Base field 4.4.17989.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} - 3x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 2, 2]$ |
| Dimension: | $22$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $36$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{22} - 3x^{21} - 41x^{20} + 124x^{19} + 701x^{18} - 2161x^{17} - 6453x^{16} + 20693x^{15} + 34270x^{14} - 119008x^{13} - 102455x^{12} + 422209x^{11} + 140101x^{10} - 912106x^{9} + 43939x^{8} + 1129329x^{7} - 384050x^{6} - 680969x^{5} + 403073x^{4} + 109618x^{3} - 112303x^{2} + 13046x + 2364\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{3} + 2w^{2} + 4w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{3} - 2w^{2} - 6w + 2]$ | $-\frac{39621127182097927}{51266790348844050}e^{21} + \frac{75087038409270089}{51266790348844050}e^{20} + \frac{1708633388622323443}{51266790348844050}e^{19} - \frac{504872241688396817}{8544465058140675}e^{18} - \frac{31167299437892861399}{51266790348844050}e^{17} + \frac{10268789117284616821}{10253358069768810}e^{16} + \frac{313115522932182941897}{51266790348844050}e^{15} - \frac{158836199406800940461}{17088930116281350}e^{14} - \frac{944986751301606724097}{25633395174422025}e^{13} + \frac{441591481693033091369}{8544465058140675}e^{12} + \frac{1402142605111221617509}{10253358069768810}e^{11} - \frac{395463465080263586167}{2228990884732350}e^{10} - \frac{5214868089274227803927}{17088930116281350}e^{9} + \frac{9591691847766793174412}{25633395174422025}e^{8} + \frac{1295749854316706558413}{3417786023256270}e^{7} - \frac{7932245274699499341811}{17088930116281350}e^{6} - \frac{5439061407296751334904}{25633395174422025}e^{5} + \frac{15347843115684452674273}{51266790348844050}e^{4} + \frac{737611870547447026613}{51266790348844050}e^{3} - \frac{359274614703494902286}{5126679034884405}e^{2} + \frac{555072772349337258431}{51266790348844050}e + \frac{14368958147447112409}{8544465058140675}$ |
| 11 | $[11, 11, w^{3} - 2w^{2} - 4w]$ | $-\frac{139929828267129518}{76900185523266075}e^{21} + \frac{267410016459229489}{76900185523266075}e^{20} + \frac{6027915919950911279}{76900185523266075}e^{19} - \frac{3595272666910245746}{25633395174422025}e^{18} - \frac{109820376668401333033}{76900185523266075}e^{17} + \frac{182748040950423165484}{76900185523266075}e^{16} + \frac{1101721410976617535327}{76900185523266075}e^{15} - \frac{565009985037642879997}{25633395174422025}e^{14} - \frac{6639110737597424632148}{76900185523266075}e^{13} + \frac{627738508936508973856}{5126679034884405}e^{12} + \frac{24580428830388857086798}{76900185523266075}e^{11} - \frac{32277770464198732623526}{76900185523266075}e^{10} - \frac{18243109754728619878924}{25633395174422025}e^{9} + \frac{67932039700247712040592}{76900185523266075}e^{8} + \frac{4520269832177782358021}{5126679034884405}e^{7} - \frac{28010024115240378346844}{25633395174422025}e^{6} - \frac{7556427131677367776834}{15380037104653215}e^{5} + \frac{54023204963234013587411}{76900185523266075}e^{4} + \frac{2469976987271619269569}{76900185523266075}e^{3} - \frac{2524749030420048258053}{15380037104653215}e^{2} + \frac{1953562547880307607509}{76900185523266075}e + \frac{101268686870092033414}{25633395174422025}$ |
