# Stored data for newform 18.6.a.a, downloaded from the LMFDB on 16 April 2024. {"label": "18.6.a.a", "space_label": "18.6.a", "level": 18, "weight": 6, "hecke_orbit": 1, "hecke_orbit_code": 100663314, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1095039734589225822, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[5, [96, 1]]], "qexp_display": "q-4q^{2}+2^{4}q^{4}-96q^{5}-148q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 648, "fricke_eigenval": 1, "atkin_lehner_string": "++", "analytic_conductor": 2.8869087566336513, "hecke_ring_index": 1, "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": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": 0, "analytic_rank_proved": true, "char_values": [18, 1, [11], [1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.989", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.940", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.783", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [3, 1]], "trace_display": [-4, 0, -96, -148], "traces": [0, 1, -4, 0, 16, -96, 0, -148, -64, 0, 384, 384, 0, -334, 592, 0, 256, 576, 0, -664, -1536, 0, -1536, -3840, 0, 6091, 1336, 0, -2368, 96, 0, -4564, -1024, 0, -2304, 14208, 0, 5798, 2656, 0, 6144, -6720, 0, -14872, 6144, 0, 15360, -19200, 0, 5097, -24364, 0, -5344, 7776, 0, -36864, 9472, 0, -384, -13056, 0, 42782, 18256, 0, 4096, 32064, 0, 36656, 9216, 0, -56832, 64512, 0, -16810, -23192, 0, -10624, -56832, 0, 28076, -24576, 0, 26880, -66432, 0, -55296, 59488, 0, -24576, -81792, 0, 49432, -61440, 0, 76800, 63744, 0, -29938, -20388, 0, 97456, 178656, 0, -115228, 21376, 0, -31104, -76032, 0, -231118, 147456, 0, -37888, 142464, 0, 368640, 1536, 0, 52224, -85248, 0, -13595, -171128, 0, -73024, -284736, 0, -988, -16384, 0, -128256, 224256, 0, 98272, -146624, 0, -36864, -278976, 0, 177200, 227328, 0, -258048, -128256, 0, -9216, 67240, 0, 92768, 236064, 0, -482836, 42496, 0, 227328, 438144, 0, 381086, -112304, 0, 98304, 568320, 0, 162920, -107520, 0, 265728, -566016, 0, -259737, 221184, 0, -237952, -218208, 0, -901468, 98304, 0, 327168, -412416, 0, -25558, -197728, 0, 245760, -556608, 0, 221184, -307200, 0, -254976, 400128, 0, 699650, 119752, 0, 81552, 406368, 0, -361996, -389824, 0, -714624, -14208, 0, 645120, 460912, 0, -85504, -254976, 0, 151856, 124416, 0, 304128, 1427712, 0, 675472, 924472, 0, -589824, -192384, 0, -1093324, 151552, 0, -569856, -566400, 0, -587206, -1474560, 0, -6144, 579456, 0, 1843200, -208896, 0, 340992, -584448, 0, -414130, 54380, 0, 684512, -489312, 0, 221776, 292096, 0, 1138944, -1899648, 0, -1474560, 3952, 0, 65536, 447744, 0, -858104, 513024, 0, -897024, -67584, 0, -746496, -393088, 0, 586496, 564192, 0, 720308, 147456, 0, 1115904, 2338944, 0, -141142, -708800, 0, -909312, 584448, 0, 177056, 1032192, 0, 513024, 994560, 0, -1088081, 36864, 0, -268960, -956832, 0, 1253376, -371072, 0, -944256, 1282560, 0, 2201056, 1931344, 0, -169984, -4107072, 0, 2882864, -909312, 0, -1752576, -2600448, 0, -2580790, -1524344, 0, 449216, 2311008, 0, 