# Stored data for newform 384.7.b.b, downloaded from the LMFDB on 25 April 2024. {"label": "384.7.b.b", "space_label": "384.7.b", "level": 384, "weight": 7, "hecke_orbit": 2, "hecke_orbit_code": 4503668464288128, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 2062430997899132173, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [10800, 0, 1]]], "qexp_display": "q+3\\zeta_{12}q^{3}-5\\zeta_{12}^{2}q^{5}-\\zeta_{12}^{3}q^{7}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 8, "char_orbit_label": "b", "char_is_real": true, "Nk2": 18816, "analytic_conductor": 88.34076811002278, "hecke_ring_index": 15552, "level_radical": 6, "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": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.759", "prec": 17}, "analytic_rank_proved": true, "char_values": [384, 2, [127, 133, 257], [1, 1, 2]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 4, "level_primes": [2, 3], "conrey_indexes": [319], "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [[2, 6], [3, 5]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.791", "prec": 17}, {"__RealLiteral__": 0, "data": "0.993", "prec": 17}, {"__RealLiteral__": 0, "data": "118.894", "prec": 24}, {"__RealLiteral__": 0, "data": "77.290", "prec": 20}, {"__RealLiteral__": 0, "data": "4545.711", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "6.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, 0, 0, 0, 0, 0, 972, 0, 0, 0, 0, 0, 0, 0, 3896, 0, 0, 0, 0, 0, 0, 0, 19300, 0, 0, 0, 0, 0, 0, 0, 24624, 0, 0, 0, 0, 0, 0, 0, 133192, 0, 0, 0, 0, 0, 0, 0, 423940, 0, 0, 0, 0, 0, 0, 0, 60912, 0, 0, 0, 0, 0, 0, 0, 915840, 0, 0, 0, 0, 0, 0, 0, -454472, 0, 0, 0, 0, 0, 0, 0, 236196, 0, 0, 0, 0, 0, 0, 0, -1857160, 0, 0, 0, 0, 0, 0, 0, 206776, 0, 0, 0, 0, 0, 0, 0, -699840, 0, 0, 0, 0, 0, 0, 0, -321272, 0, 0, 0, 0, 0, 0, 0, -6462436, 0, 0, 0, 0, 0, 0, 0, 1019952, 0, 0, 0, 0, 0, 0, 0, -4412600, 0, 0, 0, 0, 0, 0, 0, -3948480, 0, 0, 0, 0, 0, 0, 0, 946728, 0, 0, 0, 0, 0, 0, 0, 9051264, 0, 0, 0, 0, 0, 0, 0, -108572, 0, 0, 0, 0, 0, 0, 0, 4679856, 0, 0, 0, 0, 0, 0, 0, 21392640, 0, 0, 0, 0, 0, 0, 0, -2506760, 0, 0, 0, 0, 0, 0, 0, 16307568, 0, 0, 0, 0, 0, 0, 0, 1543104, 0, 0, 0, 0, 0, 0, 0, 6765120, 0, 0, 0, 0, 0, 0, 0, 4689900, 0, 0, 0, 0, 0, 0, 0, 21615992, 0, 0, 0, 0, 0, 0, 0, -77451272, 0, 0, 0, 0, 0, 0, 0, 35944560, 0, 0, 0, 0, 0, 0, 0, 19979272, 0, 0, 0, 0, 0, 0, 0, -68454720, 