Base field \(\Q(\sqrt{401}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 100\); narrow class number \(5\) and class number \(5\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[2, 2, w]$ |
| Dimension: | $48$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $90$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{48} + 4x^{47} + 25x^{46} + 85x^{45} + 362x^{44} + 1029x^{43} + 3687x^{42} + 9610x^{41} + 31664x^{40} + 79059x^{39} + 229634x^{38} + 530405x^{37} + 1386787x^{36} + 2875333x^{35} + 6756362x^{34} + 13008266x^{33} + 28168548x^{32} + 50622794x^{31} + 100397402x^{30} + 162938234x^{29} + 290805944x^{28} + 403646526x^{27} + 606423454x^{26} + 695198617x^{25} + 896192233x^{24} + 700884278x^{23} + 853347968x^{22} + 474834450x^{21} + 599033547x^{20} + 128866653x^{19} + 603290027x^{18} + 16028699x^{17} + 409202318x^{16} - 100057959x^{15} + 136625041x^{14} - 20689110x^{13} + 44587703x^{12} + 6126974x^{11} + 4501347x^{10} + 671035x^{9} + 376296x^{8} + 34562x^{7} + 22013x^{6} + 2300x^{5} + 1267x^{4} + 182x^{3} + 40x^{2} + 4x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $...$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $...$ |
| 5 | $[5, 5, w + 4]$ | $...$ |
| 7 | $[7, 7, w + 1]$ | $...$ |
| 7 | $[7, 7, w + 5]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 11 | $[11, 11, w + 3]$ | $...$ |
| 11 | $[11, 11, w + 7]$ | $...$ |
| 29 | $[29, 29, w + 6]$ | $...$ |
| 29 | $[29, 29, w + 22]$ | $...$ |
| 41 | $[41, 41, w + 13]$ | $...$ |
| 41 | $[41, 41, w + 27]$ | $...$ |
| 43 | $[43, 43, w + 16]$ | $...$ |
| 43 | $[43, 43, w + 26]$ | $...$ |
| 47 | $[47, 47, w + 2]$ | $...$ |
| 47 | $[47, 47, w + 44]$ | $...$ |
| 73 | $[73, 73, w + 33]$ | $...$ |
| 73 | $[73, 73, w + 39]$ | $...$ |
| 83 | $[83, 83, -4w - 37]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-\frac{108026389903208805581185482343119852461289171861433698364543542822}{900719656368706644011289329279101518703795255018047493737445578731}e^{47} - \frac{436801361022902163968110820208936765229588480085771495214690061323}{900719656368706644011289329279101518703795255018047493737445578731}e^{46} - \frac{2722221257192647806266203944733160890301473602567683260559910038810}{900719656368706644011289329279101518703795255018047493737445578731}e^{45} - \frac{9309840701508430133991871118278527010470379857787748207046434665827}{900719656368706644011289329279101518703795255018047493737445578731}e^{44} - \frac{39570367163640645232519554757075204036466479441409835014204843394609}{900719656368706644011289329279101518703795255018047493737445578731}e^{43} - \frac{113071895384055037517729154282887863893616255572099871016970538210553}{900719656368706644011289329279101518703795255018047493737445578731}e^{42} - \frac{404050200677795410248818665428615442972684177077672598966212840814469}{900719656368706644011289329279101518703795255018047493737445578731}e^{41} - \frac{1057965148461664064167281192346723015408488998705289153978450546536300}{900719656368706644011289329279101518703795255018047493737445578731}e^{40} - \frac{3474932503401222993920429758502605755639282035665311189448916752221179}{900719656368706644011289329279101518703795255018047493737445578731}e^{39} - \frac{8712356354541077174709575285440875824435964233217508084226714585635728}{900719656368706644011289329279101518703795255018047493737445578731}e^{38} - \frac{25256513161378591248737216618666546158796644497233732197058752105136578}{900719656368706644011289329279101518703795255018047493737445578731}e^{37} - \frac{58565649889996737343275022213854269586007049508221270411955230015783325}{900719656368706644011289329279101518703795255018047493737445578731}e^{36} - \frac{152862133708950637094789728474002863344094215649234597796431404576698899}{900719656368706644011289329279101518703795255018047493737445578731}e^{35} - \frac{318378462806383082184300859130425142666909599199383671665685486790385709}{900719656368706644011289329279101518703795255018047493737445578731}e^{34} - \frac{746707716169366567374600679617619796638441537008410095519060112893575674}{900719656368706644011289329279101518703795255018047493737445578731}e^{33} - \frac{1443622051604346534437871153973591063259107195598666591721453171464902582}{900719656368706644011289329279101518703795255018047493737445578731}e^{32} - \frac{3120007182542318531845210502171251256050481099844588019676408610866840451}{900719656368706644011289329279101518703795255018047493737445578731}e^{31} - \frac{5630507018458730367655028048804814934803970595613544138000382817308436963}{900719656368706644011289329279101518703795255018047493737445578731}e^{30} - \frac{11148850468585862234044288477414020435