# Stored data for newform 384.4.f.g, downloaded from the LMFDB on 29 March 2024. {"label": "384.4.f.g", "space_label": "384.4.f", "level": 384, "weight": 4, "hecke_orbit": 7, "hecke_orbit_code": 27021941428715904, "dim": 8, "is_polredabs": true, "nf_label": "8.0.12745506816.1", "trace_hash": 1581524386762022547, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [1600, 0, -304, 0, 1]], [23, [5056, 160, 1]]], "qexp_display": "q+(\\beta _{3}+\\beta _{4})q^{3}+(-2\\beta _{3}+\\beta _{6})q^{5}+(-3\\beta _{2}+\\cdots)q^{7}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 24, "char_orbit_label": "f", "char_is_real": true, "Nk2": 6144, "analytic_conductor": 22.656733442204395, "hecke_ring_index": 16384, "level_radical": 6, "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": "0.758", "prec": 17}, "analytic_rank_proved": true, "char_values": [384, 2, [127, 133, 257], [1, 1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 4, "level_primes": [2, 3], "conrey_indexes": [191], "field_disc": 12745506816, "field_disc_factorization": [[2, 16], [3, 4], [7, 4]], "field_poly": [1, 0, 0, 0, 23, 0, 0, 0, 1], "hecke_ring_index_factorization": [[2, 14]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.095", "prec": 17}, {"__RealLiteral__": 0, "data": "7.528", "prec": 17}, {"__RealLiteral__": 0, "data": "9.167", "prec": 17}, {"__RealLiteral__": 0, "data": "611.912", "prec": 24}, {"__RealLiteral__": 0, "data": "1210.424", "prec": 27}, {"__RealLiteral__": 0, "data": "72315.870", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "3.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 8, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, 0, -640, 0, 216, 0, 0, 0, 0, 0, 0, 0, 336, 0, 0, 0, 0, 0, 1344, 0, 0, 0, 0, 0, 0, 0, 0, 0, -776, 0, 0, 0, 0, 0, 0, 0, 672, 0, 0, 0, 0, 0, 2688, 0, 0, 0, 0, 0, 0, 0, -640, 0, -1232, 0, 0, 0, 0, 0, 0, 0, -2232, 0, 0, 0, 0, 0, 1344, 0, 0, 0, 0, 0, 0, 0, -9856, 0, 5712, 0, 0, 0, 0, 0, 0, 0, -1344, 0, 0, 0, 0, 0, 9408, 0, 0, 0, 0, 0, 0, 0, -11008, 0, 1784, 0, 0, 0, 0, 0, 0, 0, 4704, 0, 0, 0, 0, 0, 10944, 0, 0, 0, 0, 0, 0, 0, -9856, 0, -15680, 0, 0, 0, 0, 0, 0, 0, 2688, 0, 0, 0, 0, 0, 6720, 0, 0, 0, 0, 0, 0, 0, -11648, 0, 552, 0, 0, 0, 0, 0, 0, 0, -1680, 0, 0, 0, 0, 0, 22848, 0, 0, 0, 0, 0, 0, 0, 7424, 0, 15344, 0, 0, 0, 0, 0, 0, 0, -8736, 0, 0, 0, 0, 0, 9600, 0, 0, 0, 0, 0, 0, 0, -11648, 0, 1344, 0, 0, 0, 0, 0, 0, 0, -3240, 0, 0, 0, 0, 0, 6528, 0, 0, 0, 0, 0, 0, 0, -30720, 0, 5488, 0, 0, 0, 0, 0, 0, 0, 12432, 0, 0, 0, 0, 0, 16128, 0, 0, 0, 0, 0, 0, 0, -22656, 0, -6720, 0, 0, 0, 0, 0, 0, 0, -2688, 0, 0, 0, 0, 0, -8064, 0, 0, 0, 0, 0, 0, 0, -30720, 0, -11640, 0, 0, 0, 0, 0, 0, 0, -1008, 0, 0, 0, 0, 0, 2880, 0, 0, 0, 0, 0, 0, 0, 34944, 0, -22288, 0, 0, 0, 0, 0, 0, 0, -1680, 0, 0, 0, 0, 0, -20160, 0, 0, 0, 0, 0, 0, 0, 49280, 0, -10320, 0, 0, 0, 0, 0, 0, 0, 9984, 0, 0, 0, 0, 0, -4032, 0, 0, 0, 0, 0, 0, 0, 23936, 0, 69224, 0, 0, 0, 0, 0, 0, 0, 32256, 0, 0, 0, 0, 0, -2688, 0, 0, 0, 0, 0, 0, 0, 23296, 