# Stored data for newform 240.2.bc.e, downloaded from the LMFDB on 18 April 2024.
{"label": "240.2.bc.e", "space_label": "240.2.bc", "level": 240, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18016322688385264, "dim": 16, "is_polredabs": true, "trace_hash": 213209137315463847, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[7, [2304, -23040, 115200, -251904, 314752, -202368, 56832, 7360, 7856, -7648, 2432, 1264, 392, -32, 8, 4, 1]], [11, [952576, 31232, 512, -36096, 1229440, -4608, -128, 3264, 335152, 4864, 32, -400, 1288, -8, 0, 0, 1]]], "qexp_display": "q+\\beta _{2}q^{2}-\\beta _{5}q^{3}+(-\\beta _{1}+2\\beta _{2}+\\beta _{3}+\\cdots)q^{4}+\\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": 32, "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": "0.258", "prec": 17}, "analytic_rank_proved": true, "char_values": [240, 4, [31, 181, 161, 97], [2, 1, 4, 3]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [43, 67], "field_disc": 70508245065092038656, "field_disc_factorization": [[2, 24], [3, 8], [25309, 2]], "field_poly": [256, -768, 896, -320, -416, 624, -264, -148, 233, -74, -66, 78, -26, -10, 14, -6, 1], "hecke_ring_index_factorization": [[2, 5]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.074", "prec": 17}, {"__RealLiteral__": 0, "data": "14.318", "prec": 20}, {"__RealLiteral__": 0, "data": "6.238", "prec": 17}, {"__RealLiteral__": 0, "data": "834.722", "prec": 24}, {"__RealLiteral__": 0, "data": "251.805", "prec": 24}, {"__RealLiteral__": 0, "data": "83038.477", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "1.2.3.c4", "trace_display": [2, 0, -8, -4], "traces": [0, 16, 2, 0, 8, -8, 2, -4, 8, -16, -2, 0, -4, -8, 4, 4, -8, -8, -2, -8, 4, -4, 0, 0, 4, -32, 20, 0, 12, -12, 2, 0, -28, 0, 0, 12, -8, -24, 16, 0, 16, 0, 24, 24, -52, 8, -16, 32, -16, 0, 6, -8, 24, 0, -2, -4, 20, -8, 12, 24, 24, 40, 28, 4, 8, -4, -8, 16, -8, 0, 12, 0, -8, -8, -64, 24, 16, 0, 12, 48, 0, 16, -32, 0, -12, -8, -8, 12, 24, 0, 2, -40, -16, -32, 20, -8, -28, 48, 62, 0, -24, -28, 20, -36, -80, 20, -8, 0, 4, 8, -72, 0, -32, -24, 16, -16, 8, 8, -40, 0, -20, 0, -12, -24, -68, 16, -4, 4, -40, 0, -20, -32, -20, 0, -4, -4, 12, 72, -32, 8, 64, -32, -56, -8, 8, 16, 20, 16, -8, 28, 10, -40, 112, 8, -52, 28, 8, 0, 24, -16, 116, 0, 2, 0, 104, 4, -4, 40, 28, 32, -44, 8, 