Base field 3.3.1929.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x + 13\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[13, 13, -w]$ |
| Dimension: | $22$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $44$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{22} + 4x^{21} - 32x^{20} - 142x^{19} + 400x^{18} + 2096x^{17} - 2383x^{16} - 16836x^{15} + 5530x^{14} + 80630x^{13} + 10902x^{12} - 235904x^{11} - 101418x^{10} + 411310x^{9} + 260130x^{8} - 388892x^{7} - 305939x^{6} + 149634x^{5} + 141979x^{4} + 3172x^{3} - 3849x^{2} + 170x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 2]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w - 1]$ | $\phantom{-}\frac{892202232127941}{20551123892057105}e^{21} + \frac{2238002675188917}{20551123892057105}e^{20} - \frac{60777889741727477}{41102247784114210}e^{19} - \frac{30620291835010663}{8220449556822842}e^{18} + \frac{169562110748006201}{8220449556822842}e^{17} + \frac{1078238037749313771}{20551123892057105}e^{16} - \frac{1259886302241602267}{8220449556822842}e^{15} - \frac{8174284631569245776}{20551123892057105}e^{14} + \frac{13512296079207046652}{20551123892057105}e^{13} + \frac{72997259791592509677}{41102247784114210}e^{12} - \frac{6701239342523625364}{4110224778411421}e^{11} - \frac{196570519409728690493}{41102247784114210}e^{10} + \frac{8758076782756170911}{4110224778411421}e^{9} + \frac{31195191814329482101}{4110224778411421}e^{8} - \frac{7539198855317644027}{8220449556822842}e^{7} - \frac{268211359881781015209}{41102247784114210}e^{6} - \frac{5993591315220782713}{8220449556822842}e^{5} + \frac{98902103495513335523}{41102247784114210}e^{4} + \frac{27329723085511071267}{41102247784114210}e^{3} - \frac{375469256016189438}{4110224778411421}e^{2} - \frac{561087131128139053}{41102247784114210}e + \frac{54036614147104993}{20551123892057105}$ |
| 7 | $[7, 7, w^{2} + w - 7]$ | $\phantom{-}\frac{3009707952424953}{20551123892057105}e^{21} + \frac{13771859050746167}{41102247784114210}e^{20} - \frac{105819692915938053}{20551123892057105}e^{19} - \frac{96490966798761207}{8220449556822842}e^{18} + \frac{307428028727134961}{4110224778411421}e^{17} + \frac{3505527905235585983}{20551123892057105}e^{16} - \frac{2404072450355206225}{4110224778411421}e^{15} - \frac{55330950209118355961}{41102247784114210}e^{14} + \frac{109978856266041748227}{41102247784114210}e^{13} + \frac{129965850481307746878}{20551123892057105}e^{12} - \frac{29598883265966765286}{4110224778411421}e^{11} - \frac{745461160311173710339}{41102247784114210}e^{10} + \frac{86535156639640126171}{8220449556822842}e^{9} + \frac{255169235166497508547}{8220449556822842}e^{8} - \frac{47205719588698740353}{8220449556822842}e^{7} - \frac{596200967292639873416}{20551123892057105}e^{6} - \frac{13086308255809489798}{4110224778411421}e^{5} + \frac{233827474024281593742}{20551123892057105}e^{4} + \frac{79198529162474249013}{20551123892057105}e^{3} - \frac{354522804092804962}{4110224778411421}e^{2} - \frac{4001285528413667209}{41102247784114210}e + \frac{185562221605292423}{41102247784114210}$ |
