# Stored data for newform 882.5.c.b, downloaded from the LMFDB on 20 April 2024.
{"label": "882.5.c.b", "space_label": "882.5.c", "level": 882, "weight": 5, "hecke_orbit": 2, "hecke_orbit_code": 4503737150210930, "dim": 4, "is_polredabs": true, "nf_label": "4.0.576.2", "trace_hash": 1828958410659169254, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [21609, 0, 678, 0, 1]], [11, [441, 54, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+8q^{4}+(-9\\beta _{2}-2\\beta _{3})q^{5}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 7, "char_orbit_label": "c", "char_is_real": true, "Nk2": 22050, "analytic_conductor": 91.1723074399507, "hecke_ring_index": 16, "level_radical": 42, "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": "0.507", "prec": 17}, "analytic_rank_proved": true, "char_values": [882, 2, [785, 199], [2, 1]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [685], "field_disc": 576, "field_disc_factorization": [[2, 6], [3, 2]], "field_poly": [4, 0, 2, 0, 1], "hecke_ring_index_factorization": [[2, 4]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.735", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "67.744", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1701.543", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "4.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, 32, 0, 0, 0, 0, 0, 0, -108, 0, 0, 0, 0, 256, 0, 0, 0, 0, 0, 192, -972, 0, 1144, 0, 0, 0, -3240, 0, 0, 0, 0, 0, 0, 0, 892, 0, 0, 0, 0, 0, 2344, -864, 0, -7680, 0, 0, 0, 3456, 0, 0, 5508, 0, 0, 0, 0, -768, 0, 0, 0, 0, 0, 2048, -6048, 0, 10124, 0, 0, 0, -18792, 0, 0, -8640, 0, 0, 0, 0, -1588, 0, 0, 0, 0, 0, 10380, -20736, 0, 1536, 0, 0, 0, -7776, 0, 0, 17820, 0, 0, 0, 0, 9152, 0, 0, 0, 0, 0, -24768, -62316, 0, -56420, 0, 0, 0, 38232, 0, 0, -25920, 0, 0, 0, 0, -54496, 0, 0, 0, 0, 0, 3752, 0, 0, 29568, 0, 0, 0, -53568, 0, 0, -55836, 0, 0, 0, 0, 14592, 0, 0, 0, 0, 0, 7136, 115236, 0, 54892, 0, 0, 0, 44388, 0, 0, 31104, 0, 0, 0, 0, 19532, 0, 0, 0, 0, 0, -10940, -1728, 0, 18752, 0, 0, 0, -6912, 0, 0, 67284, 0, 0, 0, 0, -61440, 0, 0, 0, 0, 0, -78720, -20844, 0, -2468, 0, 0, 0, 112536, 0, 0, 27648, 0, 0, 0, 0, -47712, 0, 0, 0, 0, 0, 4840, 44064, 0, -56256, 0, 0, 0, -1728, 0, 0, -125280, 0, 0, 0, 0, 8448, 0, 0, 0, 0, 0, -6144, 180900, 0, 48036, 0, 0, 0, -74952, 0, 0, -10368, 0, 0, 0, 0, 310560, 0, 0, 0, 0, 0, -19836, -34560, 0, 16384, 0, 0, 0, -48384, 0, 0, 259956, 0, 0, 0, 0, 80992, 0, 0, 0, 0, 0, 125568, -10152, 0, -33988, 0, 0, 0, 129816, 0, 0, -150336, 0, 0, 0, 0, -45128, 0, 0, 0, 0, 0, 250620, -69120, 