0, 0, 0, 0, 0, 0, 0, 14836608, 0, 0, 0, 0, 0, 0, 0, 18303992, 0, 0, 0, 0, 0, 0, 0, -92755572, 0, 0, 0, 0, 0, 0, 0, 5983632, 0, 0, 0, 0, 0, 0, 0, 2004480, 0, 0, 0, 0, 0, 0, 0, -115469560, 0, 0, 0, 0, 0, 0, 0, 79158384, 0, 0, 0, 0, 0, 0, 0, -31632768, 0, 0, 0, 0, 0, 0, 0, -210042424, 0, 0, 0, 0, 0, 0, 0, 135768960, 0, 0, 0, 0, 0, 0, 0, 279274888, 0, 0, 0, 0, 0, 0, 0, -184366372, 0, 0, 0, 0, 0, 0, 0, 32365656, 0, 0, 0, 0, 0, 0, 0, 83707776, 0, 0, 0, 0, 0, 0, 0, -17729280, 0, 0, 0, 0, 0, 0, 0, 210002544, 0, 0, 0, 0, 0, 0, 0, 272016440, 0, 0, 0, 0, 0, 0, 0, -197030584, 0, 0, 0, 0, 0, 0, 0, 190681776, 0, 0, 0, 0, 0, 0, 0, 18798200, 0, 0, 0, 0, 0, 0, 0, -420278984, 0, 0, 0, 0, 0, 0, 0, 103017420, 0, 0, 0, 0, 0, 0, 0, 518441912, 0, 0, 0, 0, 0, 0, 0, -467205688, 0, 0, 0, 0, 0, 0, 0, 101476800, 0, 0, 0, 0, 0, 0, 0, 25838784, 0, 0, 0, 0, 0, 0, 0, -453523968, 0, 0, 0, 0, 0, 0, 0, 410856624, 0, 0, 0, 0, 0, 0, 0, 71570304, 0, 0, 0, 0, 0, 0, 0, -333564480, 0, 0, 0, 0, 0, 0, 0, 14801616, 0, 0, 0, 0, 0, 0, 0, -130578488, 0, 0, 0, 0, 0, 0, 0, -1163801660, 0, 0, 0, 0, 0, 0, 0, 534961584, 0, 0, 0, 0, 0, 0, 0, 419402880, 0, 0, 0, 0, 0, 0, 0, -284368320, 0, 0, 0, 0, 0, 0, 0, 23983776, 0, 0, 0, 0, 0, 0, 0, -85023800, 0, 0, 0, 0, 0, 0, 0, -996577336, 0, 0, 0, 0, 0, 0, 0, 222549120, 0, 0, 0, 0, 0, 0, 0, 470072584, 0, 0, 0, 0, 0, 0, 0, 309670840, 0, 0, 0, 0, 0, 0, 0, -63965376, 0, 0, 0, 0, 0, 0, 0, -96871816, 0, 0, 0, 0, 0, 0, 0, -581877500, 0, 0, 0, 0, 0, 0, 0, 754680240, 0, 0, 0, 0, 0, 0, 0, 1425910328, 0, 0, 0, 0, 0, 0, 0, 118556352, 0, 0, 0, 0, 0, 0, 0, -110436696, 0, 0, 0, 0, 0, 0, 0, -43856640, 0, 0, 0, 0, 0, 0, 0, -462883400, 0, 0, 0, 0, 0, 0, 0, 960770160, 0, 0, 0, 0, 0, 0, 0, 1451240064, 0, 0, 0, 0, 0, 0, 0, 129729008, 0, 0, 0, 0, 0, 0, 0, -474491520, 0, 0, 0, 0, 0, 0, 0, -1312433280, 0, 0, 0, 0, 0, 0, 0, 313201728, 0, 0, 0, 0, 0, 0, 0, 57395628, 0, 0, 0, 0, 0, 0, 0, 413125056, 0, 0, 0, 0, 0, 0, 0, 795839040, 0, 0, 0, 0, 0, 0, 0, -812147472, 0, 0, 0, 0, 0, 0, 0, -1834539704, 0, 0, 0, 0, 0, 0, 0, -516241160, 0, 0, 0, 0, 0, 0, 0, 346560768, 0, 0, 0, 0, 0, 0, 0, 1659052800, 0, 0, 0, 0, 0, 0, 0, -42494976, 0, 0, 0, 0, 0, 0, 0, -451289880, 0, 0, 0, 0, 0, 0, 0, -2640025016, 0, 0, 0, 0, 0, 0, 0, 63916992, 0, 0, 0, 0, 0, 0, 0, 118810800, 0, 0, 0, 0, 0, 0, 0, 412917560, 0, 0, 0, 0, 0, 0, 0, 2018402212, 0, 0, 0, 0, 0, 0, 0, -2095923600, 0, 0, 0, 0, 0, 0, 0, -4201534520, 0, 0, 