| 7 | $[7, 7, -w^{2} + 11]$ | $\phantom{-}\frac{10252932602333813}{82204495568228420}e^{21} + \frac{14994993616147301}{82204495568228420}e^{20} - \frac{378662730598697633}{82204495568228420}e^{19} - \frac{104570756002441491}{16440899113645684}e^{18} + \frac{1173038422843883613}{16440899113645684}e^{17} + \frac{7562748216427673163}{82204495568228420}e^{16} - \frac{4993881313769441717}{8220449556822842}e^{15} - \frac{14863673392278787577}{20551123892057105}e^{14} + \frac{64211025858794950464}{20551123892057105}e^{13} + \frac{139379809107392253959}{41102247784114210}e^{12} - \frac{82263654908208171797}{8220449556822842}e^{11} - \frac{200294944872190539813}{20551123892057105}e^{10} + \frac{162334105670242354361}{8220449556822842}e^{9} + \frac{69332272515433738815}{4110224778411421}e^{8} - \frac{186798530054188287581}{8220449556822842}e^{7} - \frac{670177531227677166133}{41102247784114210}e^{6} + \frac{220012226849568907169}{16440899113645684}e^{5} + \frac{588690930320239369687}{82204495568228420}e^{4} - \frac{119289836968609317331}{41102247784114210}e^{3} - \frac{4820106455794622889}{8220449556822842}e^{2} + \frac{4739407357926240223}{82204495568228420}e - \frac{67748845696373551}{82204495568228420}$ |
| 7 | $[7, 7, -w^{2} + 9]$ | $-\frac{1061343619847387}{41102247784114210}e^{21} - \frac{3964087553842529}{41102247784114210}e^{20} + \frac{33818580661677357}{41102247784114210}e^{19} + \frac{13757624590327805}{4110224778411421}e^{18} - \frac{84496774729141083}{8220449556822842}e^{17} - \frac{1972565188544592047}{41102247784114210}e^{16} + \frac{510873675829641407}{8220449556822842}e^{15} + \frac{7636290732948470471}{20551123892057105}e^{14} - \frac{3302132952082928327}{20551123892057105}e^{13} - \frac{34922723750597996931}{20551123892057105}e^{12} - \frac{506812424527198535}{4110224778411421}e^{11} + \frac{192814956524335396433}{41102247784114210}e^{10} + \frac{15715917081495689173}{8220449556822842}e^{9} - \frac{62335584578198146271}{8220449556822842}e^{8} - \frac{41088493035359537171}{8220449556822842}e^{7} + \frac{131783002332537202637}{20551123892057105}e^{6} + \frac{47161617737848306241}{8220449556822842}e^{5} - \frac{77334993719899804753}{41102247784114210}e^{4} - \frac{52116153107044085286}{20551123892057105}e^{3} - \frac{1441417947506347511}{4110224778411421}e^{2} + \frac{1279082713417402713}{41102247784114210}e + \frac{56164960098622319}{41102247784114210}$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}\frac{2138552524530137}{82204495568228420}e^{21} + \frac{16080594826654469}{82204495568228420}e^{20} - \frac{48740333240420717}{82204495568228420}e^{19} - \frac{112336620578318221}{16440899113645684}e^{18} + \frac{35967284316792511}{16440899113645684}e^{17} + \frac{8118097854637351797}{82204495568228420}e^{16} + \frac{445001895281353311}{8220449556822842}e^{15} - \frac{15866163655483970613}{20551123892057105}e^{14} - \frac{15194487676831230654}{20551123892057105}e^{13} + \frac{146776098434715207581}{41102247784114210}e^{12} + \frac{17422098919692971942}{4110224778411421}e^{11} - \frac{205208475870661956422}{20551123892057105}e^{10} - \frac{54708552141588334363}{4110224778411421}e^{9} + \frac{134501369768136901259}{8220449556822842}e^{8} + \frac{194821072041185761347}{8220449556822842}e^{7} - \frac{575994969098705098187}{41102247784114210}e^{6} - \frac{368706162175093958447}{16440899113645684}e^{5} + \frac{340379142659147055203}{82204495568228420}e^{4} + \frac{182341857372131686968}{20551123892057105}e^{3} + \frac{6511535964727021841}{8220449556822842}e^{2} - \frac{15628771969823834443}{82204495568228420}e + \frac{201699582927396141}{82204495568228420}$ |
