Base field \(\Q(\sqrt{114}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 114\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $32$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $62$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{32} - 166x^{30} + 11993x^{28} - 496380x^{26} + 13049272x^{24} - 228590392x^{22} + 2726867576x^{20} - 22281994976x^{18} + 123974635808x^{16} - 461698065344x^{14} + 1116269298192x^{12} - 1671951895104x^{10} + 1465593782016x^{8} - 733652793344x^{6} + 203176308736x^{4} - 28748431360x^{2} + 1615396864\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -3w - 32]$ | $...$ |
| 3 | $[3, 3, w]$ | $...$ |
| 5 | $[5, 5, w + 2]$ | $...$ |
| 5 | $[5, 5, w + 3]$ | $...$ |
| 7 | $[7, 7, -w + 11]$ | $...$ |
| 7 | $[7, 7, w + 11]$ | $...$ |
| 11 | $[11, 11, w + 2]$ | $...$ |
| 11 | $[11, 11, w + 9]$ | $...$ |
| 13 | $[13, 13, w + 6]$ | $...$ |
| 13 | $[13, 13, w + 7]$ | $...$ |
| 19 | $[19, 19, w]$ | $...$ |
| 37 | $[37, 37, w + 15]$ | $...$ |
| 37 | $[37, 37, w + 22]$ | $...$ |
| 41 | $[41, 41, 37w + 395]$ | $...$ |
| 41 | $[41, 41, 5w + 53]$ | $...$ |
| 67 | $[67, 67, w + 28]$ | $...$ |
| 67 | $[67, 67, w + 39]$ | $...$ |
| 71 | $[71, 71, 40w + 427]$ | $...$ |
| 71 | $[71, 71, 8w + 85]$ | $...$ |
| 73 | $[73, 73, -2w + 23]$ | $...$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).