32, 40, 44, -36, -32, -24, 40, -32, -4, 72, -52, 40, -40, -36, 40, 0, 0, 4, -32, 0, 16, -8, 112, 4, 20, 0, 0, 0, -76, 0, 0, 40, -24, -16, 4, 0, -24, 0, 48, -48, -20, 0, -8, 8, -4, -40, -16, -8, 72, 80, -24, -68, 96, 32, -104, -104, -56, 32, 96, -72, 96, -32, -20, -48, 4, 0, 0, -112, 16, 64, -22, 0, 164, -108, 8, -24, 12, 8, -114, 8, -12, -48, 68, 8, -64, -16, -48, 16, -156, 12, 0, 80, 16, 80, 0, 0, 24, 36, -2, 0, -72, -40, 68, 24, 0, -88, 12, 0, -12, 0, -44, -80, -72, -16, 52, -96, 28, 0, -32, 48, 4, 0, -30, -12, 32, 0, 104, -24, -20, -48, 12, 28, -80, -52, 0, 32, -40, 36, 88, 32, -24, -8, 4, -12, 4, 0, -28, 88, 152, -16, -24, 0, 8, 144, -36, -8, 40, -32, -80, 8, 0, 24, 76, -64, -24, -24, 90, 24, -4, 80, -16, 72, 8, 0, 104, 0, 88, -40, -116, 0, -72, -8, 120, 64, 48, 0, 8, 0, -16, 0, 64, 32, -248, -20, 40, 68, -168, 0, 80, 48, 60, 0, -84, -28, 48, -40, -24, 24, 192, -4, -88, 104, -16, -56, -8, -24, -108, 44, -20, -32, 140, 32, 0, -60, 52, 0, -24, 64, 64, 24, 12, 0, 96, -8, -36, -88, -20, 0, -32, -72, -92, -56, 16, 0, 0, -8, -136, 64, -8, -32, -12, -32, -76, 96, 40, 0, 0, -8, -32, 0, 16, -48, -76, -56, 4, -96, 40, 0, -152, 0, 148, -24, -64, 16, -48, 28, -8, 0, -6, 88, -128, 0, -188, 160, 48, 64, 12, 8, 40, -60, -44, 172, 96, 60, -124, 104, -24, -64, 68, 24, 80, 48, -20, 80, -112, 0, -56, -112, -36, -192, -168, 0, 156, 36, 2, 100, 36, -88, 22, -104, 0, 16, 128, 4, -136, 104, -12, 24, -200, 40, 160, -72, -20, -112, 40, 0, 100, -124, -40, 0, -136, 8, 36, 52, -16, 128, 20, 0, -104, 0, -12, 40, 20, 12, 108, 112, 16, 0, -76, -24, -56, 0, -56, -112, 40, -32, -64, 88, -24, 120, 96, -72, 40, -4, -68, 24, -80, -40, 156, 0, -24, 40, -72, -20, -136, 0, -28, -192, 216, 80, 48, 0, 80, -152, 44, -4, -72, 120, -88, 32, 224, 16, 200, 176, -8, -56, 58, 8, -68, -32, 52, 16, -132, 4, 116, 0, 96, 16, -56, 0, 40, -16, 8, -8, 112, -104, 72, 0, -24, 0, 248, -16, -180, 44, -24, -60, 0, 0, 184, 0, 8, 0, -168, -24, -8, 16, 8, 0, 148, 0, -88, -88, 32, 64, -12, 128, 48, -96, -12, 176, 228, 48, -60, 172, -44, 0, -12, 0, 56, -280, 32, 0, 112, 128, -16, 0, 8, -128, -8, 40, -24, 248, 132, -148, 24, 8, -112, -152, 40, 40, -68, 80, -32, -192, 64, 0, 16, -68, -44, 0, 72, 64, 20, -24, -80, 200, -4, 0, -228, 0, 104, 8, -16, -48, -72, 32, 168, 0, 104, -192, -76, 0, -100, -48, 80, -112, -136, -32, -172, 