368816294281337394487747748490365714}{900719656368706644011289329279101518703795255018047493737445578731}e^{29} - \frac{18186491871116848626235345042982927248898422941070751983392935373693652748}{900719656368706644011289329279101518703795255018047493737445578731}e^{28} - \frac{32409182106528177414561378592728864556798725566823063800704428363274991348}{900719656368706644011289329279101518703795255018047493737445578731}e^{27} - \frac{45325243562031219755791002696954854610724226117229644022235037986405425702}{900719656368706644011289329279101518703795255018047493737445578731}e^{26} - \frac{68052460057406760682670407189652737772826730140531679463462959697158351518}{900719656368706644011289329279101518703795255018047493737445578731}e^{25} - \frac{78784933826989674377775535719257635261044741197401373677365682100013687590}{900719656368706644011289329279101518703795255018047493737445578731}e^{24} - \frac{101359195564785721580931622415995701286353977131488070216226856210766727811}{900719656368706644011289329279101518703795255018047493737445578731}e^{23} - \frac{81255822734723284066431977543469011497428359334863193861870071306744798171}{900719656368706644011289329279101518703795255018047493737445578731}e^{22} - \frac{97261518723013872527859357658075236068724150943817535369794605951530133776}{900719656368706644011289329279101518703795255018047493737445578731}e^{21} - \frac{56358014637246387795853832499393720481976142993467491650244496831090617020}{900719656368706644011289329279101518703795255018047493737445578731}e^{20} - \frac{68572519706146295090284374404783284320211203116244291557715204409083851793}{900719656368706644011289329279101518703795255018047493737445578731}e^{19} - \frac{17211253329632684904146568442140264922982412981293004673903056121044516606}{900719656368706644011289329279101518703795255018047493737445578731}e^{18} - \frac{66910917489030237981102716446110450568384788056675038454121886685610791409}{900719656368706644011289329279101518703795255018047493737445578731}e^{17} - \frac{4341944425102112633321270039708534637145394818529222336247950447176755863}{900719656368706644011289329279101518703795255018047493737445578731}e^{16} - \frac{45767935092346717503978524233000448168389196847464651131948383837318850481}{900719656368706644011289329279101518703795255018047493737445578731}e^{15} + \frac{9387790211767451585647939246446054674779033272051740948638000613395875360}{900719656368706644011289329279101518703795255018047493737445578731}e^{14} - \frac{15326279716550292310377618667106183087024087310742706460641475707569727332}{900719656368706644011289329279101518703795255018047493737445578731}e^{13} + \frac{2220246773970847822052623568486777372340158251012552895098552068099523230}{900719656368706644011289329279101518703795255018047493737445578731}e^{12} - \frac{5128474104111941022854637364336539354860273232830357899647041904679540841}{900719656368706644011289329279101518703795255018047493737445578731}e^{11} - \frac{720933770511666611073889489465728773042595530938226264978443951395130643}{900719656368706644011289329279101518703795255018047493737445578731}e^{10} - \frac{631390244577830726938089912701159568612110379501986323453742447333947793}{900719656368706644011289329279101518703795255018047493737445578731}e^{9} - \frac{78697663594477769892830391614105662038551383986504823876340685644247640}{900719656368706644011289329279101518703795255018047493737445578731}e^{8} - \frac{43311734740761409287759335223114926624795155295547473299944722190295377}{900719656368706644011289329279101518703795255018047493737445578731}e^{7} - \frac{4061815035256741553129359084704945969703658981747924290721492485513869}{900719656368706644011289329279101518703795255018047493737445578731}e^{6} - \frac{2535043987145550685712586289635332022273405858413662024578493598171686}{900719656368706644011289329279101518703795255018047493737445578731}e^{5} - \frac{11416890961538900177916643247757686232359848133472883090954491874354}{900719656368706644011289329279101518703795255018047493737445578731}e^{4} - \frac{146362462371622931657702698906679367689328800462173122583063975503409}{900719656368706644011289329279101518703795255018047493737445578731}e^{3} - \frac{21099295337712901971274791380778985512127539684496572969645874391439}{900719656368706644011289329279101518703795255018047493737445578731}e^{2} - \frac{4614604472514583752730334143808411677862224349806938980204352726840}{900719656368706644011289329279101518703795255018047493737445578731}e - \frac{464884711881740665121585045548292300958205881197215280584252321873}{900719656368706644011289329279101518703795255018047493737445578731}$ |