| 13 | $[13, 13, -w]$ | $\phantom{-}1$ |
| 19 | $[19, 19, -w^{2} - w + 4]$ | $\phantom{-}\frac{2580872900315573}{4110224778411421}e^{21} + \frac{5359051783134402}{4110224778411421}e^{20} - \frac{92112390569678859}{4110224778411421}e^{19} - \frac{187982215769330696}{4110224778411421}e^{18} + \frac{2730159744956744595}{8220449556822842}e^{17} + \frac{2736631110279622366}{4110224778411421}e^{16} - \frac{21940641141304271145}{8220449556822842}e^{15} - \frac{21649342123116901106}{4110224778411421}e^{14} + \frac{104374325787039631673}{8220449556822842}e^{13} + \frac{204053832873040854823}{8220449556822842}e^{12} - \frac{298831112472900188557}{8220449556822842}e^{11} - \frac{587661421961495258865}{8220449556822842}e^{10} + \frac{492414535132435657935}{8220449556822842}e^{9} + \frac{1011481747330322916697}{8220449556822842}e^{8} - \frac{197646337608726732305}{4110224778411421}e^{7} - \frac{953290640341979912433}{8220449556822842}e^{6} + \frac{53945942359216945209}{8220449556822842}e^{5} + \frac{380353980509878045153}{8220449556822842}e^{4} + \frac{37143206328636412242}{4110224778411421}e^{3} - \frac{6011838835427758917}{8220449556822842}e^{2} - \frac{515873062558037577}{4110224778411421}e + \frac{28472535594521300}{4110224778411421}$ |
| 23 | $[23, 23, w^{2} + w - 10]$ | $\phantom{-}\frac{36517058562092711}{82204495568228420}e^{21} + \frac{61510736390213257}{82204495568228420}e^{20} - \frac{1331125146081345131}{82204495568228420}e^{19} - \frac{429249659795808539}{16440899113645684}e^{18} + \frac{4057595202291419479}{16440899113645684}e^{17} + \frac{31057606297466744781}{82204495568228420}e^{16} - \frac{8467270697563471048}{4110224778411421}e^{15} - \frac{61032184284066062594}{20551123892057105}e^{14} + \frac{212428951105761434293}{20551123892057105}e^{13} + \frac{571663010803852470073}{41102247784114210}e^{12} - \frac{131811802358244657254}{4110224778411421}e^{11} - \frac{819017702725132758836}{20551123892057105}e^{10} + \frac{497900568340594517631}{8220449556822842}e^{9} + \frac{563078310958199358265}{8220449556822842}e^{8} - \frac{535430176427002799575}{8220449556822842}e^{7} - \frac{2677437778072816865681}{41102247784114210}e^{6} + \frac{555453181510406822921}{16440899113645684}e^{5} + \frac{2243434309578273095169}{82204495568228420}e^{4} - \frac{106809099074815336596}{20551123892057105}e^{3} - \frac{11957179358630361999}{8220449556822842}e^{2} + \frac{10300221203856239281}{82204495568228420}e - \frac{77120161291209627}{82204495568228420}$ |
| 29 | $[29, 29, 2w^{2} - 21]$ | $\phantom{-}\frac{2381622975363889}{8220449556822842}e^{21} + \frac{2313912682366767}{4110224778411421}e^{20} - \frac{86250201170639955}{8220449556822842}e^{19} - \frac{164084143974699885}{8220449556822842}e^{18} + \frac{1300654294738013763}{8220449556822842}e^{17} + \frac{1210636653618539400}{4110224778411421}e^{16} - \frac{10666452705661887667}{8220449556822842}e^{15} - \frac{9738273764576580433}{4110224778411421}e^{14} + \frac{51927263872547641627}{8220449556822842}e^{13} + \frac{93644114033059352865}{8220449556822842}e^{12} - \frac{152621032348478355583}{8220449556822842}e^{11} - \frac{276108282048581080493}{8220449556822842}e^{10} + \frac{259364480086156163267}{8220449556822842}e^{9} + \frac{488269790420018344685}{8220449556822842}e^{8} - \frac{217507001165156589649}{8220449556822842}e^{7} - \frac{237287705759072294936}{4110224778411421}e^{6} + \frac{18551427436759981515}{4110224778411421}e^{5} + \frac{98375958144746638713}{4110224778411421}e^{4} + \frac{38121130065075323809}{8220449556822842}e^{3} - \frac{2353920661114288508}{4110224778411421}e^{2} - \frac{1022425003935712687}{8220449556822842}e + \frac{19086402152551071}{4110224778411421}$ |
| 37 | $[37, 37, 2w^{2} + w - 17]$ | $\phantom{-}\frac{13198000811794603}{41102247784114210}e^{21} + \frac{11393907743860518}{20551123892057105}e^{20} - \frac{475044362905303343}{41102247784114210}e^{19} - \frac{156436533827814365}{8220449556822842}e^{18} + \frac{1427076621339765059}{8220449556822842}e^{17} + \frac{11077147730234236293}{41102247784114210}e^{16} - \frac{5862417405186436657}{4110224778411421}e^{15} - \frac{42333616906662733004}{20551123892057105}e^{14} + \frac{144806068911470248193}{20551123892057105}e^{13} + \frac{191258431979180635039}{20551123892057105}e^{12} - \frac{177501789611524609689}{8220449556822842}e^{11} - \frac{1047000233789875568067}{41102247784114210}e^{10} + \frac{334271963315339180337}{8220449556822842}e^{9} + \frac{169809174327066995469}{4110224778411421}e^{8} - \frac{367105017351392707405}{8220449556822842}e^{7} - \frac{749642955053592069318}{20551123892057105}e^{6} + \frac{103878678231334146345}{4110224778411421}e^{5} + \frac{564290028747209504207}{41102247784114210}e^{4} - \frac{225300486162658836467}{41102247784114210}e^{3} - \frac{1396899668456774776}{4110224778411421}e^{2} + \frac{9479725581323176123}{41102247784114210}e - \frac{206015932635514628}{20551123892057105}$ |
| 43 | $[43, 43, 3w^{2} + 3w - 22]$ | $\phantom{-}\frac{5218107534239927}{82204495568228420}e^{21} + \frac{9507820305107049}{82204495568228420}e^{20} - \frac{184973845995299317}{82204495568228420}e^{19} - \frac{64159555366350819}{16440899113645684}e^{18} + \frac{545980443072907367}{16440899113645684}e^{17} + \frac{4441365880429592537}{82204495568228420}e^{16} - \frac{1100345371457495973}{4110224778411421}e^{15} - \frac{16484104902991807061}{41102247784114210}e^{14} + \frac{53377075408429501587}{41102247784114210}e^{13} + \frac{71795749197568473171}{41102247784114210}e^{12} - \frac{16144410473811514771}{4110224778411421}e^{11} - \frac{188246126891122139629}{41102247784114210}e^{10} + \frac{30428280474953075627}{4110224778411421}e^{9} + \frac{58576055031847162627}{8220449556822842}e^{8} - \frac{34513411534979754656}{4110224778411421}e^{7} - \frac{256988583314712940077}{41102247784114210}e^{6} + \frac{86036617655147030265}{16440899113645684}e^{5} + \frac{231214751993360843083}{82204495568228420}e^{4} - \frac{56651427889570426829}{41102247784114210}e^{3} - \frac{4333113221758092231}{8220449556822842}e^{2} - \frac{313611424298899963}{82204495568228420}e + \frac{458972644267729561}{82204495568228420}$ |