| 13 | $[13, 13, w^{2} - 3w - 2]$ | $\phantom{-}\frac{41948086392184313}{153800371046532150}e^{21} - \frac{15161311712402249}{30760074209306430}e^{20} - \frac{1821183746091862403}{153800371046532150}e^{19} + \frac{510996909761170663}{25633395174422025}e^{18} + \frac{33476681439363370387}{153800371046532150}e^{17} - \frac{52161881516654669257}{153800371046532150}e^{16} - \frac{2950368071410150687}{1337394530839410}e^{15} + \frac{162262717949565568873}{51266790348844050}e^{14} + \frac{1034388342929355138346}{76900185523266075}e^{13} - \frac{454780237280866525093}{25633395174422025}e^{12} - \frac{7763477034215567687089}{153800371046532150}e^{11} + \frac{379026780451957708189}{6152014841861286}e^{10} + \frac{5852954186772756375841}{51266790348844050}e^{9} - \frac{10148947040805147100597}{76900185523266075}e^{8} - \frac{1478438768596786261517}{10253358069768810}e^{7} + \frac{8555508902928215125949}{51266790348844050}e^{6} + \frac{6364280499741799514938}{76900185523266075}e^{5} - \frac{16886546195703251531189}{153800371046532150}e^{4} - \frac{1036415547847873870393}{153800371046532150}e^{3} + \frac{79917879628533876872}{3076007420930643}e^{2} - \frac{601011306918886110949}{153800371046532150}e - \frac{15764376396270148334}{25633395174422025}$ |
| 16 | $[16, 2, 2]$ | $-1$ |
| 17 | $[17, 17, -w^{3} + 3w^{2} + 2w - 2]$ | $\phantom{-}\frac{668955092133319}{10253358069768810}e^{21} - \frac{5126972475345589}{51266790348844050}e^{20} - \frac{147703236994901951}{51266790348844050}e^{19} + \frac{6931676950259027}{1708893011628135}e^{18} + \frac{2766470967598970221}{51266790348844050}e^{17} - \frac{3556969686326391667}{51266790348844050}e^{16} - \frac{28624500924753894877}{51266790348844050}e^{15} + \frac{11167844051194740679}{17088930116281350}e^{14} + \frac{89273148083202772348}{25633395174422025}e^{13} - \frac{31772520523702797712}{8544465058140675}e^{12} - \frac{29869050627725716553}{2228990884732350}e^{11} + \frac{677245883935850637271}{51266790348844050}e^{10} + \frac{532633430954094025213}{17088930116281350}e^{9} - \frac{749046857213608124794}{25633395174422025}e^{8} - \frac{139245707793825506447}{3417786023256270}e^{7} + \frac{26304866004456917189}{683557204651254}e^{6} + \frac{635175624030277518877}{25633395174422025}e^{5} - \frac{1354279598247956557997}{51266790348844050}e^{4} - \frac{155105269046091160351}{51266790348844050}e^{3} + \frac{32782769648706892609}{5126679034884405}e^{2} - \frac{8771259047140481939}{10253358069768810}e - \frac{1242113262682234073}{8544465058140675}$ |
| 17 | $[17, 17, -w^{2} + 2w + 3]$ | $-\frac{16849000987081951}{153800371046532150}e^{21} + \frac{31727377911861059}{153800371046532150}e^{20} + \frac{724329793332522337}{153800371046532150}e^{19} - \frac{212027587505813546}{25633395174422025}e^{18} - \frac{526561674345352535}{6152014841861286}e^{17} + \frac{930054821537475457}{6686972654197050}e^{16} + \frac{131683087217616517517}{153800371046532150}e^{15} - \frac{2619451149420919841}{2050671613953762}e^{14} - \frac{79094475785725599733}{15380037104653215}e^{13} + \frac{179583480446030571203}{25633395174422025}e^{12} + \frac{2918261180998076674697}{153800371046532150}e^{11} - \frac{3634464065155048483541}{153800371046532150}e^{10} - \frac{431934229281701794339}{10253358069768810}e^{9} + \frac{3751675552315438933238}{76900185523266075}e^{8} + \frac{535358094896207435341}{10253358069768810}e^{7} - \frac{3030924771844804361143}{51266790348844050}e^{6} - \frac{2276210602884863385758}{76900185523266075}e^{5} + \frac{1147538560751511761711}{30760074209306430}e^{4} + \frac{421871761862660534687}{153800371046532150}e^{3} - \frac{132197095044627225503}{15380037104653215}e^{2} + \frac{191434500417499623353}{153800371046532150}e + \frac{5001859146501489751}{25633395174422025}$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 6w + 1]$ | $-\frac{919330622749739}{3343486327098525}e^{21} + \frac{41264738050841774}{76900185523266075}e^{20} + \frac{907587475812492508}{76900185523266075}e^{19} - \frac{553720679174087419}{25633395174422025}e^{18} - \frac{16466169968234301719}{76900185523266075}e^{17} + \frac{5613645169383793762}{15380037104653215}e^{16} + \frac{164394299107141872722}{76900185523266075}e^{15} - \frac{86438995983089464856}{25633395174422025}e^{14} - \frac{985172601926617558969}{76900185523266075}e^{13} + \frac{477494887297760487643}{25633395174422025}e^{12} + \frac{144978416424543774365}{3076007420930643}e^{11} - \frac{4872088803777267238211}{76900185523266075}e^{10} - \frac{2671041309082588892042}{25633395174422025}e^{9} + \frac{10146412320560160001429}{76900185523266075}e^{8} + \frac{131350659172370767730}{1025335806976881}e^{7} - \frac{4129543591978812583291}{25633395174422025}e^{6} - \frac{5447097942028661546443}{76900185523266075}e^{5} + \frac{7855802929118806077913}{76900185523266075}e^{4} + \frac{358291867673677372643}{76900185523266075}e^{3} - \frac{363903419584900014001}{15380037104653215}e^{2} + \frac{278234190017630715731}{76900185523266075}e + \frac{14569158875691822578}{25633395174422025}$ |
| 27 | $[27, 3, -2w^{3} + 3w^{2} + 11w - 1]$ | $\phantom{-}\frac{58696975068503426}{76900185523266075}e^{21} - \frac{112362121880413984}{76900185523266075}e^{20} - \frac{2527741904986515032}{76900185523266075}e^{19} + \frac{65670594071515354}{1114495442366175}e^{18} + \frac{9206872213370035019}{15380037104653215}e^{17} - \frac{76756002669403779166}{76900185523266075}e^{16} - \frac{461605458883999000582}{76900185523266075}e^{15} + \frac{47445112944698685632}{5126679034884405}e^{14} + \frac{556026721775745077953}{15380037104653215}e^{13} - \frac{1317141163790491608446}{25633395174422025}e^{12} - \frac{10285962636872435723197}{76900185523266075}e^{11} + \frac{13535451150323894737621}{76900185523266075}e^{10} + \frac{66325012079498868406}{222899088473235}e^{9} - \frac{28458849995309130261476}{76900185523266075}e^{8} - \frac{1887701233706926278848}{5126679034884405}e^{7} + \frac{11720055892871192816378}{25633395174422025}e^{6} + \frac{684707807533069520332}{3343486327098525}e^{5} - \frac{4515470807155267875376}{15380037104653215}e^{4} - \frac{1014153340381556629732}{76900185523266075}e^{3} + \frac{1054908277980212654489}{15380037104653215}e^{2} - \frac{818811560968240465003}{76900185523266075}e - \frac{42468033703362952312}{25633395174422025}$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 5w + 4]$ | $-\frac{17874029761674523}{10253358069768810}e^{21} + \frac{34009150117149137}{10253358069768810}e^{20} + \frac{154070001484650581}{2050671613953762}e^{19} - \frac{228621360235683173}{1708893011628135}e^{18} - \frac{14042397844758186833}{10253358069768810}e^{17} + \frac{23242389988511081939}{10253358069768810}e^{16} + \frac{140961601692780578669}{10253358069768810}e^{15} - \frac{71866244721921629219}{3417786023256270}e^{14} - \frac{85005697566867830686}{1025335806976881}e^{13} + \frac{199651969641290280053}{1708893011628135