0, -157248, 0, 0, 0, -179712, 0, 0, -3348, 0, 0, 0, 0, -172992, 0, 0, 0, 0, 0, -12704, 10692, 0, 82872, 0, 0, 0, 267300, 0, 0, -188352, 0, 0, 0, 0, -35636, 0, 0, 0, 0, 0, 200680, -55296, 0, 83040, 0, 0, 0, -165888, 0, 0, 455220, 0, 0, 0, 0, 12288, 0, 0, 0, 0, 0, -414912, 139860, 0, -256616, 0, 0, 0, 138132, 0, 0, -62208, 0, 0, 0, 0, 320060, 0, 0, 0, 0, 0, -47096, 142560, 0, -72576, 0, 0, 0, -587520, 0, 0, -225180, 0, 0, 0, 0, 301824, 0, 0, 0, 0, 0, 73216, -598428, 0, 613344, 0, 0, 0, -75924, 0, 0, 193536, 0, 0, 0, 0, -283584, 0, 0, 0, 0, 0, 581096, 20736, 0, -198144, 0, 0, 0, -498528, 0, 0, -364716, 0, 0, 0, 0, -451360, 0, 0, 0, 0, 0, -553344, 96660, 0, 116244, 0, 0, 0, 1035288, 0, 0, 305856, 0, 0, 0, 0, -450884, 0, 0, 0, 0, 0, -197080, -207360, 0, -111744, 0, 0, 0, -250560, 0, 0, -187704, 0, 0, 0, 0, 49152, 0, 0, 0, 0, 0, -435968, -211680, 0, -536180, 0, 0, 0, 1143288, 0, 0, 51840, 0, 0, 0, 0, 75724, 0, 0, 0, 0, 0, -228852, 160704, 0, 30016, 0, 0, 0, 0, 0, 0, -109188, 0, 0, 0, 0, 236544, 0, 0, 0, 0, 0, 281088, 385884, 0, 960032, 0, 0, 0, -711936, 0, 0, -428544, 0, 0, 0, 0, -104932, 0, 0, 0, 0, 0, -20728, -446688, 0, -38400, 0, 0, 0, 15552, 0, 0, 253476, 0, 0, 0, 0, -1387776, 0, 0, 0, 0, 0, 116736, -606204, 0, -901204, 0, 0, 0, -1107432, 0, 0, -940032, 0, 0, 0, 0, -297324, 0, 0, 0, 0, 0, -1560660, -521856, 0, 57088, 0, 0, 0, 921888, 0, 0, 116532, 0, 0, 0, 0, 439136, 0, 0, 0, 0, 0, 391680, 1103328, 0, -656740, 0, 0, 0, -10152, 0, 0, 355104, 0, 0, 0, 0, -147068, 0, 0, 0, 0, 0, 1347752, 248832, 0, 944448, 0, 0, 0, -134784, 0, 0, 1652292, 0, 0, 0, 0, 1306560, 0, 0, 0, 0, 0, 156256, 814212, 0, 1097028, 0, 0, 0, 865944, 0, 0, -924480, 0, 0, 0, 0, 971640, 0, 0, 0, 0, 0, 1393000, -864000, 0, -87520, 0, 0, 0, -13824, 0, 0, 285012, 0, 0, 0, 0, 150016, 0, 0, 0, 0, 0, 530112, -822528, 0, -506784, 0, 0, 0, -1135944, 0, 0, -55296, 0, 0, 0, 0, 436924, 0, 0, 0, 0, 0, 340704, 538272, 0, 823296, 0, 0, 0, 86400, 0, 0, -1009584, 0, 0, 0, 0, 224832, 0, 0, 0, 0, 0, -491520, -594756, 0, -2322580, 0, 0, 0, -891432, 0, 0, 1256256, 0, 0, 0, 0, 1767916, 0, 0, 0, 0, 0, -1927064, 981504, 0, -629760, 0, 0, 0, -166752, 0, 0, 306720, 0, 0, 0, 0, -19744, 0, 0, 0, 0, 0, 339264, 1801440, 0, 594936, 0, 0, 0, -140076, 0, 0, 900288, 0, 0, 0, 0, -2673504, 0, 0, 0, 0, 0, 1185564, 221184, 0, -1300992, 0, 0, 0, -176256, 0, 0, -1252476, 0, 0, 0, 0, 276096, 0, 0, 0, 0, 0, -381696, 2544804, 0, 1737932, 0, 0, 0, 1743768, 0, 0, 556416, 0, 0, 0, 0, 999264, 0, 0, 0, 0, 0, -186292, 1928448, 0, 38720, 0, 0, 0, 352512, 0, 0, 1856844, 0, 0, 0, 0, -450048, 0, 0, 0, 