0, 0, 0, 0, 0, -349600320, 0, 0, 0, 0, 0, 0, 0, 50246568, 0, 0, 0, 0, 0, 0, 0, 4011853960, 0, 0, 0, 0, 0, 0, 0, 1327223232, 0, 0, 0, 0, 0, 0, 0, -2878301952, 0, 0, 0, 0, 0, 0, 0, -3438495360, 0, 0, 0, 0, 0, 0, 0, 910595520, 0, 0, 0, 0, 0, 0, 0, 332666352, 0, 0, 0, 0, 0, 0, 0, -461781064, 0, 0, 0, 0, 0, 0, 0, 5251785976, 0, 0, 0, 0, 0, 0, 0, -170061120, 0, 0, 0, 0, 0, 0, 0, -2324243384, 0, 0, 0, 0, 0, 0, 0, 2569072324, 0, 0, 0, 0, 0, 0, 0, 59328288, 0, 0, 0, 0, 0, 0, 0, 157422392, 0, 0, 0, 0, 0, 0, 0, 5752175040, 0, 0, 0, 0, 0, 0, 0, -3844777104, 0, 0, 0, 0, 0, 0, 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, 8, 4, -1, 2, 0], [1, 1, 4, 2, -1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 4, "minimal_twist": "384.7.b.b", "char_is_minimal": true, "conrey_index": 319, "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], [0, 0, 0, 0], [0, 3, 0, 0], [0, 0, 0, 0], [0, 0, -5, 0], [0, 0, 0, 0], [0, 0, 0, -1], [0, 0, 0, 0], [243, 0, 0, 0], [0, 0, 0, 0], [0, 76, 0, 0], [0, 0, 0, 0], [0, 0, 106, 0], [0, 0, 0, 0], [0, 0, 0, -15], [0, 0, 0, 0], [974, 0, 0, 0], [0, 0, 0, 0], [0, 188, 0, 0], [0, 0, 0, 0], [0, 0, -81, 0], [0, 0, 0, 0], [0, 0, 0, 194], [0, 0, 0, 0], [4825, 0, 0, 0], [0, 0, 0, 0], [0, 729, 0, 0], [0, 0, 0, 0], [0, 0, -457, 0], [0, 0, 0, 0], [0, 0, 0, 145], [0, 0, 0, 0], [6156, 0, 0, 0], [0, 0, 0, 0], [0, -2160, 0, 0], [0, 0, 0, 0], [0, 0, 2476, 0], [0, 0, 0, 0], [0, 0, 0, 318], [0, 0, 0, 0], [33298, 0, 0, 0], [0, 0, 0, 0], [0, 3148, 0, 0], [0, 0, 0, 0], [0, 0, -1215, 0], [0, 0, 0, 0], [0, 0, 0, -678], [0, 0, 0, 0], [105985, 0, 0, 0], [0, 0, 0, 0], [0, 2922, 0, 0], [0, 0, 0, 0], [0, 0, -7923, 0], [0, 0, 0, 0], [0, 0, 0, -380], [0, 0, 0, 0], [15228, 0, 0, 0], [0, 0, 0, 0], [0, 14444, 0, 0], [0, 0, 0, 0], [0, 0, 232, 0], [0, 0, 0, 0], [0, 0, 0, -243], [0, 0, 0, 0], [228960, 0, 0, 0], [0, 0, 0, 0], [0, 50332, 0, 0], [0, 0, 0, 0], [0, 0, 15714, 0], [0, 0, 0, 0], [0, 0, 0, 1534], [0, 0, 0, 0], [-113618, 0, 0, 0], [0, 0, 0, 0], [0, 14475, 0, 0], [0, 0, 0, 0], [0, 0, -2052, 0], [0, 0, 0, 0], [0, 0, 0, -6095], [0, 0, 0, 0], [59049, 0, 0, 0], [0, 0, 0, 0], [0, 110940, 0, 0], [0, 0, 0, 0], [0, 0, -4870, 0], [0, 0, 0, 0], [0, 0, 0, -1371], [0, 0, 0, 0], [-464290, 0, 0, 0], [0, 0, 0, 0], [0, 45792, 0, 0], [0, 0, 0, 0], [0, 0, 11745, 0], [0, 0, 0, 0], [0, 0, 0, -940], [0, 0, 0, 0], [51694, 0, 0, 0], [0, 0, 0, 0], [0, 18468, 0, 0], [0, 0, 0, 0]]}