Base field 5.5.138136.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 6x^{3} + 3x^{2} + 4x - 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[29, 29, 2w^{4} - 2w^{3} - 11w^{2} + 4w + 3]$ |
| Dimension: | $24$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $43$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{24} - 2x^{23} - 36x^{22} + 72x^{21} + 554x^{20} - 1105x^{19} - 4776x^{18} + 9461x^{17} + 25430x^{16} - 49697x^{15} - 87118x^{14} + 166112x^{13} + 194446x^{12} - 355254x^{11} - 280402x^{10} + 476992x^{9} + 252545x^{8} - 382655x^{7} - 132291x^{6} + 165646x^{5} + 36077x^{4} - 31027x^{3} - 4801x^{2} + 1473x + 99\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -2w^{4} + w^{3} + 12w^{2} + w - 5]$ | $\phantom{-}\frac{80819072488727}{81747439647048}e^{23} - \frac{32718363224891}{10218429955881}e^{22} - \frac{859582042569169}{27249146549016}e^{21} + \frac{500245817825493}{4541524424836}e^{20} + \frac{33395023153508845}{81747439647048}e^{19} - \frac{130372408747473647}{81747439647048}e^{18} - \frac{24580253362024067}{9083048849672}e^{17} + \frac{258602546236990621}{20436859911762}e^{16} + \frac{747668179397083069}{81747439647048}e^{15} - \frac{4909773257292385537}{81747439647048}e^{14} - \frac{833022259135745561}{81747439647048}e^{13} + \frac{14306679979082989255}{81747439647048}e^{12} - \frac{2379345840797169511}{81747439647048}e^{11} - \frac{8449662764217397277}{27249146549016}e^{10} + \frac{9406693496655918259}{81747439647048}e^{9} + \frac{26218238949566923181}{81747439647048}e^{8} - \frac{6377535151447674481}{40873719823524}e^{7} - \frac{7250165318185838597}{40873719823524}e^{6} + \frac{2541340382077544395}{27249146549016}e^{5} + \frac{1825934995110148327}{40873719823524}e^{4} - \frac{834123468322249405}{40873719823524}e^{3} - \frac{384741920246129255}{81747439647048}e^{2} + \frac{87254883035099533}{81747439647048}e + \frac{274906488062287}{3406143318627}$ |
| 8 | $[8, 2, w^{4} - 7w^{2} - 3w + 5]$ | $\phantom{-}\frac{313264754536733}{163494879294096}e^{23} - \frac{1026168560314297}{163494879294096}e^{22} - \frac{3326794292932603}{54498293098032}e^{21} + \frac{3922350957527523}{18166097699344}e^{20} + \frac{128933048369158897}{163494879294096}e^{19} - \frac{63888900404396101}{20436859911762}e^{18} - \frac{5905091563645747}{1135381106209}e^{17} + \frac{4055255671926649705}{163494879294096}e^{16} + \frac{2843961559109310667}{163494879294096}e^{15} - \frac{9623836662876451655}{81747439647048}e^{14} - \frac{747452028494586641}{40873719823524}e^{13} + \frac{14020843059717132055}{40873719823524}e^{12} - \frac{4924121161253716811}{81747439647048}e^{11} - \frac{8279681031305750609}{13624573274508}e^{10} + \frac{18701097679307352977}{81747439647048}e^{9} + \frac{51358873359625854277}{81747439647048}e^{8} - \frac{50200581222040278521}{163494879294096}e^{7} - \frac{3545250544770953371}{10218429955881}e^{6} + \frac{3316640897261786217}{18166097699344}e^{5} + \frac{14211173605812480995}{163494879294096}e^{4} - \frac{407678772126718070}{10218429955881}e^{3} - \frac{1476475209370943255}{163494879294096}e^{2} + \frac{21711313831792318}{10218429955881}e + \frac{8437406346030575}{54498293098032}$ |
