# Stored data for newform 128.5.f.b, downloaded from the LMFDB on 19 April 2024.
{"label": "128.5.f.b", "space_label": "128.5.f", "level": 128, "weight": 5, "hecke_orbit": 2, "hecke_orbit_code": 4503943308640384, "dim": 14, "is_polredabs": true, "trace_hash": 605409925520090164, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [2016379008, -43496175744, 469137324096, 34747646976, 1358008416, -786717792, 409777200, 14203392, 551960, -288664, 62860, -448, 2, -2, 1]]], "qexp_display": "q+\\beta _{2}q^{3}-\\beta _{3}q^{5}-\\beta _{9}q^{7}+(19\\beta _{1}-\\beta _{2}+\\cdots)q^{9}+\\cdots", "char_order": 4, "char_parity": -1, "char_degree": 2, "char_conductor": 16, "char_orbit_label": "f", "char_is_real": false, "Nk2": 3200, "analytic_conductor": 13.231355274732074, "hecke_ring_index": 4398046511104, "level_radical": 2, "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": "0.248", "prec": 17}, "analytic_rank_proved": true, "char_values": [128, 4, [127, 5], [2, 1]], "hecke_ring_generator_nbound": 9, "inner_twist_count": 2, "level_primes": [2], "conrey_indexes": [31, 95], "field_disc": -15024771810864705372613304664064, "field_disc_factorization": [[-1, 1], [2, 14], [840137, 2], [36044903, 2]], "field_poly": [2097152, -1048576, 491520, -139264, 31744, -19968, 11456, -4960, 1432, -312, 62, -34, 15, -4, 1], "hecke_ring_index_factorization": [[2, 42]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.018", "prec": 17}, {"__RealLiteral__": 0, "data": "12.822", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "600.681", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "43713.180", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 7, "sato_tate_group": "4.2.3.c4", "trace_display": [0, 2, 2, -4], "traces": [0, 14, 0, 2, 0, 2, 0, -4, 0, 0, 0, -94, 0, 2, 0, 0, 0, -4, 0, 706, 0, 164, 0, 1148, 0, 0, 0, 1664, 0, -862, 0, 0, 0, -4, 0, -1340, 0, 1826, 0, 2684, 0, 0, 0, -1694, 0, -1410, 0, 0, 0, 682, 0, 3012, 0, 482, 0, -11780, 0, 0, 0, 2786, 0, 3778, 0, 0, 0, -2020, 0, -7998, 0, -9628, 0, 19964, 0, 0, 0, -17570, 0, 9508, 0, 0, 0, 1454, 0, 17282, 0, -9948, 0, -49284, 0, 0, 0, 28036, 0, -8896, 0, 0, 0, -4, 0, -49214, 0, 23906, 0, 54524, 0, 0, 0, -54238, 0, -10334, 0, 0, 0, -3364, 0, 76484, 0, 19202, 0, -65288, 0, 0, 0, 102976, 0, 10560, 0, 0, 0, 8124, 0, -98110, 0, -28316, 0, 158080, 0, 0, 0, -104734, 0, -16960, 0, 0, 0, -4900, 0, 149446, 0, -14782, 0, -174468, 0, 0, 0, 140160, 0, -19838, 0, 0, 0, -9608, 0, -122878, 0, 28580, 0, 260348, 0, 0, 0, -179170, 0, 59906, 0, 0, 0, 35388, 0, 157826, 0, 40898, 0, -373892, 0, 0, 0, 164868, 0, 21440, 0, 0, 0, -24452, 0, -257980, 0, -27262, 0, 307708, 0, 0, 0, -229628, 0, -134272, 0, 0, 0, -27076, 0, 218882, 0, -99612, 0, -407044, 0, 0, 0, 293120, 0, 29092, 0, 0, 0, 73490, 0, -331774, 0, -9662, 0, 478328, 0, 0, 0, -325120, 0, 241920, 0, 0, 0, -128132, 0, 345666, 0, 134022, 0, -408964, 0, 0, 0, 356450, 0, -25116, 0, 0, 0, 40796, 0, -271804, 0, -33502, 0, 273404, 0, 0, 0, -410624, 0, -307294, 0, 0, 0, 118264, 0, 405314, 0, -230878, 0, -412416, 0, 0, 0, 293794, 0, -7652, 0, 0, 0, -165718, 0, -370620, 0, 128642, 0, 486140, 0, 0, 0, -262268, 0, 392292, 0, 0, 0, 231836, 0, 342082, 0, 408164, 0, -188548, 0, 0, 0, 340476, 0, 866, 0, 0, 0, -40836, 0, -210620, 0, -181598, 0, 597628, 0, 0, 0, -89438, 0, -628002, 0, 0, 0, -252004, 0, 54276, 0, -401472, 0, -297224, 0, 0, 0, 257762, 0, -170334, 0, 0, 0, 215516, 0, 19780, 0, 406792, 0, -46852, 0, 0, 0, 73954, 0, 707040, 0, 0, 0, -216576, 0, -40892, 0, 540642, 0, -230784, 0, 0, 0, -337950, 0, 285888, 0, 0, 0, 39416, 0, 77186, 0, -572254, 0, -19976, 0, 0, 0, 1920, 0, -740254, 0, 0, 0, 275324, 0, -268672, 0, -968990, 0, 173564, 0, 0, 0, -513856, 0, -241436, 0, 0, 0, -238532, 0, 222530, 0, 732098, 0, -674432, 0, 0, 0, 174724, 0, 1140772, 0, 0, 0, 300156, 0, -567356, 0, 913444, 0, 606588, 0, 0, 0, -191326, 0, 391968, 0, 0, 0, -114436, 0, 493248, 0, -1159452, 0, -1299080, 0, 0, 0, 725760, 0, -1095454, 0, 0, 0, -146560, 0, -191422, 