# Stored data for newform 240.2.bc.d, downloaded from the LMFDB on 25 April 2024.
{"label": "240.2.bc.d", "space_label": "240.2.bc", "level": 240, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13512723061014768, "dim": 6, "is_polredabs": true, "nf_label": "6.0.399424.1", "trace_hash": 1625630761121214751, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[7, [8, -56, 196, -32, 2, 2, 1]], [11, [8, -56, 196, -32, 2, 2, 1]]], "qexp_display": "q-\\beta _{1}q^{2}-\\beta _{3}q^{3}+(\\beta _{2}-\\beta _{3})q^{4}+(2+\\cdots)q^{5}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 80, "char_orbit_label": "bc", "char_is_real": false, "Nk2": 960, "analytic_conductor": 1.9164096485107291, "hecke_ring_index": 2, "level_radical": 30, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.249", "prec": 17}, "analytic_rank_proved": true, "char_values": [240, 4, [31, 181, 161, 97], [2, 1, 4, 3]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [43, 67], "field_disc": -399424, "field_disc_factorization": [[-1, 1], [2, 6], [79, 2]], "field_poly": [8, -8, 6, -6, 3, -2, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.632", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "125.490", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4506.792", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c4", "trace_display": [-2, 0, 12, -2], "traces": [0, 6, -2, 0, -2, 12, 0, -2, -8, -6, -4, -2, -4, 0, 6, -6, 10, -2, 2, 10, -8, -2, 6, 10, -6, 18, 0, 0, 14, 6, 2, 0, -12, -2, 26, -6, 2, 8, -34, 0, -22, 0, -14, 4, 14, -12, 2, -10, 16, 0, -6, -2, 0, 0, 0, -6, -34, 10, -2, 6, -6, -14, -20, 2, 22, 0, -14, -36, -10, -10, -2, -16, 8, 10, 32, -24, -2, 0, 0, -16, 36, 6, 0, 0, 26, -6, 24, -6, -34, 28, 4, 0, 10, 4, 38, 30, 10, -10, -56, 2, -22, -14, 10, 18, 0, -2, 56, 0, 4, -26, -2, 0, 6, 14, 2, 10, -6, 0, 2, 0, -4, 0, 30, 24, 12, 12, -6, -26, 12, 0, 0, 34, 26, 0, -32, 6, -6, -38, 34, -18, 54, 10, 24, 0, -10, 6, -54, 18, -56, -2, 8, 0, 38, 2, -56, 4, 0, 0, 24, 12, -14, -28, -2, 0, 16, -2, 40, -2, -10, -78, 62, -10, -16, -8, 2, -14, 6, -6, -44, 10, 8, 2, 0, -14, -18, 16, 8, 0, -18, 2, -66, 0, -8, 14, -18, 0, -4, -16, -6, 0, -48, 0, -14, -4, -42, 24, -10, -10, 0, 0, -34, -6, 24, 0, -72, 8, 6, 60, 58, 10, 54, 0, -16, 58, 42, -18, -14, 44, 10, -26, 38, 60, -14, -14, 0, -10, -70, 0, -4, 32, 22, -4, -56, 0, -14, 18, -8, 0, 24, 40, -4, -26, -14, -28, -6, -2, 2, 46, -36, -40, 0, -6, 22, -70, -10, 12, 80, 0, 104, -34, -2, 0, -58, 0, 62, -14, 2, 40, -18, 0, -78, 0, 38, 68, -72, 10, 0, 8, 12, 0, -2, -10, 22, 0, -22, 6, -8, 2, -50, 0, -4, 20, 0, 14, 46, -42, -26, 92, 24, -18, -32, 64, 0, 18, -32, 6, -72, 0, 12, -4, 36, 40, -28, 0, -2, 0, -40, 26, 24, -132, -34, 