| 19 | $[19, 19, -2w^{4} + w^{3} + 12w^{2} - 5]$ | $\phantom{-}\frac{80996880144253}{40873719823524}e^{23} - \frac{135460134097969}{20436859911762}e^{22} - \frac{856805607645755}{13624573274508}e^{21} + \frac{258859726976413}{1135381106209}e^{20} + \frac{32989563008984279}{40873719823524}e^{19} - \frac{134910270542710855}{40873719823524}e^{18} - \frac{23871009251417647}{4541524424836}e^{17} + \frac{535133500753000171}{20436859911762}e^{16} + \frac{695578860471869111}{40873719823524}e^{15} - \frac{5079068032425032537}{40873719823524}e^{14} - \frac{585242488061812837}{40873719823524}e^{13} + \frac{14796269013564093455}{40873719823524}e^{12} - \frac{3088717543585338599}{40873719823524}e^{11} - \frac{8735248299046003561}{13624573274508}e^{10} + \frac{10615393147459485815}{40873719823524}e^{9} + \frac{27083129716754396113}{40873719823524}e^{8} - \frac{3481049527265850892}{10218429955881}e^{7} - \frac{7476100268612648419}{20436859911762}e^{6} + \frac{911275178996553695}{4541524424836}e^{5} + \frac{937755307249999222}{10218429955881}e^{4} - \frac{891066658736103503}{20436859911762}e^{3} - \frac{394754466920969665}{40873719823524}e^{2} + \frac{92723496096471617}{40873719823524}e + \frac{1139835752088335}{6812286637254}$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 5w - 1]$ | $-\frac{85331919348341}{81747439647048}e^{23} + \frac{271758329298133}{81747439647048}e^{22} + \frac{910571939836003}{27249146549016}e^{21} - \frac{1038592202959567}{9083048849672}e^{20} - \frac{35572621119019177}{81747439647048}e^{19} + \frac{33825943574505203}{20436859911762}e^{18} + \frac{6616098947614721}{2270762212418}e^{17} - \frac{1073127885591304861}{81747439647048}e^{16} - \frac{826718039074853563}{81747439647048}e^{15} + \frac{2545238965613263721}{40873719823524}e^{14} + \frac{132675282311906347}{10218429955881}e^{13} - \frac{1852311770894469449}{10218429955881}e^{12} + \frac{981754854762950453}{40873719823524}e^{11} + \frac{1092082546047357688}{3406143318627}e^{10} - \frac{4457922966900992159}{40873719823524}e^{9} - \frac{13509027386216630419}{40873719823524}e^{8} + \frac{12359732540848851989}{81747439647048}e^{7} + \frac{1854115941516415529}{10218429955881}e^{6} - \frac{822794152173187953}{9083048849672}e^{5} - \frac{3662951873185285655}{81747439647048}e^{4} + \frac{200222498084170102}{10218429955881}e^{3} + \frac{368678588916488951}{81747439647048}e^{2} - \frac{20818912669722199}{20436859911762}e - \frac{1987025726284091}{27249146549016}$ |
| 29 | $[29, 29, 2w^{4} - 2w^{3} - 11w^{2} + 4w + 3]$ | $\phantom{-}1$ |
| 31 | $[31, 31, -2w^{4} + w^{3} + 12w^{2} + 2w - 5]$ | $\phantom{-}\frac{20958627344393}{10218429955881}e^{23} - \frac{135517775897111}{20436859911762}e^{22} - \frac{223226692360702}{3406143318627}e^{21} + \frac{518114783110299}{2270762212418}e^{20} + \frac{8693314512690565}{10218429955881}e^{19} - \frac{67534111458528835}{20436859911762}e^{18} - \frac{12858270489360813}{2270762212418}e^{17} + \frac{536033227371707789}{20436859911762}e^{16} + \frac{197960582065337347}{10218429955881}e^{15} - \frac{2545481514871405097}{20436859911762}e^{14} - \frac{472702299180836731}{20436859911762}e^{13} + \frac{7421907408066570557}{20436859911762}e^{12} - \frac{1107745586204392673}{20436859911762}e^{11} - \frac{4386657197458149115}{6812286637254}e^{10} + \frac{4637324529738883781}{20436859911762}e^{9} + \frac{13619748618793232371}{20436859911762}e^{8} - \frac{6345562429226640541}{20436859911762}e^{7} - \frac{3764582067542372164}{10218429955881}e^{6} + \frac{632965054826515475}{3406143318627}e^{5} + \frac{1885166980863060253}{20436859911762}e^{4} - \frac{414960353821381313}{10218429955881}e^{3} - \frac{96679034104625771}{10218429955881}e^{2} + \frac{44202885653735027}{20436859911762}e + \frac{1060155901210759}{6812286637254}$ |
