# Stored data for newform 5.8.a.a, downloaded from the LMFDB on 19 April 2024. {"label": "5.8.a.a", "space_label": "5.8.a", "level": 5, "weight": 8, "hecke_orbit": 1, "hecke_orbit_code": 134217733, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1280164571890564447, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[2, [14, 1]]], "qexp_display": "q-14q^{2}-48q^{3}+68q^{4}+5^{3}q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 320, "fricke_eigenval": -1, "atkin_lehner_string": "-", "analytic_conductor": 1.5619251274206087, "hecke_ring_index": 1, "level_radical": 5, "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": [5, 1, [2], [1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [5], "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": "0.998", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.965", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.828", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "7.2.3.c1", "atkin_lehner_eigenvals": [[5, -1]], "trace_display": [-14, -48, 125, -1644], "traces": [0, 1, -14, -48, 68, 125, 672, -1644, 840, 117, -1750, 172, -3264, 3862, 23016, -6000, -20464, -12254, -1638, -25940, 8500, 78912, -2408, 12972, -40320, 15625, -54068, 99360, -111792, -81610, 84000, -156888, 178976, -8256, 171556, -205500, 7956, 110126, 363160, -185376, 105000, 467882, -1104768, -499208, 11696, 14625, -181608, -396884, 982272, 1879193, -218750, 588192, 262616, -1280498, -1391040, 21500, -1380960, 1245120, 1142540, -1337420, -408000, -923978, 2196432, -192348, 113728, 482750, 115584, -797304, -833272, -622656, 2877000, 5103392, 98280, -4267478, -1541764, -750000, -1763920, -282768, 2595264, -960, -2558000, -5025159, -6550348, 6140832, 5366016, -1531750, 6988912, 3917280, 144480, 2010570, -204750, -6349128, 882096, 7530624, 5556376, -3242500, -8590848, -4881934, -26308702, 20124, 1062500, 9726702, -8234688, 16315052, 3244080, 9864000, 17926972, -4089744, 6756480, -26831770, -301000, -5286048, 33642816, -17481038, -17431680, 1621500, -5549480, 451854, 18723880, 20145576, -5040000, -19457587, 12935692, -22458336, -10668384, 1953125, 2692872, -12501764, -24501120, 23961984, -6758500, -7756188, -561408, 42645360, 11162256, 12420000, -10293360, 36172026, 8717184, 10909220, -13974000, 19050432, -71447488, 664264, -2394288, -10201250, 59744692, -90201264, 7488568, -36458050, 10500000, 7189552, -21789600, -1433718, 3958752, -19611000, -12605568, 87993206, 13440, 61463904, 22372000, -21325968, 70352226, -54887488, 31815976, -1032000, -85971648, 8614596, 66286080, -47833473, 21444500, -3034980, -33946144, -51252378, -54841920, -25687500, -3519808, 64196160, -28147980, -50162660, 994500, 69081662, 88887792, 44350944, 10896480, 13765750, -105428736, -2107688, -26988112, -163347840, 45395000, 154745432, -5458944, -15940558, 68347076, -23172000, 127785124, -168188034, -281736, 177772600, 13125000, 38270592, -136173828, 134166840, 39997056, 58485250, -228410728, 1517724, -79031968, -4461680, -138096000, -161996428, -87073864, -244962816, 57256416, -62401000, 83462400, 257923872, 375644780, 204838944, 1462000, -47324948, 74004672, 17593172, -294236544, 1828125, 244734532, -203035864, 84668160, 159558990, -22701000, 13572864, -68552400, -19498518, -6325956, -49610500, -90944560, 46080, -282038064, -160220480, 122784000, -378778718, 272406218, 23907312, -62830504, 234899125, 314416704, -100180280, -131785920, -294759936, -27343750, 161304252, -13079664, 