6, 8, -8, 82, -72, -14, -82, 26, -14, -62, 60, 34, 72, -52, -30, 72, 0, -2, 62, -38, 0, 42, -2, -54, -32, 44, -36, 42, 0, 22, 0, -10, -6, 0, 30, 14, 46, 74, 0, 48, -76, -40, 0, -4, -66, 58, 0, 14, -2, 6, 26, 36, -62, -42, 60, 54, -4, -62, -50, 0, -108, 74, -34, -48, -32, -14, 0, -20, -28, 94, 20, -4, 0, 102, 12, -8, -40, 14, 76, -8, 38, 46, -20, -2, 40, 0, 18, 80, 2, 38, -86, -14, 10, -44, -14, 40, 0, -24, 0, 12, 0, -16, 6, 20, -18, -26, 156, -22, 0, -78, 0, 0, -124, -40, 56, 26, -2, -14, 0, 6, 8, 30, 0, -24, 0, -18, -38, -38, 2, 22, -30, -36, -62, 26, 8, -42, -36, 0, 108, 114, -52, -10, 20, 40, 70, 20, 0, 8, 112, 32, 0, -36, 0, -20, -30, 0, 6, -2, 56, -134, 78, -8, -4, 0, 6, -20, -112, -32, 10, -48, -2, 14, -14, 34, -14, -28, 0, 50, 38, -6, 0, -116, -10, 82, 18, -28, -132, 64, 0, 0, 0, 2, -12, -146, 2, -30, -36, -14, 0, 124, -6, -56, 0, 16, 40, -4, 10, -66, 86, 6, -22, 20, -2, 14, -26, 0, -148, -14, 14, -38, 20, -38, -112, -16, -8, 86, 0, 20, 0, -2, -36, 16, 0, 38, 14, -16, -2, 120, 92, 38, -114, 0, -92, 56, -10, -22, 118, 80, -14, -14, -104, 62, -76, 10, 0, -112, 0, -30, -28, -50, 0, -72, 6, 14, -36, 18, 76, 0, 0, 14, 0, -28, 36, 0, -6, 46, -58, -78, 0, 74, 0, 10, 0, -56, 48, 116, 66, 62, -18, -16, 10, -72, 28, 0, -42, -6, -28, -104, 136, 2, 48, 120, 6, -56, -26, 20, 0, -8, 16, -18, 124, -64, 0, 164, -4, -60, -10, -8, -20, 0, -60, 56, 48, 38, 34, -64, -10, 76, -38, 38, 114, -94, 0, 0, -28, -32, 0, -14, 58, -68, 0, -22, -2, 6, 24, 26, -64, 30, 0, 2, 0, 20, 116, 2, -38, 16, -26, -80, 0, 66, 122, -104, 0, -32, -18, 2, 8, 10, -14, 146, 26, 0, -88, -14, 30, 10, 84, 2, -106, 88, 16, -40, 28, 56, 0, -30, 0, -108, 48, -36, 4, -56, 0, 42, -6, -14, 6, 0, -6, -130, 100, -30, 24, -70, 36, -110, 108, 0, 122, -152, 0, -44, 74, 44, -6, -112, 0, 20, 56, 22, 0, -2, -26, 0, 0, -26, 56, 94, 0, 58, 0, -14, -180, -36, 6, -10, 0, 32, 0, -148, 46, -110, 0, -24, 16, 142, -40, -34, -40, 0, -112, 64, 6, -32, -52, -34, 156, 136, 70, 88, 28, 34, 0, -16, 24, 60, 0, -28, -20, 4, -28, -4, 0, 68, -56, 0, 34, 14, -60, -4, 126, 40, -76, 64, 56, -34, -116, 60, 0, 24, 66, 34, 34, -46, 2, 60, 0, -10, -10, 48, 0, 0, 70, 14, -6, -56, -4, 66, 0, 14, 0, 78, -64, -54, -156, -38, 78, -48, 0, 118, -88, -8, 0, -44, -30, 112, 18, 0, -26, -60, -8, -4, -14, -10, -16, 38, 38, -68, -112, 6, 0, 110, 10, -68, -26, 78, 0, -52, -12, -2, -44, 56, 0, 0, -18, -56, -58, 8, 76, -72, -2, -14, 132, -18, 30, -90, 0, 48, 4, 22, -60, 56, 20, -42, 2, 0, 0, 24, 14, 0, 0, 74, -104, -46, -14, -58, -156, -10, 0, -74, 0, 82, 0, -44, 24, 66, -18, -2, 0, 36, -174, -54, 0, -48, -36, 0, -6, -180, 18, 2, -22, -52, 40, -30, 2, -28, 12, -8, 0, -94, -60, -32, 122, -56, -92, -88, 0, -56, -172, -38, 