| 37 | $[37, 37, -2w^{4} + 13w^{2} + 5w - 7]$ | $-\frac{29857428720397}{9083048849672}e^{23} + \frac{96597764221135}{9083048849672}e^{22} + \frac{953022389364553}{9083048849672}e^{21} - \frac{3322793864834953}{9083048849672}e^{20} - \frac{12349899523268453}{9083048849672}e^{19} + \frac{24051784988125537}{4541524424836}e^{18} + \frac{40962888674859741}{4541524424836}e^{17} - \frac{381593535101391159}{9083048849672}e^{16} - \frac{277962460931356899}{9083048849672}e^{15} + \frac{226334832390597404}{1135381106209}e^{14} + \frac{158577560099723297}{4541524424836}e^{13} - \frac{2636834965372058635}{4541524424836}e^{12} + \frac{211813470678274959}{2270762212418}e^{11} + \frac{4668232777323820991}{4541524424836}e^{10} - \frac{426122139710974628}{1135381106209}e^{9} - \frac{2410454457416138255}{2270762212418}e^{8} + \frac{4631894410943610563}{9083048849672}e^{7} + \frac{1328563690739379797}{2270762212418}e^{6} - \frac{2766690405405313165}{9083048849672}e^{5} - \frac{1325644548078333073}{9083048849672}e^{4} + \frac{151173015634039195}{2270762212418}e^{3} + \frac{136281293516080779}{9083048849672}e^{2} - \frac{16043394053287235}{4541524424836}e - \frac{2230021208771555}{9083048849672}$ |
| 53 | $[53, 53, 3w^{4} - 2w^{3} - 18w^{2} + 3w + 9]$ | $\phantom{-}\frac{9040710838347}{4541524424836}e^{23} - \frac{182722776494873}{27249146549016}e^{22} - \frac{286406779565083}{4541524424836}e^{21} + \frac{2094823407146587}{9083048849672}e^{20} + \frac{916232077127023}{1135381106209}e^{19} - \frac{90966635053802005}{27249146549016}e^{18} - \frac{47453046132596899}{9083048849672}e^{17} + \frac{240502941989252223}{9083048849672}e^{16} + \frac{226802380558711213}{13624573274508}e^{15} - \frac{1141008470682575843}{9083048849672}e^{14} - \frac{332906418923884007}{27249146549016}e^{13} + \frac{9967768234851478273}{27249146549016}e^{12} - \frac{2244183179049662003}{27249146549016}e^{11} - \frac{5880951848856936507}{9083048849672}e^{10} + \frac{2476162233119024441}{9083048849672}e^{9} + \frac{18215480505890272361}{27249146549016}e^{8} - \frac{9665415252570467479}{27249146549016}e^{7} - \frac{1673307591929333989}{4541524424836}e^{6} + \frac{1421645308536536347}{6812286637254}e^{5} + \frac{2511736653766833677}{27249146549016}e^{4} - \frac{621148958576185943}{13624573274508}e^{3} - \frac{22045572700296361}{2270762212418}e^{2} + \frac{65879746662707063}{27249146549016}e + \frac{1543787181395623}{9083048849672}$ |