36864, -393216, 0, -2273280, -382464, 0, -2034394, -651680, 0, 430080, 2841600, 0, -637024, -1062912, 0, 2264064, -3518976, 0, 3386654, 1038948, 0, -884736, -1752576, 0, 1733080, 951808, 0, 872832, 2778240, 0, 1555358, 3605872, 0, -393216, 2117760, 0, -6193152, -1308672, 0, 1649664, 2174976, 0, -2035203, 102232, 0, 790912, 1613760, 0, 1053356, -983040, 0, 2226432, -1150848, 0, -677098, -884736, 0, 1228800, -32064, 0, -5107480, 1019904, 0, -1600512, 1632000, 0, 5455872, -2798600, 0, -479008, -4465632, 0, -2211840, -326208, 0, -1625472, -2695296, 0, -611026, 1447984, 0, 1559296, -6091584, 0, 1524376, 2858496, 0, 56832, 2226432, 0, 2891078, -2580480, 0, -1843648, 1932288, 0, 6377472, 342016, 0, 1019904, -2984064, 0, 822074, -607424, 0, -497664, 3508416, 0, -6331736, -1216512, 0, -5710848, 6324480, 0, -851902, -2701888, 0, -3697888, 2549760, 0, -334732, 2359296, 0, 769536, -1762176, 0, 7852032, 4373296, 0, -606208, 6518592, 0, -2580480, 2279424, 0, 2265600, -4745472, 0, -92074, 2348824, 0, 5898240, 257568, 0, 3962276, 24576, 0, -2317824, -3489408, 0, -5425088, -7372800, 0, 835584, -5710848, 0, -4044424, -1363968, 0, 2337792, 513024, 0, -1936532, 1656520, 0, -217520, 2874048, 0, 4144988, -2738048, 0, 1957248, 2758656, 0, 55296, -887104, 0, -1168384, -9547776, 0, 660896, -4555776, 0, 7598592, -944640, 0, -17150976, 5898240, 0, -15808, -7837728, 0, 2487880, -262144, 0, -1790976, 11061888, 0, -7372800, 3432416, 0, -2052096, 3296448, 0, 6502376, 3588096, 0, 270336, -2628864, 0, 8309257, 2985984, 0, 1572352, 2244480, 0, 7299072, -2345984, 0, -2256768, 1957248, 0, 9827138, -2881232, 0, -589824, 22187328, 0, -3425800, -4463616, 0, -9355776, -63744, 0, -4155248, 564568, 0, 2835200, -6433632, 0, 4967248, 3637248, 0, -2337792, 753024, 0, -13676544, -708224, 0, -4128768, -11148096, 0, 191024, -2052096, 0, -3978240, -23389440, 0, 10372178, 4352324, 0, -147456, 9831936, 0, 2985984, 1075840, 0, 3827328, -2970624, 0, 3030496, -5013504, 0, 1484288, -7558272, 0, 8183808, 3777024, 0, -5130240, 6691584, 0, -3203590, -8804224, 0, -7725376, 1305120, 0, -13558492, 679936, 0, 16428288, 6412800, 0, -10765402, -11531456, 0, 3637248, -9335040, 0, 9076640, 7010304, 0, 10401792, 12105216, 0, 8300281, 10323160, 0, 6097376, 3339648, 0, -11336740, -1796864, 0, -9244032, 94848, 0, -1702398, -147456, 0, 1572864, 15544896, 0, -8800264, 9093120, 0, 1529856, 10844928, 0, -5013504, 8137576, 0, 2606720, -9887712, 0, -21528576, -1720320, 0, -11366400, -14615040, 0, 15779222, 2548096, 0, 4251648, -9434112, 0, -368640, -9056256, 0, 14075904, 16428288, 0, 6649394, -13546616, 0, -4155792, 4425504, 0, 4430824, 3538944, 0, 7010304, -4678272, 0, 26781696, -6932320, 0, -3807232, -2597184, 0, -5541016, -3491328, 0, -11112960, -17011200, 0, -3870720, -6221432, 0, -14423488, -6534432, 0, -3849872, 1572864, 0, -8471040, -26441088, 0, -3865414, 24772608, 0, 5234688, 17525760, 0, 12312576, -6598656, 0, -8699904, 4806144, 0, 17053744, 8140812, 0, -408928, 584736, 0, -19058980, -3163648, 0, -6455040, -8566272, 0, 