}e^{12} + \frac{629958866598293369491}{2050671613953762}e^{11} - \frac{4107848947007216177723}{10253358069768810}e^{10} - \frac{2339962789331564099471}{3417786023256270}e^{9} + \frac{865049854698216767548}{1025335806976881}e^{8} + \frac{2902620805232409436319}{3417786023256270}e^{7} - \frac{3569858982170123670067}{3417786023256270}e^{6} - \frac{2431818383850734327756}{5126679034884405}e^{5} + \frac{6892110648454361015173}{10253358069768810}e^{4} + \frac{326482120732096619789}{10253358069768810}e^{3} - \frac{161128320686824063322}{1025335806976881}e^{2} + \frac{248859231714517214609}{10253358069768810}e + \frac{1291299190141727414}{341778602325627}$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 6w - 3]$ | $-\frac{161772809721901682}{76900185523266075}e^{21} + \frac{305614093475776396}{76900185523266075}e^{20} + \frac{6982047201212824271}{76900185523266075}e^{19} - \frac{4112835690878249969}{25633395174422025}e^{18} - \frac{127480290469768891972}{76900185523266075}e^{17} + \frac{209339160114756446686}{76900185523266075}e^{16} + \frac{1282097873993590489018}{76900185523266075}e^{15} - \frac{648474358098904309213}{25633395174422025}e^{14} - \frac{7748426462731861790432}{76900185523266075}e^{13} + \frac{722447455110129424003}{5126679034884405}e^{12} + \frac{28782543392468015842747}{76900185523266075}e^{11} - \frac{37289655196333748422039}{76900185523266075}e^{10} - \frac{21442372957144331108851}{25633395174422025}e^{9} + \frac{78879268114196458285973}{76900185523266075}e^{8} + \frac{5336000576233263423392}{5126679034884405}e^{7} - \frac{32725704533451919463681}{25633395174422025}e^{6} - \frac{8967956076340074067357}{15380037104653215}e^{5} + \frac{63525455342796695386724}{76900185523266075}e^{4} + \frac{2994178058230986137701}{76900185523266075}e^{3} - \frac{2980155238721894218454}{15380037104653215}e^{2} + \frac{2309449028387958312946}{76900185523266075}e + \frac{5191433447632089002}{1114495442366175}$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 5w + 1]$ | $-\frac{38521521501919058}{76900185523266075}e^{21} + \frac{73577704568280082}{76900185523266075}e^{20} + \frac{1661964956471821151}{76900185523266075}e^{19} - \frac{991560322753968266}{25633395174422025}e^{18} - \frac{6066475212940091693}{15380037104653215}e^{17} + \frac{50555751426967343503}{76900185523266075}e^{16} + \frac{304918770910682150611}{76900185523266075}e^{15} - \frac{31387058950568883734}{5126679034884405}e^{14} - \frac{368352234199687218694}{15380037104653215}e^{13} + \frac{876385496540559524093}{25633395174422025}e^{12} + \frac{6836246275670790529081}{76900185523266075}e^{11} - \frac{9073209261688565247823}{76900185523266075}e^{10} - \frac{1017288107207415713777}{5126679034884405}e^{9} + \frac{19250390414771965540268}{76900185523266075}e^{8} + \frac{1262281324364868284246}{5126679034884405}e^{7} - \frac{8007261297073706622029}{25633395174422025}e^{6} - \frac{10509057996385306317248}{76900185523266075}e^{5} + \frac{3113638365023059041496}{15380037104653215}e^{4} + \frac{590715556903165512541}{76900185523266075}e^{3} - \frac{146208993622751303740}{3076007420930643}e^{2} + \frac{578220594305351777659}{76900185523266075}e + \frac{29515028131213672156}{25633395174422025}$ |