0, -5504, 0, 0, 0, 0, 0, 0, 0, -46032, 0, 0, 0, 0, 0, -45696, 0, 0, 0, 0, 0, 0, 0, 12928, 0, -40880, 0, 0, 0, 0, 0, 0, 0, -38880, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30720, 0, 58576, 0, 0, 0, 0, 0, 0, 0, 11640, 0, 0, 0, 0, 0, -52416, 0, 0, 0, 0, 0, 0, 0, 3584, 0, 4048, 0, 0, 0, 0, 0, 0, 0, 25536, 0, 0, 0, 0, 0, -57792, 0, 0, 0, 0, 0, 0, 0, 82432, 0, -47488, 0, 0, 0, 0, 0, 0, 0, 19488, 0, 0, 0, 0, 0, -59136, 0, 0, 0, 0, 0, 0, 0, -8064, 0, -75584, 0, 0, 0, 0, 0, 0, 0, -38304, 0, 0, 0, 0, 0, -53952, 0, 0, 0, 0, 0, 0, 0, -16128, 0, -35384, 0, 0, 0, 0, 0, 0, 0, 88368, 0, 0, 0, 0, 0, -71232, 0, 0, 0, 0, 0, 0, 0, 183680, 0, 107072, 0, 0, 0, 0, 0, 0, 0, 46464, 0, 0, 0, 0, 0, -80640, 0, 0, 0, 0, 0, 0, 0, 25728, 0, 59696, 0, 0, 0, 0, 0, 0, 0, -102144, 0, 0, 0, 0, 0, 60480, 0, 0, 0, 0, 0, 0, 0, -4224, 0, -30800, 0, 0, 0, 0, 0, 0, 0, -55104, 0, 0, 0, 0, 0, -43008, 0, 0, 0, 0, 0, 0, 0, 97024, 0, 25864, 0, 0, 0, 0, 0, 0, 0, 15456, 0, 0, 0, 0, 0, 9600, 0, 0, 0, 0, 0, 0, 0, 31360, 0, 3360, 0, 0, 0, 0, 0, 0, 0, 18480, 0, 0, 0, 0, 0, 32256, 0, 0, 0, 0, 0, 0, 0, -52864, 0, 3920, 0, 0, 0, 0, 0, 0, 0, -113904, 0, 0, 0, 0, 0, -12096, 0, 0, 0, 0, 0, 0, 0, 155520, 0, -70656, 0, 0, 0, 0, 0, 0, 0, 43008, 0, 0, 0, 0, 0, 2688, 0, 0, 0, 0, 0, 0, 0, -19712, 0, -170688, 0, 0, 0, 0, 0, 0, 0, 154440, 0, 0, 0, 0, 0, -45888, 0, 0, 0, 0, 0, 0, 0, -296832, 0, 188608, 0, 0, 0, 0, 0, 0, 0, 43344, 0, 0, 0, 0, 0, 16128, 0, 0, 0, 0, 0, 0, 0, 13440, 0, 122864, 0, 0, 0, 0, 0, 0, 0, -110976, 0, 0, 0, 0, 0, -76608, 0, 0, 0, 0, 0, 0, 0, -125440, 0, -189056, 0, 0, 0, 0, 0, 0, 0, -34944, 0, 0, 0, 0, 0, 40512, 0, 0, 0, 0, 0, 0, 0, -56448, 0, -48832, 0, 0, 0, 0, 0, 0, 0, 181104, 0, 0, 0, 0, 0, 122304, 0, 0, 0, 0, 0, 0, 0, 133504, 0, 79512, 0, 0, 0, 0, 0, 0, 0, -58464, 0, 0, 0, 0, 0, 147840, 0, 0, 0, 0, 0, 0, 0, -32000, 0, 162496, 0, 0, 0, 0, 0, 0, 0, -85680, 0, 0, 0, 0, 0, 26688, 0, 0, 0, 0, 0, 0, 0, -183680, 0, -66752, 0, 0, 0, 0, 0, 0, 0, -69888, 0, 0, 0, 0, 0, 196224, 0, 0, 0, 0, 0, 0, 0, -58880, 0, -196896, 0, 0, 0, 0, 0, 0, 0, 104160, 0, 0, 0, 0, 0, 249984, 0, 0, 0, 0, 0, 0, 0, -200192, 0, 65296, 0, 0, 0, 0, 0, 0, 0, 4032, 0, 0, 0, 0, 0, 28224, 0, 0, 0, 0, 0, 0, 0, -175616, 0, 212792, 0, 0, 0, 0, 0, 0, 0, -325248, 0, 0, 0, 0, 0, 186816, 0, 0, 0, 0, 0, 0, 0, 292992, 0, -132160, 0, 0, 0, 0, 0, 0, 0, 672, 0, 0, 0, 0, 0, -28224, 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, 8, 2, 1, 2, 0], [1, 1, 12, 2, 1, 2, 0], [1, 1, 24, 6, 1, 2, 0]], "char_orbit_index": 6, "prim_orbit_index": 6, "minimal_twist": "384.4.f.g", "char_is_minimal": true, "conrey_index": 191, "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], [1, 0, 0, 0, 0, 0, 0, 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, -2, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -3, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-15, 0, 0, 0, 0, -3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -8, 0, -1, -2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -7, 