66, 0, 0, 156, 14, -80, -26, 50, -108, 26, -82, -4, 108, 46, 0, -46, -82, 0, 28, -38, 26, 30, 2, -32, -32, 36, 0, 0, -116, 2, 0, -64, 6, 160, 76, 64, 0, -34, 0, -82], "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, 80, 10, 1, 4, 0]], "char_orbit_index": 29, "prim_orbit_index": 10, "minimal_twist": "240.2.y.d", "char_is_minimal": true, "conrey_index": 43, "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, 0, 0], [1, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0], [0, 0, 1, -1, 0, 0], [2, 0, 0, -1, 0, 0], [0, 0, 0, 0, -1, 0], [0, 1, 1, 0, 1, -1], [-2, 1, -1, -1, -1, 0], [-1, 0, 0, 0, 0, 0], [0, -2, 0, 0, -1, 0], [0, 1, 1, 0, 1, -1], [-1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0], [0, 1, -2, -2, -1, 0], [-1, 0, 0, -2, 0, 0], [1, 1, 0, 2, -1, 1], [-1, 0, -2, 1, 2, 0], [0, 1, 0, 0, 0, 0], [2, -1, 1, 0, -3, 1], [-1, 0, 2, -2, 0, 1], [0, -1, 1, 0, 1, 1], [0, 1, -2, -2, -1, 0], [0, 3, -1, -2, -1, 1], [-1, 1, 0, 2, 1, -1], [3, 0, 0, -4, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [3, -2, 1, 3, -2, 1], [1, 0, 0, -1, 0, 0], [0, 1, 0, 0, -2, 0], [0, -2, 0, 0, 0, 2], [-2, -1, -1, 3, 3, 0], [0, -1, 1, 0, 1, 1], [6, -1, 2, 2, 1, -2], [0, 1, 3, 0, 3, -1], [0, 0, -1, 1, 0, 0], [2, -2, -2, 2, 2, -2], [-6, -1, 0, 0, 1, 2], [0, 0, 0, 0, 0, 0], [-5, 3, -2, 0, -1, -1], [0, 0, 0, 4, 0, 0], [-2, 1, 0, 0, 1, -2], [2, -2, 0, 2, 4, -2], [3, -2, 1, 3, -2, 1], [-2, 0, 0, 1, 0, 0], [0, -1, -2, 6, -1, 0], [-4, 5, -3, 2, -3, -1], [2, 1, -1, -1, 1, 0], [2, -6, 2, 1, -2, 2], [0, -3, 0, 0, -4, 0], [1, -2, 0, 1, 0, -2], [0, 0, 0, 0, 0, 0], [-2, 6, -2, 4, 2, -2], [0, 0, 0, 0, 1, 0], [0, 1, 3, 0, 3, -1], [-5, -2, 1, -1, 4, 1], [0, 3, -1, -2, -1, 1], [0, -1, 0, 0, -1, 0], [4, -5, 1, 0, 1, -3], [-2, 0, -1, 1, 0, 2], [-3, 0, -2, -1, 2, 0], [-2, 0, 2, 2, 2, -2], [0, -1, -1, 0, -1, 1], [5, 1, 2, 0, 3, -3], [0, 0, 0, 0, 0, 0], [-2, 1, 0, 0, 1, -2], [-6, 2, 4, -2, 0, 2], [-1, -4, -1, -7, 0, 1], [-2, 1, -1, 0, 3, -1], [-2, 3, -4, -4, -1, -2], [-4, 0, -4, 0, -4, 0], [2, -1, 1, 1, 1, 0], [3, 0, 4, -1, -4, 0], [8, -4, 4, -4, 0, 0], [-4, 0, 0, -3, 0, 0], [-1, 6, 1, 3, 2, -3], [2, -6, 2, 8, -2, 2], [0, 0, 0, 0, 0, 0], [-4, 0, -4, 0, -4, 0], [4, 3, -1, 3, -1, 2], [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 4, 0], [0, 4, 0, 8, 0, -4], [3, 2, -1, -3, -2, 1], [-1, -2, -4, 3, 4, -2], [6, -2, 2, -6, 0, -2], [-1, 0, 0, -1, 0, 0], [-5, -2, 1, -1, 4, 1], [4, 2, 2, -2, -2, 2], [0, 2, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], [3, -2, 3, 1, 6, 1], [0, 0, -2, 0, -2, 0], [4, 1, -2, 6, 1, 4], [4, 1, 1, -2, -7, 3], [3, -3, 0, 2, -1, -1], [-3, -4, -4, -3, -4, 4], [-8, 0, 4, -4, 3, 0], [0, -1, -1, 0, -1, 1], [-4, 0, 3, -3, 0, 4]]}