0, 0, -875136, -1547532, 0, 1527444, 0, 0, 0, 229500, 0, 0, -13824, 0, 0, 0, 0, 2004188, 0, 0, 0, 0, 0, 705448, -1002240, 0, -660672, 0, 0, 0, 88128, 0, 0, -2723220, 0, 0, 0, 0, -810240, 0, 0, 0, 0, 0, 67584, -2999808, 0, 2490124, 0, 0, 0, -1304424, 0, 0, 2947968, 0, 0, 0, 0, -2769236, 0, 0, 0, 0, 0, -678008, -200448, 0, -49152, 0, 0, 0, 1447200, 0, 0, -290628, 0, 0, 0, 0, 384288, 0, 0, 0, 0, 0, 672384, -4405644, 0, -3386784, 0, 0, 0, 1717848, 0, 0, -599616, 0, 0, 0, 0, 484312, 0, 0, 0, 0, 0, -1085464, -82944, 0, 1016064, 0, 0, 0, 3096576, 0, 0, -4457052, 0, 0, 0, 0, -10752, 0, 0, 0, 0, 0, 2484480, 4407048, 0, 268876, 0, 0, 0, -3560220, 0, 0, -3761856, 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, 7, 2, -1, 2, 0]], "char_orbit_index": 3, "prim_orbit_index": 2, "minimal_twist": "14.5.d.a", "char_is_minimal": true, "conrey_index": 685, "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, 1, 0, 0], [0, 0, 0, 0], [8, 0, 0, 0], [0, 0, -9, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 8, 0, 0], [0, 0, 0, 0], [0, 0, 16, 9], [-27, 6, 0, 0], [0, 0, 0, 0], [0, 0, 8, -36], [0, 0, 0, 0], [0, 0, 0, 0], [64, 0, 0, 0], [0, 0, 153, -32], [0, 0, 0, 0], [0, 0, 5, 90], [0, 0, -72, -16], [0, 0, 0, 0], [48, -27, 0, 0], [-243, -240, 0, 0], [0, 0, 0, 0], [286, 108, 0, 0], [0, 0, 288, -8], [0, 0, 0, 0], [0, 0, 0, 0], [-810, -24, 0, 0], [0, 0, 0, 0], [0, 0, 91, 180], [0, 64, 0, 0], [0, 0, 0, 0], [0, 0, 256, -153], [0, 0, 0, 0], [0, 0, 0, 0], [223, -270, 0, 0], [0, 0, -720, -5], [0, 0, 0, 0], [0, 0, 128, 72], [0, 0, -72, -208], [0, 0, 0, 0], [586, -648, 0, 0], [-216, 48, 0, 0], [0, 0, 0, 0], [-1920, -243, 0, 0], [0, 0, -117, 316], [0, 0, 0, 0], [0, 0, 0, 0], [864, 286, 0, 0], [0, 0, 0, 0], [0, 0, 64, -288], [1377, -774, 0, 0], [0, 0, 0, 0], [0, 0, 339, 108], [0, 0, 0, 0], [0, 0, 0, 0], [-192, -810, 0, 0], [0, 0, 2061, 146], [0, 0, 0, 0], [0, 0, 1281, -738], [0, 0, -1440, -91], [0, 0, 0, 0], [512, 0, 0, 0], [-1512, 924, 0, 0], [0, 0, 0, 0], [2531, -1674, 0, 0], [0, 0, 1224, -256], [0, 0, 0, 0], [0, 0, 0, 0], [-4698, 456, 0, 0], [0, 0, 0, 0], [0, 0, 2879, -900], [-2160, 223, 0, 0], [0, 0, 0, 0], [0, 0, 40, 720], [0, 0, 0, 0], [0, 0, 0, 0], [-397, 972, 0, 0], [0, 0, -576, -128], [0, 0, 0, 0], [0, 0, 1664, 72], [0, 0, -2448, -100], [0, 0, 0, 0], [2595, -54, 0, 0], [-5184, 586, 0, 0], [0, 0, 0, 0], [384, -216, 0, 0], [0, 0, 2079, -564], [0, 0, 0, 0], [0, 0, 0, 0], [-1944, -1920, 0, 0], [0, 0, 0, 0], [0, 0, -2528, 117], [4455, -2460, 0, 0], [0, 0, 0, 0], [0, 0, 216, -1224], [0, 0, 0, 0], [0, 0, 0, 0], [2288, 864, 0, 0]]}