4, -12, -40, 120, -40, -56, -184, -68, -64, 136, -48, 24, -104, -128, -64, -196, 0, -112, 176, 0, 144, -210, 0, 172, -84, -106, -52, -144, -16, -64, -104, 20, -248, 8, -16, -64, 40, 32, -96, 12, -24, 104, -200, -4, 88, 44, 0, 184, 104, 62, 0, -264, 8, 52, 108, 12, -152, 16, 0, -232, 0, 8, 24, -72, 8, 112, -64, 64, 0, 204, -16, -28, 0, 8, 136, 84, 16, 40, -112, 4, -112, 48, -12, 112, 28, -104, 56, -44, -80, -84, 48, -24, 160, -112, -24, 124, 0, -120, 48, 116, 0, -92, 0, -16, 64, -80, -36, -128, -24, -2, 120, 48, 104, 148, -56, -24, 0, 164, 40, 16, -44, 120, 36, -116, -48, 156, 0, 16, -40, -228, 0, -80, 176, -12, -8, 296, 32, 48, 0, 68, 0, 80, 32, -48, -72, -20, -148, 96, 0, 96, 104, 16, 0, -20, 8, 144, -8, 100, -80, 200, 96, -16, 72, 28, 104, -92, -128, -40, 96, -48, 144, 132, -48, 40, -76, 68, 0, 128, -160, -64, 288, -62, 0, 48, 52, 52, -96, 0, 176, -8, 0, -84, -80, 96, 44, 24, 24, 100, 40, 24, -48, -160, -48, 100, 196, 56, 0, -136, 28, -36, 0, 32, -80, 12, -92, 92, 8, -20, 0, -16, 0, -32, -208, -24, 32, 20, 36, 160, 0, 84, 184, -48, 0, -276, -168, 80, 128, -136, -8, 40, -188, -164, 48, 168, -20, -264, -96, -68, 200, 200, 104, -120, -16, 8, 184, -32, 0, -64, 16, 32, -304, -148, 0, 48, 316, 16, 4, -124, 128, -316, 208, -4, 336, -40, -24, -112, 8, -140, 32, -224, -8, 144, 0, 8, -152, -84, 0, 88, 48, 72, 0, -248, 8, 32, -148, -112, 136, 100, 0, -20], "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.e", "char_is_minimal": true, "conrey_index": 43, "id": null, "nf_label": 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 2, 1, -1, -1, -1, 0, 0, 0, -1, 0, 0, 1, -1, -1], [-1, -1, 1, 0, 1, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 1, -1, 1, -1, 1, 0, -1, 1, 0, 1, 1, -1, 0, 0], [2, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, -1], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 0, -1, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0], [2, 2, 0, 1, 0, 2, -1, 0, 1, -1, 0, -1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [-2, 0, 2, 1, -2, 0, 1, 0, 0, 0, -1, 0, -1, 0, -1, 1], [-1, -3, 2, 1, 1, 0, -1, -1, -1, 0, -1, 1, 1, 2, 0, -1], [0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 1], [0, -1, 0, 1, 1, -1, -1, 0, 0, -1, 1, 0, -1, 1, 0, -1], [0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 1, -1, 0, -1, 0, 1], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 4, 0, -1, 1, 1, 1, 0, -1, 1, 1, 0, 1, -1, 0, 1], [2, 0, -1, -1, 1, 2, -1, -1, 1, 0, 1, 0, 1, 1, 1, 0], [-1, 0, 2, 0, 0, -1, 0, -1, -1, 1, -1, 0, 1, 1, 0, -1], [0, 0, -3, -1, -1, 0, 1, 1, 1, -1, 1, -2, -3, -1, -1, 0], [0, 0, 1, 1, 1, 0, -1, 1, 0, 0, -1, -1, 0, 0, 0, -1], [0, -1, 0, 0, 0, -1, 0, -1, 1, 0, 0, 0, 0, 0, 0, -1], [-2, 1, 0, 0, -3, 2, 0, 2, 1, 0, -1, -1, -1, -1, -1, 1], [2, 1, 3, 2, -2, 3, 0, 1, 3, 0, -4, 0, 1, 0, -2, -1], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, -2, 2, -2, -1, 0, -2, 1, 0, 1, 2, -1, 1, -1], [-2, 0, -2, -2, 2, 0, 2, -3, -1, 1, 1, 2, 1, -1, 2, 1], [0, 1, 1, 0, 0, 0, -1, 0, -1, 0, -1, -1, 1, 0, 0, 0], [-3, -3, 6, 3, 3, -4, -1, -2, 0, 3, -5, 4, 3, 1, 0, -3], [-4, 0, 2, 0, 0, -4, 2, 0, -2, 2, -2, 2, 0, 0, 0, -2], [1, 0, -2, 0, 1, 1, 0, 0, 2, 0, 1, 1, 0, -1, 2, 1], [0, 0, 0, 1, -3, 2, 0, 1, 1, -1, -1, -2, -2, 1, -2, 0], [0, 0, -1, 0, -2, 2, 0, 0, -1, -1, 0, 0, -1, 0, -2, 2], [0, 1, -2, -1, 1, 1, 1, 0, 0, 0, 1, 0, 0, -1, 1, 1], [0, 0, -4, -1, 0, 0, -1, 2, 0, 0, 1, -2, -1, 0, -1, -1], [-2, -2, 0, 0, 0, 0, 2, 0, -2, 0, -2, 0, -3, 2, -1, 0], [0, 0, 1, 0, 1, 2, 2, 1, 0, 0, -2, 1, 1, 0, -1, 0], [1, 1, -2, -3, 1, -2, 0, -1, -3, 0, 3, -1, -1, 0, -1, 1], [1, 2, -7, -4, 0, -1, 2, 1, -1, -1, 6, -1, -3, -3, 2, 4], [3, 1, -4, -1, -1, 0, -1, 1, -1, -2, 3, -1, -2, 0, 1, 1], [4, -2, -3, 1, 1, 0, -5, 1, 0, -2, 3, -1, 0, 2, 2, 1], [-3, 0, 0, 1, -3, -1, 0, 0, 2, 0, 1, 1, -1, 0, 1, 2], [1, 1, -1, 0, -1, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0], [-2, -2, 0, 2, -2, -4, -2, 2, 0, 0, 0, 0, -1, 0, 1, 0], [1, 0, 1, 0, 4, -1, 2, -1, 1, 1, -2, 1, 1, -1, 2, 0], [0, 1, -2, -1, -1, 1, 1, 0, 0, -1, 3, 0, -1, -1, 0, 1], [-3, -4, 4, 1, 3, 0, 1, -4, 1, 3, -5, 2, 3, 3, 0, -1], [4, 0, -1, 3, -1, 4, -4, 1, 5, -1, -1, -2, 1, 1, -1, 0], [-1, 0, 2, 1, 0, 1, 1, 0, 1, 1, -2, 1, 1, 0, 0, 0], [5, 0, -2, 1, 1, 5, 0, 2, 6, -2, 1, -1, -1, -2, -1, 0], [2, 1, -4, -1, -4, -1, -1, 2, 1, -2, 3, -2, -3, 0, 1, 1], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, -6, -2, 0, 0, 0, 3, 0, -3, 5, -2, -5, -1, 2, 1], [0, -4, -2, 0, 2, -2, -2, -2, -2, 0, 4, 0, -1, 2, 3, 0], [1, 0, 2, 1, -1, 1, -1, 0, 3, 1, -1, 0, 1, 1, 0, -1], [-1, 1, -3, -3, 1, 2, 2, -3, -3, 0, 3, 1, 0, -2, 1, 3], [1, 0, -3, -1, -2, -3, -1, -1, -2, 0, 2, 0, 0, -1, -2, 