0, -4, -8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-24, 0, 7, 0, 0, 6, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -16, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 7, 0, 0, -16, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 9, 0, 10, -8, 0, 9, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-80, 0, 0, 0, 0, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [27, 0, 0, 0, 0, 0, 0, -8], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -30, -3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 14, 0, 0, -23, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -7, 0, 0, -6, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [42, 0, 16, 0, 0, 3, 0, -8], [0, 0, 0, 0, 0, 0, 0, 0], [0, -8, 0, 4, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 31, 0, -28, -56, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [168, 0, 14, 0, 0, 12, 0, -7], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -16, 0, 0, 24, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 49, 0, 0, 16, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -42, 0, 6, -48, 0, -15, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 16], [0, 0, 0, 0, 0, 0, 0, 0], [-97, 0, 0, 0, 0, 0, 0, -24], [0, 0, 0, 0, 0, 0, 0, 0], [0, 48, 0, 10, -8, 0, 48, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 70, 0, 0, 45, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -78, 0, 0, -44, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [84, 0, -112, 0, 0, -21, 0, -16], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 5, 10, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -7, 0, -68, -136, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [336, 0, 45, 0, 0, -30, 0, 18], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -112, 0, 0, -76, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -91, 0, 0, 32, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 42, 0, -80, -80, 0, -12, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-80, 0, 0, 0, 0, 0, 0, -50], [0, 0, 0, 0, 0, 0, 0, 0], [-154, 0, 0, 0, 0, 0, 0, -24], [0, 0, 0, 0, 0, 0, 0, 0], [0, 168, 0, 27, 27, 0, -48, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 68, 0, 0, 46, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 189, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-279, 0, 0, 0, 0, 90, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -168, 0, -37, -74, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -164, 0, -48, -96, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [168, 0, -161, 0, 0, -42, 0, -23], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 128, 0, 0, -26, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -28, 0, 0, -16, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 21, 0, -30, 24, 0, 21, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1232, 0, 0, 0, 0, 0, 0, 78], [0, 0, 0, 0, 0, 0, 0, 0], [714, 0, 0, 0, 0, 0, 0, -16], [0, 0, 0, 0, 0, 0, 0, 0], [0, 120, 0, 57, 30, 0, -96, 0], [0, 0, 0, 0, 0, 0, 0, 0]]}