| 31 | $[31, 31, w^{3} - 2w^{2} - 6w]$ | $-\frac{25654805438523631}{15380037104653215}e^{21} + \frac{246578027536212742}{76900185523266075}e^{20} + \frac{5519371142582905823}{76900185523266075}e^{19} - \frac{662534334907913557}{5126679034884405}e^{18} - \frac{100419170322648090373}{76900185523266075}e^{17} + \frac{168206491669989544306}{76900185523266075}e^{16} + \frac{1005815533910852529811}{76900185523266075}e^{15} - \frac{519290265768638815867}{25633395174422025}e^{14} - \frac{6049986212971259737403}{76900185523266075}e^{13} + \frac{2878841625319199267897}{25633395174422025}e^{12} + \frac{22351251208508100874492}{76900185523266075}e^{11} - \frac{29523018745793787349138}{76900185523266075}e^{10} - \frac{16547652998674177205314}{25633395174422025}e^{9} + \frac{61907505243885658433534}{76900185523266075}e^{8} + \frac{817704994928214308686}{1025335806976881}e^{7} - \frac{5082739510149288760936}{5126679034884405}e^{6} - \frac{34060899417573677208092}{76900185523266075}e^{5} + \frac{48792761014517950503116}{76900185523266075}e^{4} + \frac{2210888513863734721963}{76900185523266075}e^{3} - \frac{2273730387528661260617}{15380037104653215}e^{2} + \frac{352207303426226367773}{15380037104653215}e + \frac{90906923075594420548}{25633395174422025}$ |
| 31 | $[31, 31, -w^{2} + 2w + 1]$ | $-\frac{119460583690510217}{76900185523266075}e^{21} + \frac{226729018329272014}{76900185523266075}e^{20} + \frac{5151284706315681068}{76900185523266075}e^{19} - \frac{3049384215022025924}{25633395174422025}e^{18} - \frac{93957590944038418399}{76900185523266075}e^{17} + \frac{31016181962262833381}{15380037104653215}e^{16} + \frac{943843862069101266997}{76900185523266075}e^{15} - \frac{479840338416231391291}{25633395174422025}e^{14} - \frac{5696530558912796737619}{76900185523266075}e^{13} + \frac{2668594317804516333998}{25633395174422025}e^{12} + \frac{4225726257399517890593}{15380037104653215}e^{11} - \frac{27488236557485431767331}{76900185523266075}e^{10} - \frac{15714458713191544625002}{25633395174422025}e^{9} + \frac{57981895937123250476279}{76900185523266075}e^{8} + \frac{3903961924821411740588}{5126679034884405}e^{7} - \frac{23974971313084953470981}{25633395174422025}e^{6} - \frac{32763370101105572992913}{76900185523266075}e^{5} + \frac{46379632307113299966533}{76900185523266075}e^{4} + \frac{2211882225400480293478}{76900185523266075}e^{3} - \frac{2170985548460357278664}{15380037104653215}e^{2} + \frac{1675023257787392768146}{76900185523266075}e + \frac{86871095070983995378}{25633395174422025}$ |
| 37 | $[37, 37, w^{3} - w^{2} - 7w - 1]$ | $-\frac{281597533051619051}{153800371046532150}e^{21} + \frac{535421628389541547}{153800371046532150}e^{20} + \frac{12142910656333786139}{153800371046532150}e^{19} - \frac{3601838781117079306}{25633395174422025}e^{18} - \frac{221483899500174413557}{153800371046532150}e^{17} + \frac{73303287742571644823}{30760074209306430}e^{16} + \frac{2224903419775013649031}{153800371046532150}e^{15} - \frac{1134685998248243049553}{51266790348844050}e^{14} - \frac{6714038119802506652086}{76900185523266075}e^{13} + \frac{3157457038269780594922}{25633395174422025}e^{12} + \frac{9960321950144092799681}{30760074209306430}e^{11} - \frac{65103640881368554139353}{153800371046532150}e^{10} - \frac{37031791727515905841861}{51266790348844050}e^{9} + \frac{68730321073391311185376}{76900185523266075}e^{8} + \frac{399720103646510460229}{445798176946470}e^{7} - \frac{56895900163975623801413}{51266790348844050}e^{6} - \frac{38475499881958570821847}{76900185523266075}e^{5} + \frac{110164364489890139242259}{153800371046532150}e^{4} + \frac{4951940568614098405009}{153800371046532150}e^{3} - \frac{2580565840579224834094}{15380037104653215}e^{2} + \frac{4017579149114937450643}{153800371046532150}e + \frac{103638592899267898712}{25633395174422025}$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $-\frac{119460583690510217}{76900185523266075}e^{21} + \frac{226729018329272014}{76900185523266075}e^{20} + \frac{5151284706315681068}{76900185523266075}e^{19} - \frac{3049384215022025924}{25633395174422025}e^{18} - \frac{93957590944038418399}{76900185523266075}e^{17} + \frac{31016181962262833381}{15380037104653215}e^{16} + \frac{943843862069101266997}{76900185523266075}e^{15} - \frac{479840338416231391291}{25633395174422025}e^{14} - \frac{5696530558912796737619}{76900185523266075}e^{13} + \frac{2668594317804516333998}{25633395174422025}e^{12} + \frac{4225726257399517890593}{15380037104653215}e^{11} - \frac{27488236557485431767331}{76900185523266075}e^{10} - \frac{15714458713191544625002}{25633395174422025}e^{9} + \frac{57981895937123250476279}{76900185523266075}e^{8} + \frac{3903961924821411740588}{5126679034884405}e^{7} - \frac{23974971313084953470981}{25633395174422025}e^{6} - \frac{32763370101105572992913}{76900185523266075}e^{5} + \frac{46379632307113299966533}{76900185523266075}e^{4} + \frac{2211882225400480293478}{76900185523266075}e^{3} - \frac{2170970168423252625449}{15380037104653215}e^{2} + \frac{1675023257787392768146}{76900185523266075}e + \frac{86768561490286307278}{25633395174422025}$ |
| 71 | $[71, 71, w^{3} - 2w^{2} - 6w - 1]$ | $-\frac{94414777253311834}{76900185523266075}e^{21} + \frac{182480952246012323}{76900185523266075}e^{20} + \frac{4058595577037492641}{76900185523266075}e^{19} - \frac{2450261527919443003}{25633395174422025}e^{18} - \frac{73760094499541905973}{76900185523266075}e^{17} + \frac{24864519650263897639}{15380037104653215}e^{16} + \frac{737843636262710295944}{76900185523266075}e^{15} - \frac{383397327505731495047}{25633395174422025}e^{14} - \frac{4431531294728189660533}{76900185523266075}e^{13} + \frac{2122200294936844097146}{25633395174422025}e^{12} + \frac{3268822955581267118356}{15380037104653215}e^{11} - \frac{21716281765305563076047}{76900185523266075}e^{10} - \frac{12077246590089109677989}{25633395174422025}e^{9} + \frac{45403924257316735925593}{76900185523266075}e^{8} + \frac{2977917407551609078636}{5126679034884405}e^{7} - \frac{18570924896089431518917}{25633395174422025}e^{6} - \frac{24765199938038217569041}{76900185523266075}e^{5} + \frac{35517070992465995741881}{76900185523266075}e^{4} + \frac{1624271425322282497811}{76900185523266075}e^{3} - \frac{330204806784764387429}{3076007420930643}e^{2} + \frac{1271348427660956391902}{76900185523266075}e + \frac{65833403721596678546}{25633395174422025}$ |
| 71 | $[71, 71, 5w^{3} - 8w^{2} - 29w + 3]$ | $\phantom{-}\frac{4219777271121416}{5126679034884405}e^{21} - \frac{38923448246446379}{25633395174422025}e^{20} - \frac{913215702738419401}{25633395174422025}e^{19} + \frac{104805867769275092}{1708893011628135}e^{18} + \frac{16727922917136668321}{25633395174422025}e^{17} - \frac{26692624158450159347}{25633395174422025}e^{16} - \frac{168860407911802318517}{25633395174422025}e^{15} + \frac{82792768345594639319}{8544465058140675}e^{14} + \frac{1024844975707372143001}{25633395174422025}e^{13} - \frac{462149630014279637464}{8544465058140675}e^{12} - \frac{3825463204588954275899}{25633395174422025}e^{11} + \frac{4786248590646256213811}{25633395174422025}e^{10} + \frac{2866192085519319667343}{8544465058140675}e^{9} - \frac{10171852468505104415398}{25633395174422025}e^{8} - \frac{718527814150428978304}{1708893011628135}e^{7} + \frac{169843520972554848769}{341778602325627}e^{6} + \frac{6117865598621224848199}{25633395174422025}e^{5} - \frac{8296834083265925222797}{25633395174422025}e^{4} - \frac{465891190845019297766}{25633395174422025}e^{3} + \frac{390317028661617880942}{5126679034884405}e^{2} - \frac{59431347590787974623}{5126679034884405}e - \frac{15437038625885584166}{8544465058140675}$ |
| 89 | $[89, 89, -2w^{3} + 4w^{2} + 10w - 7]$ | $\phantom{-}\frac{9181202995121563}{51266790348844050}e^{21} - \frac{18471576467571461}{51266790348844050}e^{20} - \frac{390922951134450727}{51266790348844050}e^{19} + \frac{123089688444090368}{8544465058140675}e^{18} + \frac{7025675795883260111}{51266790348844050}e^{17} - \frac{21500346438670417}{89159635389294}e^{16} - \frac{69366923209812039083}{51266790348844050}e^{15} + \frac{37581020881496744909}{17088930116281350}e^{14} + \frac{205162379771125081223}{25633395174422025}e^{13} - \frac{101934240309371582696}{8544465058140675}e^{12} - \frac{59487702030979401221}{2050671613953762}e^{11} + \frac{2028488989233554182829}{51266790348844050}e^{10} + \frac{1078162914776529871673}{17088930116281350}e^{9} - \frac{2042138796906005235668}{25633395174422025}e^{8} - \frac{261002959335423269821}{3417786023256270}e^{7} + \frac{1593873875586339086479}{17088930116281350}e^{6} + \frac{1079900295758276364806}{25633395174422025}e^{5} - \frac{2897792280434685415957}{51266790348844050}e^{4} - \frac{192553049858781571517}{51266790348844050}e^{3} + \frac{65074287459345735266}{5126679034884405}e^{2} - \frac{91101885865830071969}{51266790348844050}e - \frac{2455663398735523261}{8544465058140675}$ |
| 97 | $[97, 97, -w^{3} + 2w^{2} + 4w - 4]$ | $\phantom{-}\frac{354043237959745631}{153800371046532150}e^{21} - \frac{683850053046853603}{153800371046532150}e^{20} - \frac{15226867960505086373}{153800371046532150}e^{19} + \frac{4594188920425985986}{25633395174422025}e^{18} + \frac{276895213291202004151}{153800371046532150}e^{17} - \frac{466608509882498265703}{153800371046532150}e^{16} - \frac{2771827756689046963339}{153800371046532150}e^{15} + \frac{1440641959005164944459}{51266790348844050}e^{14} + \frac{8330856349916537769778}{76900185523266075}e^{13} - \frac{798674965371863294513}{5126679034884405}e^{12} - \frac{61510506073568327431321}{153800371046532150}e^{11} + \frac{81895970870364295134547}{153800371046532150}e^{10} + \frac{45500981914732852815193}{51266790348844050}e^{9} - \frac{85835365086148936248427}{76900185523266075}e^{8} - \frac{11230341269433861939659}{10253358069768810}e^{7} + \frac{70425575219609334035723}{51266790348844050}e^{6} + \frac{9337779059379380522486}{15380037104653215}e^{5} - \frac{135082695815988399401897}{153800371046532150}e^{4} - \frac{5923749192756352996453}{153800371046532150}e^{3} + \frac{629039980636829575328}{3076007420930643}e^{2} - \frac{4872691580875068616483}{153800371046532150}e - \frac{125724728640800692994}{25633395174422025}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $16$ | $[16, 2, 2]$ | $1$ |