2231184, 175024696, 73524000, 328458496, 227387106, -335467776, -181047144, 32827000, -9548370, 108586632, 457727612, -6935040, -160062250, -597035040, -96507360, -54216672, 467286310, -173880000, -44593208, 250765856, 304758144, -506408364, 2687500, -42340608, 316657086, -152729080, -18355896, -172620000, -225817638, -266706048, 20821032, 347030656, 155640000, -9299696, -769198008, 20940192, -260178157, 142817500, 234332832, -290188504, -178825458, 1262817696, -167177500, 92505840, 17089920, 510412700, 50097864, -51000000, 820697952, -100653728, -466881696, 530836160, -115497250, 20072052, -85515944, -19228224, -783122496, 274554000, -484705728, -155715840, 570821162, -1231904884, -24043500, -65280, -550190554, -860494656, -14036920, 14216000, 196307712, 298563552, 317868760, -341710812, 60343750, 768424832, 1287924960, 393020880, 652477296, 14448000, -939838788, 417576576, 12884742, -120604344, -99663000, -1614855168, 533631826, 669668622, 839089824, -104159000, -26984736, 42489720, -1735488600, -419334720, -77832000, 717533292, 1079338816, 266375040, -427217450, 359625000, 383728320, 30783872, -1489659198, -898746240, 637924000, 136718760, -966987648, 702277240, 841275480, 12285000, -220988139, -967143268, 933964176, -431740704, -533434750, -620913216, -750461604, -265459008, 54742194, -192720500, 2105138712, 512082432, 171073822, 29507632, -93750000, -333382560, -315177820, 2286869760, 46623940, -220490000, 600084672, -2166436048, -442265868, 1176053760, -35346000, 223167812, -58407336, -331971512, -464032530, 324408000, -158958888, 1578522120, 372297024, 2354632476, -120000, 1368432, -317792234, -2488816400, -2046977280, -319750000, -1195629198, -535788288, -605901456, 661415736, -628144875, -1878335760, 18941672, 494081280, 2213047130, -818793500, -1736257248, 1109423536, 2198718480, -21248136, 767604000, 691205312, -523642560, 62463520, -802298740, 670752000, 34471342, 2267949992, -46435428, -1075618320, -191468750, 3429479424, 1519019832, -278102592, -31884672, 873614000, 1726923912, -2033303040, 488307682, -3610934208, 489660000, -1824560360, -336493680, -2867745216, -2886397880, 18060000, 219865581, 662549272, 926583192, -359451264, 251321250, -246304408, 1749986400, -186968832, 1355352850, -25593750, 80475704, -1188710584, -345098496, 2842502096, -793641000, 1045900800, 46342906, -2233825860, -1217557440, 110262000, -152117178, -190020096, 1634503812, 1670067040, 941328000, 272979252, -1113803704, 30726072, 1310767776, 694547000, -4223673888, -1123432800, -85863776, -645120, -405312500, 1369899168, -149818266, 2243086720, 1277448240, -1073856000, 425306612, 5302902052, 1023646464, -1323115916, -610241750, -334702368, 979672676, -776141520, 2634599424, -3288587750, -4921252468, -1527166848, 1000048940, 1402523920, 2515500, 3210556032, -8389976448, 4126639104, -3657864500, 132812500, -413500608, -2258259528, -3883580548, -161572320, 1215837750, -31236576, 2296006704, -850119952, 3900717430, -1029336000, 7015733832, -1462275584, -2577398400, -3183419484, 2039381500, 1629414912, -68264048, 2534660016, 2460114144, 405510000, 2883986042, 133677180, 877188472, -527420784, 1233000000, -6408186568, 1922505552, 168950784, -3236552663, 2240871500, -156478140, 2899884480, 1806960284, 1351103040, -511218000, -669735360, 2407807680, -6542008340, 323221196, 844560000, -653484618, 624304912, -3315919776, -2193171904, -3353971250, -4266614016, -4592987384, 2459697768, -108105426, -37625000, 