Base field \(\Q(\sqrt{229}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 57\); narrow class number \(3\) and class number \(3\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[5, 5, w + 1]$ |
| Dimension: | $24$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $72$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{24} - 2x^{23} + 26x^{22} - 60x^{21} + 438x^{20} - 983x^{19} + 4586x^{18} - 9613x^{17} + 34279x^{16} - 64514x^{15} + 174161x^{14} - 277075x^{13} + 605743x^{12} - 817322x^{11} + 1411315x^{10} - 1445035x^{9} + 1947583x^{8} - 1525257x^{7} + 1739979x^{6} - 937953x^{5} + 663147x^{4} - 109836x^{3} + 76545x^{2} - 10935x + 6561\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $...$ |
| 4 | $[4, 2, 2]$ | $...$ |
| 5 | $[5, 5, w + 1]$ | $...$ |
| 5 | $[5, 5, w + 3]$ | $...$ |
| 11 | $[11, 11, w + 1]$ | $...$ |
| 11 | $[11, 11, w + 9]$ | $...$ |
| 17 | $[17, 17, w + 2]$ | $...$ |
| 17 | $[17, 17, w + 14]$ | $...$ |
| 19 | $[19, 19, w]$ | $...$ |
| 19 | $[19, 19, w + 18]$ | $...$ |
| 37 | $[37, 37, -w - 4]$ | $...$ |
| 37 | $[37, 37, w - 5]$ | $...$ |
| 43 | $[43, 43, w + 16]$ | $...$ |
| 43 | $[43, 43, w + 26]$ | $...$ |
| 49 | $[49, 7, -7]$ | $...$ |
| 53 | $[53, 53, -w - 10]$ | $...$ |
| 53 | $[53, 53, w - 11]$ | $...$ |
| 61 | $[61, 61, w + 15]$ | $...$ |
| 61 | $[61, 61, w + 45]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w + 1]$ | $\frac{9327619910659385252468198631620873169312709}{298303296055845757781886149266824105760890904251}e^{23} - \frac{14467485588855353430715171293052189579594694}{298303296055845757781886149266824105760890904251}e^{22} + \frac{232984934848955477803011143406285834436827731}{298303296055845757781886149266824105760890904251}e^{21} - \frac{149444612549051668253381074167449535004819574}{99434432018615252593962049755608035253630301417}e^{20} + \frac{1268151274082883303757498782026482670911477838}{99434432018615252593962049755608035253630301417}e^{19} - \frac{7263465204224465616956701666522535127081428093}{298303296055845757781886149266824105760890904251}e^{18} + \frac{38160523230468843848366621954739291782278739492}{298303296055845757781886149266824105760890904251}e^{17} - \frac{69307989947118385069312397355692094180788317654}{298303296055845757781886149266824105760890904251}e^{16} + \frac{274312166059042817226505656775670832220423354564}{298303296055845757781886149266824105760890904251}e^{15} - \frac{63878551726661924360781898025892355819840626659}{42614756579406536825983735609546300822984414893}e^{14} + \frac{1316210660201206757877411235256646844772658795785}{298303296055845757781886149266824105760890904251}e^{13} - \frac{1782332967419660808278747394763864877859383057884}{298303296055845757781886149266824105760890904251}e^{12} + \frac{4300798474050775566271574857619145903512398326655}{298303296055845757781886149266824105760890904251}e^{11} - \frac{4785640272757988913607871724489074503816901351774}{298303296055845757781886149266824105760890904251}e^{10} + \frac{9110466405800494407809579810027310983274256228657}{298303296055845757781886149266824105760890904251}e^{9} - \frac{6719544179993992175052029252617436722240946761174}{298303296055845757781886149266824105760890904251}e^{8} + \frac{10733415557943378859141093960743587259699739434508}{298303296055845757781886149266824105760890904251}e^{7} - \frac{523363681285969844179468710780587513202634576987}{33144810672871750864654016585202678417876767139}e^{6} + \frac{101238261456097499925264094232779008297617106386}{3682756741430194540517112953911408713097418571}e^{5} - \frac{183819957380801435021460398480927190393204299}{225474902536542522888802833912943390597801137}e^{4} + \frac{1364017334124386475606294376007195668571328043}{409195193492243837835234772656823190344157619}e^{3} + \frac{3389602075509466220425781529526472004352580423}{409195193492243837835234772656823190344157619}e^{2} + \frac{46789554599111489132847227001119125804777383}{136398397830747945945078257552274396781385873}e + \frac{2010766671777706624990977320200504750848658}{136398397830747945945078257552274396781385873}$ |