 0, -28, 0, 40, 0, 0, 0, 0, 0, 0, -6, -54, 0, 0, 0, 0, 0, 0, 100, 10, 0, 0, 6, 0, 0, -16, 0, 0, 0, 0, -36, 0, 0, -28, 0, 0, 0, 0, 42, 0, 0, 0, 50, -68, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, -84, 0, 0, 0, 0, 0, 0, -36, -38, 78, 0, 0, -56, 0, 0, 0, -60, 46, 0, 0, -58, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 38, 0, 52, 0, 0, 0, 28, 0, 0, 0, 0, 26, 0, 0, 24, -6, 0, 0, 0, 72, 0, 0, 0, -40, -82, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 40, 10, 0, 0, 0, 0, 0, 0, 0, -82, 0, 0, 0, 0, 0, 0, 0, -84, 74, 0, 0, -80, 0, 0, 0, -80, -6, 0, 24, 0, 0, 0, 0, -92, -60, 0, 0, 114, 0, 0, 120, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 68, -60, 0, 0, 78, 0, 0, 84, 0, -14, 0, 0, 70, 0, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 8, 0, 0, 0, -10, 0, 0, 64, 0, 30, 0, 0, 0, 0, 0, 88, 44, -78, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, -18, 0, 0, 0, 0, 104, 0, 0, 0, 0, 0, -40, -80, 0, 0, -76, -90, 0, 0, 0, 0, 20, 0, 0, -18, 0, 0, 0, 0, -86, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 46, -108, 0, 44, 0, 0, 0, 0, -24, 76, 0, 0, 0, 0, 0, -88, 62, 0, 0, 84, 0, 0, 0, 0, -48, 0, 0, 0, -44, 0, 0, 0, 0, 6, 0, 60, -106, 0, 0, 0, -102, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 112, -20, 0, 0, 0, 0, -150, 0, 0, 42, 0, 0, -32, -8, 0, 0, 0, 0, 0, 0, -36, 0, 68, 0, 0, -70, 0, 0, 96, -12, 0, 0, 0, 36, 0, 0, 0, 0, -42, 0, 0, 0, 0, 0, 0, 68, -50, 0, 48, 100, 0, 0, -92, 0, 0, 0, 0, 66, 0, 0, 0, 130, 0, 0, -60, 0, 0, 0, 0, 22, 20, 0, 0, 208, 0, 0, 0, 0, -18, 0, 0, -30, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, -24, 0, -38, 0, -120, -106, 0, 0, 0, 0, 88, 0, 0, -58, 0, 0, 0, 0, -42, 0, -76, 0, 0, 0, 0, 82, 0, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, -70, 0, 0, 0, 0, 0, 0, 0, 90, 0, 0, 0, 100, 0, 0, -76, 78, 0, 0, 104, 0, -94, 0, 0, 0, 0, 0, 0, 148, 0, 0, -104, 0, 0, 0, 0, 48, 0, 0, 0, 30, 0, 0, -112, 0, -34, 0, 0, 0, 0, 0, -124, -30, -54, 0, 0, 0, 0, 0, 0, 0, 80, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, -48, -70, 0, 0, 0, 0, 0, 0, 0, 100, 54, 0, 0, 4, 0, 0, -128, 0, -42, 0, 0, -82, 0, 0, 0, -50, 0, 0, 0, 0, 0, 0, 0, -90, 0, 0, 0, 0, 0, 0, 160, 78, 0, 0, 0, 128, 0, 0, 0, -32, 42, 0, -100, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 160, 0, 36, -106, 0, 0, 60, -96, 0, 0, 0, 0, 0, 0, 0, 0, 150, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, 34, 0, 0, 32, 40, 0, 0, -20, 0, 0, 0, 24, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 70, 0, 0, 0, -30, 60, 0, 0, 0, 0, 0, 0, -124, 84, 0, 60, 38, 0, 0, -44, 0, 52, 0, 0, 0, 0, 0, -96, -78, 0, 0, -56, 0, 0, 0, 0, -156, -114, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 86, 0, 0, -72], "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, 4, 2, -1, 2, -4], [1, 1, 65, 18, -1, 12, 0], [1, 1, 260, 33, 1, 12, 0]], "char_orbit_index": 33, "prim_orbit_index": 33, "minimal_twist": "260.2.bg.a", "char_is_minimal": true, "conrey_index": 23, "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], [0, 0, 0, 0], [0, -2, 0, 2], [0, -1, 2, 1], [0, 0, 0, 0], [0, 0, 0, 0], [-2, 0, 0, -2], [0, -3, 0, 3], [-3, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0], [-2, 3, 2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [4, 0, -4, 0], [3, -4, 1, 1], [-3, 0, 0, -3], [0, 0, 0, 0], [2, -4, -2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-3, -4, 3, 0], [0, -5, 1, 5], [0, 0, 0, 0], [0, 0, 0, 0], [5, 2, 5, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 4, 4, -4], [0, 0, 0, 0], [-5, 6, 0, -3], [0, 0, 0, 0], [6, 0, -6, 0], [1, -1, -6, -5], [0, 0, 0, 0], [0, 0, 0, 0], [0, 6, -2, -6], [4, 5, 4, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [3, -6, -3, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 7, 0, 0], [0, 1, -7, -1], [0, 0, 0, 0], [-6, 0, 0, -4], [2, 9, -9, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-10, 3, 7, 7], [0, 0, 0, 0], [0, 0, 0, 0], [0, 5, -6, 5], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 8], [-7, 0, 0, 4], [0, 0, 0, 0], [0, 0, 0, 0], [8, -8, -2, 6], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 6, 6, -6], [-8, 5, 5, -8], [10, 7, -5, -7], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [8, 0, 0, 4], [9, 0, -9, 0], [-8, -1, 9, 9], [0, 0, 0, 0], [0, 0, 0, 0], [2, -6, 7, -3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-10, 0, 10, 0], [0, 9, -3, -9], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -13, -13, 13], [0, -7, 7, 7], [0, 0, 0, 0], [8, 0, 0, -6]]}