0], [2, -1, -3, 0, -2, -1, -2, 1, 1, -1, 2, -2, -2, 0, 1, 1], [1, 2, -1, -1, -1, 1, 3, -1, -2, 2, 3, 1, -4, 0, 0, 1], [0, 0, -1, 0, 4, 2, 5, 2, -2, 2, 0, 4, 2, -4, 2, 0], [1, 0, -1, 1, -1, 1, -1, 0, 1, -1, 0, -1, -1, 1, 0, 0], [2, 0, -4, 2, 2, 2, 0, 0, 0, -2, 2, 2, 0, 0, 4, 0], [1, -1, -1, 1, -1, 0, -1, 0, 1, -2, -1, 0, 1, 1, 1, -3], [-2, 0, 3, 1, 1, 0, 1, -1, -1, 1, -1, 0, 2, -1, -2, 0], [2, 2, 0, 0, -2, 2, 2, 0, 2, 0, 0, 0, -2, 0, -2, 0], [3, 3, -2, 0, -2, 2, -1, 2, 4, -1, 0, -1, -1, -1, 0, 1], [0, 0, 1, 1, 1, 0, 1, -1, 0, 0, 1, 1, 0, 0, 0, -1], [1, 2, 2, -2, 2, 5, 2, -1, 3, 3, -4, 1, 2, -1, 0, 0], [-3, -2, -2, -1, 3, -3, 1, 0, -3, 1, -1, 0, 3, -3, 2, -1], [-2, -1, 0, 0, 0, -1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 1], [-5, -6, 3, 1, -3, -5, -3, -1, 0, 0, -1, -1, 0, 0, 0, 1], [-2, 1, -7, -2, 2, -1, 0, 1, -1, 0, 4, 0, -1, 0, 4, 3], [0, -1, 4, 1, 2, 2, 1, 0, 0, 1, -4, 1, 2, 0, -1, -2], [0, 2, 2, 0, 0, -4, 0, 0, 0, 2, -2, 4, 2, -2, 4, 2], [1, 0, 1, 2, 0, -5, -2, -1, 1, -1, 2, -3, -1, 1, 0, -2], [0, -3, 1, 0, 4, -1, 0, -1, 1, 0, -2, 2, 2, 0, 1, -1], [7, 3, 0, -1, 1, 2, -1, 0, 2, 1, 1, 0, 1, 1, 0, -1], [-4, -1, 2, -3, -1, -3, 3, -2, -4, 3, -1, 2, -2, 3, 1, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-6, -2, 8, 2, -2, -2, 0, -4, -2, 2, -4, 0, 2, 4, -2, 0], [3, 2, -3, -2, -4, 3, 0, 3, 1, -3, 2, -3, -1, -1, -2, 2], [-1, 1, 2, 0, 0, -2, -1, -2, 0, 1, 0, -1, 0, 1, 1, -1], [0, -2, -1, 1, -2, 0, -1, 3, -1, -3, 1, -1, -2, 1, -1, -1], [-2, 2, 4, -2, 2, -6, 0, 0, -4, 4, -2, -2, 3, 0, -1, -2], [0, 0, -1, -1, -1, 0, -1, 0, -1, 1, 0, -1, -1, 1, 0, 2], [4, 4, 2, 2, 0, 6, 2, 0, 2, 0, -4, -2, 3, 0, -5, -2], [1, -2, 0, -1, 1, 1, -1, -2, 1, -3, 1, 2, -3, 3, 0, -1], [1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0], [2, 2, -2, 2, 0, 2, 0, 2, 4, -4, -2, 0, 0, 0, 0, -4], [2, 2, 2, 4, 0, 2, -2, 2, 2, 0, -2, -2, 4, 0, 0, -2], [-3, -3, 2, -1, 1, -2, -1, -2, -2, -1, 1, 2, -1, 3, 0, -1], [-4, -4, 4, 2, -2, -6, 2, 0, -2, 0, 0, 2, 0, -2, 0, 2], [-2, -2, -7, -3, 1, 0, 5, 3, -4, -4, 3, 1, -6, 0, 0, 3], [-2, 0, 2, 0, 0, 2, 0, -2, 0, 0, -2, 0, 0, 2, -2, -2], [3, 0, 7, 1, 1, 3, -5, -1, 0, 0, -5, 1, 6, 0, 0, -1], [4, 4, -6, -6, 2, 0, 5, 2, -4, 0, 4, 2, 1, -6, 1, 6], [-2, -2, 0, -1, 0, -2, 1, 0, -1, 1, 0, 1, -1, 0, 0, 0], [1, 4, -4, -3, 1, 3, 4, 4, 2, 1, 1, -3, -1, -4, -3, 2]]}