| 59 | $[59, 59, 2w^{4} - 13w^{2} - 6w + 5]$ | $-\frac{37146476293043}{13624573274508}e^{23} + \frac{60768182517239}{6812286637254}e^{22} + \frac{394097519312741}{4541524424836}e^{21} - \frac{348308243244046}{1135381106209}e^{20} - \frac{15247968494322745}{13624573274508}e^{19} + \frac{60491417349890693}{13624573274508}e^{18} + \frac{33410229645190411}{4541524424836}e^{17} - \frac{239841783651713639}{6812286637254}e^{16} - \frac{332358022869974197}{13624573274508}e^{15} + \frac{2275012133249086327}{13624573274508}e^{14} + \frac{330737682658642667}{13624573274508}e^{13} - \frac{6621950782707896101}{13624573274508}e^{12} + \frac{1239440767290979297}{13624573274508}e^{11} + \frac{3904943651284344491}{4541524424836}e^{10} - \frac{4566712063046073505}{13624573274508}e^{9} - \frac{12089504269678812779}{13624573274508}e^{8} + \frac{1523147970079909643}{3406143318627}e^{7} + \frac{3331353983598648125}{6812286637254}e^{6} - \frac{1204989334822323123}{4541524424836}e^{5} - \frac{416875503901691666}{3406143318627}e^{4} + \frac{394013900946742123}{6812286637254}e^{3} + \frac{174764119484676011}{13624573274508}e^{2} - \frac{41173290737523619}{13624573274508}e - \frac{485647586626339}{2270762212418}$ |
| 61 | $[61, 61, -3w^{4} + 2w^{3} + 18w^{2} - 2w - 11]$ | $\phantom{-}\frac{117624302580067}{27249146549016}e^{23} - \frac{387249187953359}{27249146549016}e^{22} - \frac{1247373705177717}{9083048849672}e^{21} + \frac{4439882860713399}{9083048849672}e^{20} + \frac{48227681912487887}{27249146549016}e^{19} - \frac{24101250022555604}{3406143318627}e^{18} - \frac{13191270749220590}{1135381106209}e^{17} + \frac{1529361702588620567}{27249146549016}e^{16} + \frac{1046209781375615573}{27249146549016}e^{15} - \frac{3628005067816281157}{13624573274508}e^{14} - \frac{254559982229510623}{6812286637254}e^{13} + \frac{5282532610894267577}{6812286637254}e^{12} - \frac{2003886641495145157}{13624573274508}e^{11} - \frac{3116754173999496683}{2270762212418}e^{10} + \frac{7301941981701867883}{13624573274508}e^{9} + \frac{19307126568161157563}{13624573274508}e^{8} - \frac{19435442740766094127}{27249146549016}e^{7} - \frac{2659729105899735460}{3406143318627}e^{6} + \frac{3841372010568623341}{9083048849672}e^{5} + \frac{5312405372443784005}{27249146549016}e^{4} - \frac{314390038162333874}{3406143318627}e^{3} - \frac{551734545100562977}{27249146549016}e^{2} + \frac{16563314773798687}{3406143318627}e + \frac{3085536826313657}{9083048849672}$ |
| 61 | $[61, 61, w^{2} - w - 3]$ | $\phantom{-}\frac{20467380791852}{10218429955881}e^{23} - \frac{265631105640001}{40873719823524}e^{22} - \frac{217665399093097}{3406143318627}e^{21} + \frac{1015462895499761}{4541524424836}e^{20} + \frac{16909464176666531}{20436859911762}e^{19} - \frac{132340988660279207}{40873719823524}e^{18} - \frac{24882842884929711}{4541524424836}e^{17} + \frac{1050171965404038181}{40873719823524}e^{16} + \frac{189045236626482328}{10218429955881}e^{15} - \frac{4985142261768038395}{40873719823524}e^{14} - \frac{838474873656415733}{40873719823524}e^{13} + \frac{14526540996590969359}{40873719823524}e^{12} - \frac{2423263785178428433}{40873719823524}e^{11} - \frac{8577178005013962413}{13624573274508}e^{10} + \frac{9542442459776305825}{40873719823524}e^{9} + \frac{26584562216994318359}{40873719823524}e^{8} - \frac{12917569414746151679}{40873719823524}e^{7} - \frac{7325514250901092241}{20436859911762}e^{6} + \frac{1284547129033343809}{6812286637254}e^{5} + \frac{3648664936975038233}{40873719823524}e^{4} - \frac{841501041999759691}{20436859911762}e^{3} - \frac{187386784347214813}{20436859911762}e^{2} + \frac{89001704784770569}{40873719823524}e + \frac{2100876811978691}{13624573274508}$ |