5696162, -4213424, 0, 3932160, 14075904, 0, 18490160, -8905728, 0, 4603392, 9903360, 0, -22662144, 2708392, 0, 3538944, 11252736, 0, -9059140, -4915200, 0, 128256, 46352256, 0, -11667670, 20429920, 0, -4079616, -12739776, 0, 34205464, 6402048, 0, -6528000, 4360704, 0, 10678274, -21823488, 0, 11194400, -9186336, 0, -27799324, 1916032, 0, 17862528, 4462080, 0, 24772608, 8847360, 0, 1304832, -36584256, 0, -9282088, 6501888, 0, 10781184, -21084672, 0, -14289188, 2444104, 0, -5791936, 21792, 0, -11059200, -6237184, 0, 24366336, -6455040, 0, -54558720, -6097504, 0, -11433984, 12308544, 0, -23463592, -227328, 0, -8905728, -15640320, 0, 9875008, -11564312, 0, 10321920, -14420640, 0, 34341884, 7374592, 0, -7729152, 21332736, 0, 2637506, -25509888, 0, -1368064, 2935872, 0, 54337536, -4079616, 0, 11936256, -10057728, 0, -20501933, -3288296, 0, 2429696, 24934752, 0, 2012060, 1990656, 0, -14033664, -22264320, 0, -23074762, 25326944, 0, 4866048, 35164608, 0, 16602200, 22843392, 0, -25297920, -29700864, 0, 20947968, 3407608, 0, 10807552, 10781184, 0, -12243104, 14791552, 0, -10199040, 42140928, 0, -11794258, 1338928, 0, -9437184, -21037824, 0, 21219176, -3078144, 0, 7048704, 22881792, 0, 146224, -31408128, 0, -17493184, 12748800, 0, 39591936, 2424832, 0, -26074368, -438144, 0, 4478976, 10321920, 0, -9117696, 2453568, 0, -9686920, -9062400, 0, 18981888, 9381120, 0, -25509888, 368296, 0, -9395296, -33189888, 0, -42187012, -23592960, 0, -1030272, -21547008, 0, 35315618, -15849104, 0, -98304, -30455616, 0, -3384408, 9271296, 0, 13957632, -21233664, 0, 14784698, 21700352, 0, 29491200, -9919968, 0, 25804800, -3342336, 0, 22843392, 2916096, 0, 5614540, 16177696, 0, 5455872, 14086080, 0, -38412288, -9351168, 0, -2052096, 41288448, 0, -7799055, 7746128, 0, -6626080, -67166400, 0, 15194852, 870080, 0, -11496192, -56121984, 0, -26225600, -16579952, 0, 10952192, 34562496, 0, -31408128, -7828992, 0, -11034624, 55638528, 0, -39011328, -221184, 0, 3548416, 57108480, 0, -36002788, 4673536, 0, 38191104, 34751616, 0, 23581094, -2643584, 0, 18223104], "weight_parity": 1, "has_non_self_twist": 0, "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]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "18.6.a.a", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0], [1], [-4], [0], [16], [-96], [0], [-148], [-64], [0], [384], [384], [0], [-334], [592], [0], [256], [576], [0], [-664], [-1536], [0], [-1536], [-3840], [0], [6091], [1336], [0], [-2368], [96], [0], [-4564], [-1024], [0], [-2304], [14208], [0], [5798], [2656], [0], [6144], [-6720], [0], [-14872], [6144], [0], [15360], [-19200], [0], [5097], [-24364], [0], [-5344], [7776], [0], [-36864], [9472], [0], [-384], [-13056], [0], [42782], [18256], [0], [4096], [32064], [0], [36656], [9216], [0], [-56832], [64512], [0], [-16810], [-23192], [0], [-10624], [-56832], [0], [28076], [-24576], [0], [26880], [-66432], [0], [-55296], [59488], [0], [-24576], [-81792], [0], [49432], [-61440], [0], [76800], [63744], [0], [-29938], [-20388], [0], [97456]]}