| 47 | $[47, 47, w^{2} - 6]$ | $-\frac{877125329685567}{8220449556822842}e^{21} - \frac{2435352845718045}{4110224778411421}e^{20} + \frac{12348046447208296}{4110224778411421}e^{19} + \frac{85352471997562739}{4110224778411421}e^{18} - \frac{118129850460359475}{4110224778411421}e^{17} - \frac{1238981937931585973}{4110224778411421}e^{16} + \frac{245049290036106008}{4110224778411421}e^{15} + \frac{19480638212488347467}{8220449556822842}e^{14} + \frac{7139602586477207765}{8220449556822842}e^{13} - \frac{90764135477885036419}{8220449556822842}e^{12} - \frac{31129378971341112916}{4110224778411421}e^{11} + \frac{128135016357804048128}{4110224778411421}e^{10} + \frac{113887001472484378867}{4110224778411421}e^{9} - \frac{425760237874668550735}{8220449556822842}e^{8} - \frac{220796087751061296962}{4110224778411421}e^{7} + \frac{186622245194405900462}{4110224778411421}e^{6} + \frac{221524303568482823210}{4110224778411421}e^{5} - \frac{118387058592403072545}{8220449556822842}e^{4} - \frac{91528282754845084024}{4110224778411421}e^{3} - \frac{16704215381096614033}{8220449556822842}e^{2} + \frac{3582755778264792733}{8220449556822842}e - \frac{11671295729102099}{4110224778411421}$ |
| 47 | $[47, 47, w^{2} - 3]$ | $-\frac{12696123505342447}{20551123892057105}e^{21} - \frac{50501057183984533}{41102247784114210}e^{20} + \frac{910751901924843259}{41102247784114210}e^{19} + \frac{177091147038419068}{4110224778411421}e^{18} - \frac{1358538025552638733}{4110224778411421}e^{17} - \frac{12887617667521980737}{20551123892057105}e^{16} + \frac{11013696593211533545}{4110224778411421}e^{15} + \frac{203904724162366958429}{41102247784114210}e^{14} - \frac{530387991620752707023}{41102247784114210}e^{13} - \frac{480641805450580008652}{20551123892057105}e^{12} + \frac{154701336490809262384}{4110224778411421}e^{11} + \frac{1385568026652860244218}{20551123892057105}e^{10} - \frac{263432135990499501282}{4110224778411421}e^{9} - \frac{955929094949132979699}{8220449556822842}e^{8} + \frac{229055698082277712279}{4110224778411421}e^{7} + \frac{2262325208793288295299}{20551123892057105}e^{6} - \frac{114492447570770071269}{8220449556822842}e^{5} - \frac{1827396054504155501191}{41102247784114210}e^{4} - \frac{250327952718134215729}{41102247784114210}e^{3} + \frac{8397949947591724413}{8220449556822842}e^{2} + \frac{3386303446995291631}{41102247784114210}e - \frac{98497747657493821}{20551123892057105}$ |
| 47 | $[47, 47, -w^{2} + 12]$ | $\phantom{-}\frac{18614055804349271}{41102247784114210}e^{21} + \frac{30578293187429217}{41102247784114210}e^{20} - \frac{680250804036400771}{41102247784114210}e^{19} - \frac{213692222933492639}{8220449556822842}e^{18} + \frac{2079569459632698637}{8220449556822842}e^{17} + \frac{15489335358234972751}{41102247784114210}e^{16} - \frac{8706551881739999895}{4110224778411421}e^{15} - \frac{61012056976949055778}{20551123892057105}e^{14} + \frac{219153584746425287326}{20551123892057105}e^{13} + \frac{286463486764024955073}{20551123892057105}e^{12} - \frac{136435706658502169795}{4110224778411421}e^{11} - \frac{822973365846844428527}{20551123892057105}e^{10} + \frac{258507417814591181811}{4110224778411421}e^{9} + \frac{283459946893353500768}{4110224778411421}e^{8} - \frac{278834171134013208343}{4110224778411421}e^{7} - \frac{1346775132800065480391}{20551123892057105}e^{6} + \frac{290314168008351394767}{8220449556822842}e^{5} + \frac{1113882344691334402819}{41102247784114210}e^{4} - \frac{113738987573420253327}{20551123892057105}e^{3} - \frac{4638014172641415590}{4110224778411421}e^{2} + \frac{8533263512206231241}{41102247784114210}e + \frac{8699822141401303}{41102247784114210}$ |