| 61 | $[61, 61, 6w^{4} - 2w^{3} - 38w^{2} - 6w + 23]$ | $\phantom{-}\frac{11298740640146}{10218429955881}e^{23} - \frac{36183928246927}{10218429955881}e^{22} - \frac{120523208545198}{3406143318627}e^{21} + \frac{138333536834063}{1135381106209}e^{20} + \frac{4705180731021397}{10218429955881}e^{19} - \frac{18030133716589163}{10218429955881}e^{18} - \frac{3495470519061380}{1135381106209}e^{17} + \frac{143097317228863294}{10218429955881}e^{16} + \frac{108781460495201236}{10218429955881}e^{15} - \frac{679452397000246528}{10218429955881}e^{14} - \frac{136859735226130265}{10218429955881}e^{13} + \frac{1980756692784129076}{10218429955881}e^{12} - \frac{272548130793356830}{10218429955881}e^{11} - \frac{1170411613649587979}{3406143318627}e^{10} + \frac{1207658338306456786}{10218429955881}e^{9} + \frac{3632435945864759573}{10218429955881}e^{8} - \frac{1672240830634447904}{10218429955881}e^{7} - \frac{2006521034108036629}{10218429955881}e^{6} + \frac{111861891414106844}{1135381106209}e^{5} + \frac{501193300934997176}{10218429955881}e^{4} - \frac{220854357793910108}{10218429955881}e^{3} - \frac{50830560035839334}{10218429955881}e^{2} + \frac{11764733642429854}{10218429955881}e + \frac{251603405503712}{3406143318627}$ |
| 67 | $[67, 67, -w^{4} + 7w^{2} + 4w - 5]$ | $\phantom{-}\frac{4096057104109}{81747439647048}e^{23} - \frac{6090139306945}{40873719823524}e^{22} - \frac{44159335476311}{27249146549016}e^{21} + \frac{5840070433259}{1135381106209}e^{20} + \frac{1755371749094123}{81747439647048}e^{19} - \frac{6121498765802803}{81747439647048}e^{18} - \frac{1349412873887395}{9083048849672}e^{17} + \frac{24501706921010197}{40873719823524}e^{16} + \frac{45474956653445303}{81747439647048}e^{15} - \frac{236104576347790253}{81747439647048}e^{14} - \frac{79016894787169033}{81747439647048}e^{13} + \frac{706325247590499947}{81747439647048}e^{12} - \frac{11455046690865647}{81747439647048}e^{11} - \frac{437721647177782405}{27249146549016}e^{10} + \frac{282037355474470391}{81747439647048}e^{9} + \frac{1487984324137174981}{81747439647048}e^{8} - \frac{112138936374668827}{20436859911762}e^{7} - \frac{491749093765196791}{40873719823524}e^{6} + \frac{31664403435425839}{9083048849672}e^{5} + \frac{43575433665549404}{10218429955881}e^{4} - \frac{32178475071574487}{40873719823524}e^{3} - \frac{54895376605446205}{81747439647048}e^{2} + \frac{2254961758914077}{81747439647048}e + \frac{202106230040579}{13624573274508}$ |
| 67 | $[67, 67, -w^{4} + 6w^{2} + 2w - 1]$ | $-\frac{105594341194351}{11678205663864}e^{23} + \frac{172564276643647}{5839102831932}e^{22} + \frac{1121895473483669}{3892735221288}e^{21} - \frac{164897383480882}{162197300887}e^{20} - \frac{43512596460497417}{11678205663864}e^{19} + \frac{171895741652809345}{11678205663864}e^{18} + \frac{31930664074455913}{1297578407096}e^{17} - \frac{681907977646954903}{5839102831932}e^{16} - \frac{964478095329409325}{11678205663864}e^{15} + \frac{6472842022474518071}{11678205663864}e^{14} + \frac{1034920539869171419}{11678205663864}e^{13} - \frac{18858764644902303569}{11678205663864}e^{12} + \frac{3242942878187692709}{11678205663864}e^{11} + \frac{11134752126937312327}{3892735221288}e^{10} - \frac{12476561113499533085}{11678205663864}e^{9} - \frac{34522944223485097039}{11678205663864}e^{8} + \frac{4197707170451135353}{2919551415966}e^{7} + \frac{9525534244667816533}{5839102831932}e^{6} - \frac{3330032117448047399}{3892735221288}e^{5} - \frac{595513184047061906}{1459775707983}e^{4} + \frac{1089973760802440465}{5839102831932}e^{3} + \frac{492609580979207479}{11678205663864}e^{2} - \frac{115337373719475095}{11678205663864}e - \frac{1366966037578433}{1946367610644}$ |
