# Stored data for newform 912.2.f.i, downloaded from the LMFDB on 18 April 2024.
{"label": "912.2.f.i", "space_label": "912.2.f", "level": 912, "weight": 2, "hecke_orbit": 9, "hecke_orbit_code": 36029140649902992, "dim": 10, "is_polredabs": true, "nf_label": "10.0.20322144469993472.1", "trace_hash": 513839953833016142, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [128, 0, 600, 0, 726, 0, 301, 0, 32, 0, 1]], [7, [64, 100, 1, -21, -1, 1]], [29, [1216, 608, -140, -52, 3, 1]]], "qexp_display": "q+\\beta _{1}q^{3}-\\beta _{6}q^{5}+\\beta _{4}q^{7}+\\beta _{2}q^{9}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 57, "char_orbit_label": "f", "char_is_real": true, "Nk2": 3648, "analytic_conductor": 7.282356664340771, "hecke_ring_index": 4, "level_radical": 114, "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": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [912, 2, [799, 229, 305, 97], [2, 2, 1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3, 19], "conrey_indexes": [113], "field_disc": -20322144469993472, "field_disc_factorization": [[-1, 1], [2, 11], [19, 2], [29, 2], [5717, 2]], "field_poly": [243, -81, -27, -18, -6, 22, -2, -2, -1, -1, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.034", "prec": 17}, {"__RealLiteral__": 0, "data": "8.750", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "397.193", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "27088.157", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 10, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 1, 0, 2], "traces": [0, 10, 0, 1, 0, 0, 0, 2, 0, 3, 0, 0, 0, 0, 0, -10, 0, 0, 0, -2, 0, 5, 0, 0, 0, -14, 0, 10, 0, -6, 0, 0, 0, -10, 0, 0, 0, 0, 0, -7, 0, -4, 0, -20, 0, -2, 0, 0, 0, 16, 0, -1, 0, -26, 0, 12, 0, 9, 0, -2, 0, -4, 0, 17, 0, 32, 0, 0, 0, -27, 0, -8, 0, -26, 0, -39, 0, 0, 0, 0, 0, 23, 0, 0, 0, -8, 0, -13, 0, 4, 0, 0, 0, -18, 0, 8, 0, 0, 0, -2, 0, 0, 0, 0, 0, 22, 0, -54, 0, 0, 0, 20, 0, -60, 0, 8, 0, 11, 0, 0, 0, 10, 0, 20, 0, 0, 0, 0, 0, 26, 0, 0, 0, 12, 0, 20, 0, 0, 0, 32, 0, -26, 0, 68, 0, 0, 0, 72, 0, 0, 0, 0, 0, -3, 0, 36, 0, -32, 0, -15, 0, 0, 0, 36, 0, -16, 0, 32, 0, 16, 0, -55, 0, 68, 0, -50, 0, -3, 0, -44, 0, 0, 0, 48, 0, 100, 0, -24, 0, 76, 0, 0, 0, 0, 0, 58, 0, 0, 0, -34, 0, -43, 0, -34, 0, 0, 0, -49, 0, -40, 0, 0, 0, 24, 0, 0, 0, 0, 0, -43, 0, 30, 0, 0, 0, 23, 0, 74, 0, 12, 0, -26, 0, 0, 0, -40, 0, 60, 0, 0, 0, 0, 0, -69, 0, 0, 0, 30, 0, -38, 0, 0, 0, 44, 0, 82, 0, -36, 0, 0, 0, -113, 0, 0, 0, 0, 0, 10, 0, -36, 0, -14, 0, 15, 0, 0, 0, 56, 0, 6, 0, -92, 0, 24, 0, 10, 0, -24, 0, -32, 0, -52, 0, 94, 0, 0, 0, -92, 0, -106, 0, -32, 0, -86, 0, 0, 0, 0, 0, 34, 0, 0, 0, -34, 0, -86, 0, -26, 0, 0, 0, -49, 0, 86, 0, 0, 0, 37, 0, 0, 0, 0, 0, 60, 0, -100, 0, 0, 0, 20, 0, -56, 0, 94, 0, 46, 0, 0, 0, -20, 0, 86, 0, 0, 0, 0, 0, 93, 0, 0, 0, -2, 0, 59, 0, 0, 0, -32, 0, -100, 0, 10, 0, 0, 0, 120, 0, 0, 0, 0, 0, -56, 0, 12, 0, -116, 0, 46, 0, 0, 0, 22, 0, -30, 0, 100, 0, 80, 0, -101, 0, 4, 0, -16, 0, -34, 0, -88, 0, 0, 0, 123, 0, 90, 0, -64, 0, 142, 0, 0, 0, 0, 0, 66, 0, 0, 0, -100, 0, -34, 0, -56, 0, 0, 0, -50, 0, -38, 0, 0, 0, 46, 0, 0, 0, 0, 0, -84, 0, 212, 0, 0, 0, 50, 0, 220, 0, 66, 0, -26, 0, 0, 0, 84, 0, 124, 0, 0, 0, 0, 0, -144, 0, 0, 0, 94, 0, -63, 0, 0, 0, 28, 0, 87, 0, -160, 0, 0, 0, -118, 0, 0, 0, 0, 0, -124, 0, 16, 0, -36, 0, -16, 0, 0, 0, 108, 0, 0, 0, -100, 0, 86, 0, -30, 0, -108, 0, -60, 0, 22, 0, 32, 0, 0, 0, -183, 0, -196, 0, -28, 0, -135, 0, 0, 0, 0, 0, 72, 0, 0, 0, -96, 0, 4, 0, -16, 0, 0, 0, -104, 0, 44, 0, 0, 0, 40, 0, 0, 0, 0, 0, 106, 0, -120, 0, 0, 0, 49, 0, -176, 0, 4, 0, 7, 0, 0, 0, -34, 0, 82, 0, 0, 0, 0, 0, 166, 0, 0, 0, 76, 0, 36, 0, 0, 0, 136, 0, -105, 0, 32, 0, 0, 0, 131, 0, 0, 0, 0, 0, -91, 0, 48, 0, -64, 0, -52, 0, 0, 0, 92, 0, 22, 0, 220, 0, 134, 0, -150, 0, -8, 0, -108, 0, -13, 0, -132, 0, 0, 0, 164, 0, 236, 0, -100, 0, 176, 0, 0, 0, 0, 0, 82, 0, 0, 0, -116, 0, -59, 0, 94, 0, 0, 0, -191, 0, -212, 0, 0, 0, 50, 0, 0, 0, 0, 0, -126, 0, 90, 0, 0, 0, 81, 0, 140, 0, 80, 0, -32, 0, 0, 0, -104, 0, 66, 0, 0, 0, 0, 0, -96, 0, 0, 0, 20, 0, -132, 0, 0, 0, -40, 0, 124, 0, -40, 0, 0, 0, -171, 0, 0, 0, 0, 0, 20, 0, -46, 0, -222, 