2116963400, -523031040, 1578240, -4433199204, -660756000, 741826960, 6831640806, 256982544, -1927941296, 4205352000, 101169024, 3161446932, 3425094912, 1295429376, -2185129750, -291494448, 8261361396, 4286849280, -7509302790, -2178960000, -135841108, 45169952, -7427780736, 10768772112, 202687500, 13306176, 1637750786, 3642494198, 765146784, -693685000, -10095527808, -3280659648, -220245656, -3584681520, 56481750, 2503556412, -5972051424, -6133685952, 4069674720, 2340485000, 8073025632, -2253618464, 8313465842, -239258880, 2518197000, -2479147400, -8533084800, -701370096, 9783675800, -630000000, 5401594202, -11489771328, -93284568, 488889536, -2432198375, 6536343744, -2844394244, -4642637440, -6440008320, 1616961500, -1532766008, -97492824, -7021057538, 1197223216, -2807292000, -237525120, 3351655146, 10963714944, -3923624140, -1333548000, 1288897920, 6785880192, -3305377080, 3793534464, 244140625, -7991496268, 214160640, 5983538008, -1349484004, 336609000, -681544688, -806400, 7775828544, 7702667756, -1562720500, 4179545472, 7257443366, 196516880, 597096864, -3062640000, 9651992082, -2748307968, -5078260608, -1450165824, 2995248000, -4450162640, -2083303484, -4221133560, -230036240, -844812500, -12380345856, -3732349184, 6848810102, -18030949440, -969523500, -9574737248, -499294926, -9134682144, 6999128380, -70176000, -1995943778, 13157743032, 2271597504, 5158298880, 5330670000, -180386388, -1058644920, 585792528, -844472256, 1395282000, -158924216, 14123354112, -11793904878, -7470845564, 1552500000, -3252676164, 7802218686, -11747257536, 8025899496, -1286670000, 9745721472, 377786304, 4511529432, -206378640, 4521503250, 24296840400, -7658831520, 10215792512, -4945283276, 1089648000, -10633131068, -3485161704, -33083856, -15110743424, 1363652500, 3290515200, -5733426028, 5981044300, 935928864, -1746750000, -4385141098, -5372196480, -2856668440, 19561216, 2381304000, 20855228772, -15990698088, 4365338880, -5988049970, -8930936000, -112320, 1688878800, -2035151136, 13537827072, 83033000, -3411060880, 7690583040, -11777856720, -11776791840, -299286000, -26821945488, 3093833946, 18181378464, 4697553016, -1275156250, -13075498464, 8410505636, -5333267520, 9842471757, 7468086500, 6117294832, 3015864192, 14408392982, 10506462456, -11275158000, 2321676672, -137136288, -766390716, 8217083020, 936071000, 4808653440, -29471941968, -17253067508, 6325724160, -4557256250, -2395033508, 718477344, -143322784, 6723539136, 1312500000, 15849821752, 8121834176, -7742604096, 4412489480, 898694000, -11107653120, 7138564606, -652735160, -107096832, -2723700000, -2599929078, -8401185408, 44111429880, 10522689376, -179214750, 6191722152, -5165116040, -15766007808, -4964772190, 494844000, -10914581088, -1083957944, -14968115778, 817702704, -2451375000, -4100824560, 8690262912, 6496455420, -12136859080, -1575696000, 877783424, 2225424432, -8108769600, -38455805552, 10999150750, -5212158336, -9799901624, -11436786312, -21970925376, 1680000, 28738826472, 16904160, -3568403036, 4449091276, 7682988000, 12088536800, 3931691366, 28657681920, 4863416536, 2796500000, 235236690, 16738808772, -734006216, 2602400256, -2665746000, 8482620384, -22429742880, 8170429680, 12632426330, 8794028250, 11665325772, 9123345120, 2140473984, -265183408, -6860936000, -12036761088, 12949455520, -30982659820, -742847976, 3976997000, -8174997858, 24307601472, -17521126228, 13704643680, -129000000, -30782058720, 12222545536, 