Base field \(\Q(\sqrt{110}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 110\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[2, 2, w]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} + 192x^{14} + 13380x^{12} + 448416x^{10} + 7851438x^{8} + 71964288x^{6} + 319914900x^{4} + 567339552x^{2} + 324972729\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $...$ |
| 5 | $[5, 5, w]$ | $...$ |
| 9 | $[9, 3, 3]$ | $...$ |
| 11 | $[11, 11, -w + 11]$ | $...$ |
| 17 | $[17, 17, w + 5]$ | $...$ |
| 17 | $[17, 17, w + 12]$ | $...$ |
| 23 | $[23, 23, w + 8]$ | $...$ |
| 23 | $[23, 23, w + 15]$ | $...$ |
| 29 | $[29, 29, w + 9]$ | $...$ |
| 29 | $[29, 29, -w + 9]$ | $...$ |
| 37 | $[37, 37, w + 6]$ | $...$ |
| 37 | $[37, 37, w + 31]$ | $...$ |
| 43 | $[43, 43, w + 14]$ | $...$ |
| 43 | $[43, 43, w + 29]$ | $...$ |
| 47 | $[47, 47, w + 4]$ | $...$ |
| 47 | $[47, 47, w + 43]$ | $...$ |
| 49 | $[49, 7, -7]$ | $...$ |
| 53 | $[53, 53, w + 2]$ | $...$ |
| 53 | $[53, 53, w + 51]$ | $...$ |
| 59 | $[59, 59, -w - 13]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-\frac{43351}{3547280952000}e^{15} - \frac{8709971}{3547280952000}e^{13} - \frac{2667673}{14597864000}e^{11} - \frac{290500787}{43793592000}e^{9} - \frac{16541150263}{131380776000}e^{7} - \frac{17687501219}{14597864000}e^{5} - \frac{666140688659}{131380776000}e^{3} - \frac{697735163587}{131380776000}e$ |