0, -6, 0, 0, 0, 84, 0, 8, 0, -44, 0, 124, 0, 91, 0, -124, 0, -24, 0, -54, 0, 174, 0, 0, 0, -96, 0, -140, 0, -156, 0, -158, 0, 0, 0, 0, 0, 150, 0, 0, 0, -174, 0, -210, 0, 146, 0, 0, 0, -120, 0, 64, 0, 0, 0, 60, 0, 0, 0, 0, 0, 50, 0, -264, 0, 0, 0, 150, 0, -162, 0, 176, 0, 90, 0, 0, 0, 92, 0, 118, 0, 0, 0, 0, 0, 183, 0, 0, 0, 136, 0, 81, 0, 0, 0, -22, 0, -142, 0, 166, 0, 0, 0, 210, 0, 0, 0, 0, 0, -32, 0, 68, 0, -64, 0, 36, 0, 0, 0, 74, 0, 10, 0, 188, 0, 108, 0, -166, 0, 80, 0, -12, 0, -68, 0, -32, 0, 0, 0, 164, 0, 136, 0, 58, 0, 136, 0, 0, 0, 0, 0, 153, 0, 0, 0, -160, 0, -186, 0, 80, 0, 0, 0, -18, 0, -52, 0, 0, 0, 63, 0, 0, 0, 0, 0, -142, 0, 132, 0, 0, 0, 98, 0, 172, 0, 32, 0, -76, 0, 0, 0, 22, 0, 138, 0, 0, 0, 0, 0, -130, 0, 0, 0, 50, 0, -73, 0, 0, 0, 18, 0, 151, 0, -122, 0, 0, 0, -224, 0, 0, 0, 0, 0, -187, 0, 8, 0, -84, 0, 62, 0, 0, 0, 42, 0, 103, 0, -240, 0, 288, 0, 61, 0, 28, 0, -8, 0, 37, 0, 144, 0, 0, 0, -157, 0, -280, 0, -124, 0, -158, 0, 0, 0, 0, 0, 123, 0, 0, 0, -112, 0, -48, 0], "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, 57, 4, 1, 2, 0]], "char_orbit_index": 6, "prim_orbit_index": 4, "minimal_twist": "456.2.f.a", "char_is_minimal": false, "conrey_index": 113, "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, 0, 0, 0, 0], [1, 0, 0, 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, 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, 1, 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, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 1, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, -1, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, -1, 0, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 1, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 1, 1, 0, 2, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 0, 0, -1, 1, 0, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 1, 1, -1, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 1, 1, 0, 1, 0, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 1, 1, 0, -1, -2, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -1, -1, 0, -1, 1, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 0, -1, 0, -1, 1, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, 1, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, 0, 0, -1, -1, 0, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, -1, 0, 1, -1, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 0, 0, 1, -2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 1, 1, 2, 2, 0, -1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, -1, 1, 0, 0, 0, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, -1, 1, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, -1, 2, 0, -1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 1, 2, 0, 0, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, -1, 1, -1, -2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 0, -1, 1, -3, -2, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 1, 1, -1, 2, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -2, -2, 0, 1, -2, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, -1, 1, 0, 1, 1, 1, 1, 1, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 2, -2, 0, 0, 0, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, -1, 1, 1, 1, 0, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, -1, 1, -2, -1, 2, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, -1, 0, 1, -2, -1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, -2, -2, 0, -2, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 1, 0, 1, 4, 0, -2, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 1, 0, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 2, 1, -1, 1, -2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, -1, -1, 4, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, -1, 0, 0, 4, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 2, 1, 1, 1, 2, 3, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -3, -1, 1, -2, -1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, -2, 0, 0, -2, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -3, 0, 0, 1, 1, -2, 1, 1, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}