0, -1288476, 0, 1193340, 0, 0, 0, -598114, 0, -504802, 0, 0, 0, 136668, 0, 991880, 0, 1187620, 0, -881412, 0, 0, 0, 581858, 0, 1351524, 0, 0, 0, -724616, 0, -1034494, 0, 1963172, 0, 2097020, 0, 0, 0, -1026590, 0, 429506, 0, 0, 0, 189760, 0, 466756, 0, -1214144, 0, -1553796, 0, 0, 0, 1478178, 0, -2279652, 0, 0, 0, 480554, 0, -1575422, 0, -1659264, 0, 1525756, 0, 0, 0, -907098, 0, -457022, 0, 0, 0, 92636, 0, 1432002, 0, 1622978, 0, -1801348, 0, 0, 0, 1776380, 0, 2020418, 0, 0, 0, 703032, 0, -698686, 0, 2209092, 0, 1483516, 0, 0, 0, -1425502, 0, 555840, 0, 0, 0, -92004, 0, 2594372, 0, -1384028, 0, -1611268, 0, 0, 0, 510242, 0, -2445760, 0, 0, 0, -899044, 0, -1820152, 0, -2890716, 0, 2965628, 0, 0, 0, -2260194, 0, -628798, 0, 0, 0, -382344, 0, 794112, 0, 1646402, 0, -1598592, 0, 0, 0, 2207906, 0, 3740352, 0, 0, 0, -58994, 0, -1756540, 0, 2346724, 0, 686460, 0, 0, 0, -1071744, 0, 521350, 0, 0, 0, 81788, 0, 1656770, 0, -2306588, 0, -2459140, 0, 0, 0, 2284288, 0, -3656158, 0, 0, 0, 148768, 0, -808318, 0, -2751550, 0, 1540088, 0, 0, 0, -1420028, 0, -679872, 0, 0, 0, 1063036, 0, 1646976, 0, 1537826, 0, -1948168, 0, 0, 0, -230302, 0, 4370112, 0, 0, 0, 80732, 0, -2308606, 0, 3705764, 0, 3073532, 0, 0, 0, -2280960, 0, 1026818, 0, 0, 0, -67456, 0, -545468, 0, -1746462, 0, -1731456, 0, 0, 0, 1097348, 0, -5657856, 0, 0, 0, 338552, 0, -1355836, 0, -3464638, 0, -314756, 0, 0, 0, 733828, 0, -191774, 0, 0, 0, -2069572, 0, 856450, 0, 2343012, 0, -3476740, 0, 0, 0, 772446, 0, 4997284, 0, 0, 0, -965444, 0, 1089988, 0, 3743426, 0, 1042296, 0, 0, 0, -522492, 0, 560988, 0, 0, 0, 294524, 0, 1320068, 0, -2053918, 0, 1221888, 0, 0, 0, -1109184, 0, -4962716, 0, 0, 0, 1148444, 0, 77698, 0, -5185948, 0, 2360056, 0, 0, 0, -335108, 0, -1298878, 0, 0, 0, 2081760, 0, -1109760, 0, 2784712, 0, 2102908, 0, 0, 0, 1431330, 0, 6592064, 0, 0, 0, 547068, 0, -92988, 0, 4515938, 0, -610436, 0, 0, 0, 2198690, 0, 419266, 0, 0, 0, -450060, 0, -154684, 0, -3367680, 0, -1161220, 0, 0, 0, 61824, 0, -6087070, 0, 0, 0, -1758980, 0, 2444356, 0, -4542494, 0, -2980348, 0, 0, 0, -839710, 0, -1202432, 0, 0, 0, -1577444, 0, 217478, 0, 2968320, 0, 4141180, 0, 0, 0, -3391872, 0, 5715042, 0, 0, 0, 774428, 0, -110014, 0, 6677092, 0, -1017988, 0, 0, 0, 1005666, 0, 1078464, 0, 0, 0, -890248, 0, -2752896, 0, -2878876, 0, 4898424, 0, 0, 0, -680862, 0, -7279714, 0, 0, 0, 438268, 0, 393028, 0, -5206556, 0, -4204932, 0, 0, 0, 4471300, 0, -845250, 0, 0, 0, 3522812, 0, -574458, 0, 5074340, 0, -908552, 0, 0, 0, -1049664, 0, 6129314, 0, 0, 0, 760960, 0, 5648450, 0, 5442720, 0, -8323204, 0, 0, 0, 1647232, 0, 1581028, 0, 0, 0, 879374, 0, -4009406, 0, -4671836, 0, 6889980, 0, 0, 0, -4296478, 0, -5812252, 0, 0, 0, -1400836, 0, 830976, 0, -7417566, 0, 1813628, 0, 0, 0, 1757696, 0, -2353628, 0, 0, 0, -5836804, 0, -7236668, 0, 3901922, 0, 7137152, 0], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 16, 6, -1, 4, 0]], "char_orbit_index": 6, "prim_orbit_index": 6, "minimal_twist": "16.5.f.a", "char_is_minimal": false, "conrey_index": 31, "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], [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, 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, 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, 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, 19, -1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-7, 7, 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], [1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -24, 2, -2, -1, 2, 0, 0, -2, 0, 1, 0, -2, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 2, 1, 0, -2, 1, -1, -1, 3, -1, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [49, 49, 0, 5, 2, 0, 2, 0, 0, 2, 2, 1, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [13, 13, -15, -1, -3, 0, 2, 0, 0, -3, -1, 3, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [76, 0, -4, -8, 0, 4, 6, -2, 8, 3, 1, 2, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 47, 13, -1, -6, 13, 0, 3, -1, 