103205232, -10663419210, -10746456000, -15199540128, 439217536, -23027631022, 7330995840, 1076824500, -303394240, -15588391680, 11232182360, -2313998680, 8285760000, -10589684209, -482598788, 10839246624, -11015757104, -5979184125, 650095992, 31988273028, 26204111072, -999409536, 2680562500, 1428554472, -16657471488, -4223767698, -21266277648, -379372500, -3435384960, -3521037494, 446385408, 24493004980, -4243268000, 36921504384, -24176934768, -5405729788, 17783055360, -6406547250, -6836307548, 12488551536, 17538823296, -165120, -6855240000, -3079188048, -22538686800, -571186278, 4710911520, -3210937500, 13929048192, -28915499514, 40409570320, 8583621984, -439976000, 780642562, -3078118134, -13690694368, -3218096464, 8024520000, -12972164688, 3584034276, -4440280320, 20552900016, -3518497500, -864327348, 1196335696, 10295170960, -24499809600, -6270332500, 40279841280, -2404697472, -18974939900, 12803629680, 124312500, 15691222492, -1126659856, -39393501696, -14684071920, 8635207750, 4831378944, -30110804544, -13806438752, 1138024134, 11110974000, -24879995528, -25480135680, 1056223104, -648800684, 5543868000, 10850011320, 12751173072, 17045804160, 10842048760, 1362060000, 4104765312, 2129640492, 19709299904, 922954752, 1720718750, -22883053368, 1908861084, -14606231360, 10704503090, -13178592000, -48746266420, -1325899224, 23265874944, 15593251856, -263461000, 379557360, 34278689226, -18350748864, -27399415776, -3373514000, -3736949818, 59131434432, 6069365304, 27368962880, -20418480000, 1202092864, 33214992216, 3133440, -16481000036, 5674375000, 26409146592, 16922283840, 46989547402, 2097455724, 19343179000, -10894992640, 673772160, -17884275360, -59466810744, -682368000, -2898769567, -5954292568, -478500048, -25756952824, -1992569750, -14331050496, -14229376204, -16344373080, -15257700480, 8543384500, 545473692, 1625697216, -17934757680, -13715417464, -2896500000, 18908285792, -19791579614, -36884391936, 345818040, 15973140500, -3139317090, 68897534552, -47150273268, -18865002240, -21023504250, -14000685160, -31318910208, -6812259040, -6475726176, -35217000, 38796825032, -28079186688, 45112261824, 117459670272, 22221575000, -20043675648, -56639400834, 51210103000, 10942119360, 1640625000], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": true, "level_is_prime_power": true, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "5.8.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], [-14], [-48], [68], [125], [672], [-1644], [840], [117], [-1750], [172], [-3264], [3862], [23016], [-6000], [-20464], [-12254], [-1638], [-25940], [8500], [78912], [-2408], [12972], [-40320], [15625], [-54068], [99360], [-111792], [-81610], [84000], [-156888], [178976], [-8256], [171556], [-205500], [7956], [110126], [363160], [-185376], [105000], [467882], [-1104768], [-499208], [11696], [14625], [-181608], [-396884], [982272], [1879193], [-218750], [588192], [262616], [-1280498], [-1391040], [21500], [-1380960], [1245120], [1142540], [-1337420], [-408000], [-923978], [2196432], [-192348], [113728], [482750], [115584], [-797304], [-833272], [-622656], [2877000], [5103392], [98280], [-4267478], [-1541764], [-750000], [-1763920], [-282768], [2595264], [-960], [-2558000], [-5025159], [-6550348], [6140832], [5366016], [-1531750], [6988912], [3917280], [144480], [2010570], [-204750], [-6349128], [882096], [7530624], [5556376], [-3242500], [-8590848], [-4881934], [-26308702], [20124], [1062500]]}