| 71 | $[71, 71, -w^{2} + 3]$ | $-\frac{296085021528967}{27249146549016}e^{23} + \frac{968469730004687}{27249146549016}e^{22} + \frac{3143382541138297}{9083048849672}e^{21} - \frac{11103758863648607}{9083048849672}e^{20} - \frac{121756562350645883}{27249146549016}e^{19} + \frac{120550479005369341}{6812286637254}e^{18} + \frac{66838024022974595}{2270762212418}e^{17} - \frac{3824796719369846063}{27249146549016}e^{16} - \frac{2673747927216635849}{27249146549016}e^{15} + \frac{9073251839126697883}{13624573274508}e^{14} + \frac{343826604363165827}{3406143318627}e^{13} - \frac{6605472354545806030}{3406143318627}e^{12} + \frac{4778158538507082103}{13624573274508}e^{11} + \frac{3897327138571809861}{1135381106209}e^{10} - \frac{17927067530903795365}{13624573274508}e^{9} - \frac{48288456329435949497}{13624573274508}e^{8} + \frac{48036858766236079399}{27249146549016}e^{7} + \frac{6654232372619317282}{3406143318627}e^{6} - \frac{9519940547258368225}{9083048849672}e^{5} - \frac{13304887444006892053}{27249146549016}e^{4} + \frac{779782576575551813}{3406143318627}e^{3} + \frac{1384749848192560141}{27249146549016}e^{2} - \frac{82300250050979705}{6812286637254}e - \frac{7706828498651377}{9083048849672}$ |
| 73 | $[73, 73, 3w^{4} - w^{3} - 19w^{2} - 3w + 9]$ | $-\frac{218109427820297}{81747439647048}e^{23} + \frac{717613883131951}{81747439647048}e^{22} + \frac{2314886166914695}{27249146549016}e^{21} - \frac{2742917072566513}{9083048849672}e^{20} - \frac{89625841423312225}{81747439647048}e^{19} + \frac{178707757299317347}{40873719823524}e^{18} + \frac{32775179318175627}{4541524424836}e^{17} - \frac{2835694910142310759}{81747439647048}e^{16} - \frac{1963392820720106047}{81747439647048}e^{15} + \frac{3364494352309423975}{20436859911762}e^{14} + \frac{1000784973565441159}{40873719823524}e^{13} - \frac{19602375411726987797}{40873719823524}e^{12} + \frac{886523246736747194}{10218429955881}e^{11} + \frac{11569414497971689339}{13624573274508}e^{10} - \frac{6614534878298785093}{20436859911762}e^{9} - \frac{8958701193874494208}{10218429955881}e^{8} + \frac{35371330086679259507}{81747439647048}e^{7} + \frac{9861783305468569291}{20436859911762}e^{6} - \frac{6997555143620218427}{27249146549016}e^{5} - \frac{9796304089387011257}{81747439647048}e^{4} + \frac{1144876945157291153}{20436859911762}e^{3} + \frac{1001568379920448079}{81747439647048}e^{2} - \frac{122065516720761893}{40873719823524}e - \frac{5621601986337425}{27249146549016}$ |
| 79 | $[79, 79, 3w^{4} - w^{3} - 19w^{2} - 4w + 11]$ | $\phantom{-}\frac{12465218928473}{4541524424836}e^{23} - \frac{40822325705207}{4541524424836}e^{22} - \frac{396897318720421}{4541524424836}e^{21} + \frac{1404202472516133}{4541524424836}e^{20} + \frac{5121750606901017}{4541524424836}e^{19} - \frac{10164092328806239}{2270762212418}e^{18} - \frac{16849929197195119}{2270762212418}e^{17} + \frac{161255635080647963}{4541524424836}e^{16} + \frac{111977777479752075}{4541524424836}e^{15} - \frac{191286495774437489}{1135381106209}e^{14} - \frac{56333189720069943}{2270762212418}e^{13} + \frac{1114224382904124181}{2270762212418}e^{12} - \frac{103192606747404826}{1135381106209}e^{11} - \frac{1972597369754122263}{2270762212418}e^{10} + \frac{382751514057834067}{1135381106209}e^{9} + \frac{1018691797559931088}{1135381106209}e^{8} - \frac{2048568628329723627}{4541524424836}e^{7} - \frac{561917114916242224}{1135381106209}e^{6} + \frac{1219289676601963705}{4541524424836}e^{5} + \frac{562975816620223985}{4541524424836}e^{4} - \frac{66798876929735403}{1135381106209}e^{3} - \frac{58899054300937031}{4541524424836}e^{2} + \frac{7062147764763031}{2270762212418}e + \frac{949367692219379}{4541524424836}$ |
| 83 | $[83, 83, -w^{4} - w^{3} + 7w^{2} + 8w - 3]$ | $\phantom{-}\frac{8136936516811}{5839102831932}e^{23} - \frac{53685065720437}{11678205663864}e^{22} - \frac{86305998405305}{1946367610644}e^{21} + \frac{205193335771001}{1297578407096}e^{20} + \frac{1668917516884057}{2919551415966}e^{19} - \frac{26735424875828165}{11678205663864}e^{18} - \frac{4871850583877953}{1297578407096}e^{17} + \frac{212077181860357453}{11678205663864}e^{16} + \frac{72560286408631961}{5839102831932}e^{15} - \frac{1006147618703649025}{11678205663864}e^{14} - \frac{142893758271401651}{11678205663864}e^{13} + \frac{2929120057449898333}{11678205663864}e^{12} - \frac{547097736710449219}{11678205663864}e^{11} - \frac{1726674465605776163}{3892735221288}e^{10} + \frac{2002444848513496807}{11678205663864}e^{9} + \frac{5335532868380110037}{11678205663864}e^{8} - \frac{2661683322906915563}{11678205663864}e^{7} - \frac{1461059585491944287}{5839102831932}e^{6} + \frac{43672028251916667}{324394601774}e^{5} + \frac{717314604109827377}{11678205663864}e^{4} - \frac{170312656035554065}{5839102831932}e^{3} - \frac{18041552095246709}{2919551415966}e^{2} + \frac{18239970375916699}{11678205663864}e + \frac{412854963617711}{3892735221288}$ |
| 97 | $[97, 97, -2w^{4} + w^{3} + 12w^{2} + 2w - 3]$ | $\phantom{-}\frac{826243981420247}{81747439647048}e^{23} - \frac{2712993961091185}{81747439647048}e^{22} - \frac{8768125156366561}{27249146549016}e^{21} + \frac{10369191162379559}{9083048849672}e^{20} + \frac{339393010368214543}{81747439647048}e^{19} - \frac{675527329271232157}{40873719823524}e^{18} - \frac{124045356230229673}{4541524424836}e^{17} + \frac{10718182454362112185}{81747439647048}e^{16} + \frac{7419482985390437617}{81747439647048}e^{15} - \frac{12715860890342534683}{20436859911762}e^{14} - \frac{3741463849077212497}{40873719823524}e^{13} + \frac{74084025749691960515}{40873719823524}e^{12} - \frac{3400983262146117755}{10218429955881}e^{11} - \frac{43733103440495679037}{13624573274508}e^{10} + \frac{25240169277651678493}{20436859911762}e^{9} + \frac{33892909584933406768}{10218429955881}e^{8} - \frac{134927005180515959429}{81747439647048}e^{7} - \frac{37411548278455705735}{20436859911762}e^{6} + \frac{26716949109859078325}{27249146549016}e^{5} + \frac{37483636863744645983}{81747439647048}e^{4} - \frac{4378707570802985615}{20436859911762}e^{3} - \frac{3906646928761026089}{81747439647048}e^{2} + \frac{462765873575463911}{40873719823524}e + \frac{21687870989450135}{27249146549016}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, 2w^{4} - 2w^{3} - 11w^{2} + 4w + 3]$ | $-1$ |