| 53 | $[53, 53, w^{2} - w - 4]$ | $-\frac{3238432944389433}{16440899113645684}e^{21} - \frac{5543943710404765}{16440899113645684}e^{20} + \frac{118298244377119953}{16440899113645684}e^{19} + \frac{195996901167587971}{16440899113645684}e^{18} - \frac{1803762117391620159}{16440899113645684}e^{17} - \frac{2882514665885249801}{16440899113645684}e^{16} + \frac{3751851321005236991}{4110224778411421}e^{15} + \frac{11548744479919728745}{8220449556822842}e^{14} - \frac{37261556411112258289}{8220449556822842}e^{13} - \frac{55267410124948553859}{8220449556822842}e^{12} + \frac{56414574082816136958}{4110224778411421}e^{11} + \frac{80966592733419554652}{4110224778411421}e^{10} - \frac{202033362443263318303}{8220449556822842}e^{9} - \frac{283549176658531658391}{8220449556822842}e^{8} + \frac{95804703416603950780}{4110224778411421}e^{7} + \frac{135117453408776244341}{4110224778411421}e^{6} - \frac{133010697096811914973}{16440899113645684}e^{5} - \frac{210845623017447984467}{16440899113645684}e^{4} - \frac{8582231400656523213}{8220449556822842}e^{3} - \frac{1953515536085249199}{8220449556822842}e^{2} - \frac{820754240164320063}{16440899113645684}e + \frac{75309461229102761}{16440899113645684}$ |
| 61 | $[61, 61, w^{2} - 5]$ | $-\frac{38035375598688047}{41102247784114210}e^{21} - \frac{71539275952800769}{41102247784114210}e^{20} + \frac{1371742482163779347}{41102247784114210}e^{19} + \frac{250308821760932109}{4110224778411421}e^{18} - \frac{2061718691870439788}{4110224778411421}e^{17} - \frac{18168144013375159911}{20551123892057105}e^{16} + \frac{16894147879253616650}{4110224778411421}e^{15} + \frac{143299698284374274531}{20551123892057105}e^{14} - \frac{413282042027767941587}{20551123892057105}e^{13} - \frac{673423704220645614711}{20551123892057105}e^{12} + \frac{247261611919254831182}{4110224778411421}e^{11} + \frac{1935367063181283497059}{20551123892057105}e^{10} - \frac{881452300437848844071}{8220449556822842}e^{9} - \frac{666213565834631268861}{4110224778411421}e^{8} + \frac{425269294730756902406}{4110224778411421}e^{7} + \frac{3157520758668343354932}{20551123892057105}e^{6} - \frac{332340518817064702373}{8220449556822842}e^{5} - \frac{2591258569617207344643}{41102247784114210}e^{4} - \frac{19553734129052390926}{20551123892057105}e^{3} + \frac{19175908002305894307}{8220449556822842}e^{2} - \frac{3099516442744722817}{41102247784114210}e - \frac{75070729132941163}{20551123892057105}$ |
| 67 | $[67, 67, w^{2} - w - 7]$ | $-\frac{2781890746014731}{20551123892057105}e^{21} - \frac{6621108618280322}{20551123892057105}e^{20} + \frac{98566536566333826}{20551123892057105}e^{19} + \frac{94235303840171451}{8220449556822842}e^{18} - \frac{288656440072351633}{4110224778411421}e^{17} - \frac{6978547898306078637}{41102247784114210}e^{16} + \frac{4544544052610850647}{8220449556822842}e^{15} + \frac{56325417482697650557}{41102247784114210}e^{14} - \frac{52041647124759751672}{20551123892057105}e^{13} - \frac{271457276554161048217}{41102247784114210}e^{12} + \frac{55211519065187402161}{8220449556822842}e^{11} + \frac{400202240660053645114}{20551123892057105}e^{10} - \frac{37596474467635303679}{4110224778411421}e^{9} - \frac{140812482217957685431}{4110224778411421}e^{8} + \frac{11474462915902623285}{4110224778411421}e^{7} + \frac{671959645850816764867}{20551123892057105}e^{6} + \frac{56605040965387385521}{8220449556822842}e^{5} - \frac{520283727769730140783}{41102247784114210}e^{4} - \frac{236384395408931963247}{41102247784114210}e^{3} - \frac{1316526123374131567}{4110224778411421}e^{2} + \frac{4066671612355851783}{41102247784114210}e - \frac{144743326170388938}{20551123892057105}$ |
| 73 | $[73, 73, 7w^{2} + 3w - 66]$ | $-\frac{8905902687952123}{82204495568228420}e^{21} - \frac{20439258624930851}{82204495568228420}e^{20} + \frac{302549575117915963}{82204495568228420}e^{19} + \frac{136099416627693791}{16440899113645684}e^{18} - \frac{845373041966187747}{16440899113645684}e^{17} - \frac{9236910355232690793}{82204495568228420}e^{16} + \frac{3180908004121836385}{8220449556822842}e^{15} + \frac{33274811414377899109}{41102247784114210}e^{14} - \frac{71057229452508672013}{41102247784114210}e^{13} - \frac{138387249890770860569}{41102247784114210}e^{12} + \frac{39335423594091973139}{8220449556822842}e^{11} + \frac{168396518503609799508}{20551123892057105}e^{10} - \frac{69100038900893008265}{8220449556822842}e^{9} - \frac{46118390753091309309}{4110224778411421}e^{8} + \frac{78949615635206142729}{8220449556822842}e^{7} + \frac{320128792233826264373}{41102247784114210}e^{6} - \frac{116575984558257154609}{16440899113645684}e^{5} - \frac{187184173610567708677}{82204495568228420}e^{4} + \frac{110048564403031714491}{41102247784114210}e^{3} + \frac{1258963944616997234}{4110224778411421}e^{2} - \frac{3058189732134841753}{82204495568228420}e + \frac{553247450004784431}{82204495568228420}$ |
| 79 | $[79, 79, 2w^{2} - 19]$ | $\phantom{-}\frac{50997263721375911}{82204495568228420}e^{21} + \frac{108732952890811517}{82204495568228420}e^{20} - \frac{1817789577801952911}{82204495568228420}e^{19} - \frac{766910264935893643}{16440899113645684}e^{18} + \frac{5373200889821302321}{16440899113645684}e^{17} + \frac{56194110553836277471}{82204495568228420}e^{16} - \frac{10736250158597055598}{4110224778411421}e^{15} - \frac{112019776205479511324}{20551123892057105}e^{14} + \frac{505167150144851437191}{41102247784114210}e^{13} + \frac{532703216044045961074}{20551123892057105}e^{12} - \frac{141367263818349194775}{4110224778411421}e^{11} - \frac{1548950107845965216191}{20551123892057105}e^{10} + \frac{441391682280393939537}{8220449556822842}e^{9} + \frac{537878437122137060351}{4110224778411421}e^{8} - \frac{294961570450933364315}{8220449556822842}e^{7} - \frac{2543766915364844018938}{20551123892057105}e^{6} - \frac{110599757323193578711}{16440899113645684}e^{5} + \frac{3976378591911793805929}{82204495568228420}e^{4} + \frac{620401396844562203523}{41102247784114210}e^{3} + \frac{3246789165169597275}{8220449556822842}e^{2} - \frac{16817697921649847119}{82204495568228420}e - \frac{171307797622247477}{82204495568228420}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, -w]$ | $-1$ |