0, 1, 3, 4, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [115, -115, 0, 0, -2, 11, 6, -3, 17, 2, 0, 0, -6, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-56, 56, 0, 0, -6, 36, -2, 0, -3, 6, 0, 0, 2, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 20, 4, 16, 4, 4, 0, -2, 16, 0, 3, -2, 2, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [16, 0, -43, -4, 0, 43, 3, 0, 4, -13, -4, 0, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-102, -102, 8, -34, -6, 0, -2, 0, 0, -6, 6, 2, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [115, 115, 59, 2, 13, 0, 8, 0, 0, 13, -3, 5, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [188, 0, 10, 26, 0, -10, 4, -6, -26, 3, 2, 6, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, -67, -11, 12, -67, 0, 5, -11, 0, 3, 5, 2, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-112, 112, 0, 0, 8, 7, 4, 0, -40, -8, 0, 0, -4, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-115, 115, 0, 0, 11, -129, -6, -3, -2, -11, 0, 0, 6, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 400, 18, -34, 0, 18, 0, -4, -34, 0, -1, -4, 2, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [15, 0, 110, -16, 0, -110, -2, 4, 16, 6, 0, -4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [229, 229, 5, 53, -12, 0, -4, 0, 0, -12, -4, -3, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [65, 65, -187, -4, -3, 0, -2, 0, 0, -3, 3, -9, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-844, 0, 26, -38, 0, -26, -16, 6, 38, -13, -4, -6, 0, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -56, 165, -4, -1, 165, 0, -12, -4, 0, -4, -12, -9, -4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [194, -194, 0, 0, 6, -39, -22, 6, 50, -6, 0, 0, 22, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [303, -303, 0, 0, 5, 261, 10, 7, 14, -5, 0, 0, -10, -13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1424, -14, 30, -17, -14, 0, 12, 30, 0, -9, 12, -14, -9], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-108, 0, -177, 31, 0, 177, -10, -7, -31, 36, 17, 7, 0, -17], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-573, -573, -50, -5, 44, 0, 16, 0, 0, 44, -24, -5, 16, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-713, -713, 379, 1, -49, 0, -42, 0, 0, -49, 13, -15, -42, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1484, 0, -84, 8, 0, 84, -10, 30, -8, 3, -7, -30, 0, 7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -242, -243, 80, -41, -243, 0, -20, 80, 0, -16, -20, -17, -16], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1268, 1268, 0, 0, -58, -27, -14, 12, -24, 58, 0, 0, 14, -18], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [595, -595, 0, 0, -51, -359, 38, -5, 3, 51, 0, 0, -38, -17], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2172, -174, 2, 20, -174, 0, 22, 2, 0, -10, 22, 28, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [39, 0, 325, 88, 0, -325, -5, 0, -88, -37, 16, 0, 0, -16], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1236, 1236, -3, -16, 30, 0, -22, 0, 0, 30, -14, -4, -22, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-649, -649, -377, 29, 37, 0, -28, 0, 0, 37, 1, -15, -28, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3460, 0, -84, 64, 0, 84, -42, 6, -64, -5, 1, -6, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -534, 295, 44, 81, 295, 0, 0, 44, 0, 4, 0, -31, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2044, -2044, 0, 0, 22, -30, -14, 28, -136, -22, 0, 0, 14, 14], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-582, 582, 0, 0, 70, 310, -20, -30, -2, -70, 0, 0, 20, -14], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -3064, 20, -108, -9, 20, 0, -28, -108, 0, -16, -28, 16, -16], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [74, 0, -248, -105, 0, 248, -15, 37, 105, 23, -7, -37, 0, 7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3450, -3450, 19, 106, -122, 0, -34, 0, 0, -122, -2, -18, -34, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}