Base field \(\Q(\sqrt{34}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 34\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[11,11,-w + 1]$ |
| Dimension: | $17$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $68$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{17} - x^{16} - 25x^{15} + 22x^{14} + 253x^{13} - 190x^{12} - 1335x^{11} + 836x^{10} + 3912x^{9} - 2023x^{8} - 6207x^{7} + 2682x^{6} + 4688x^{5} - 1775x^{4} - 1124x^{3} + 441x^{2} + 25x - 11\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 6]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $...$ |
| 3 | $[3, 3, w + 2]$ | $...$ |
| 5 | $[5, 5, w + 2]$ | $...$ |
| 5 | $[5, 5, w + 3]$ | $...$ |
| 11 | $[11, 11, w + 1]$ | $...$ |
| 11 | $[11, 11, w + 10]$ | $-1$ |
| 17 | $[17, 17, -3w + 17]$ | $...$ |
| 29 | $[29, 29, w + 11]$ | $...$ |
| 29 | $[29, 29, w + 18]$ | $...$ |
| 37 | $[37, 37, w + 16]$ | $...$ |
| 37 | $[37, 37, w + 21]$ | $...$ |
| 47 | $[47, 47, -w - 9]$ | $...$ |
| 47 | $[47, 47, w - 9]$ | $...$ |
| 49 | $[49, 7, -7]$ | $...$ |
| 61 | $[61, 61, w + 20]$ | $...$ |
| 61 | $[61, 61, w + 41]$ | $...$ |
| 89 | $[89, 89, 2w - 15]$ | $...$ |
| 89 | $[89, 89, -2w - 15]$ | $...$ |
| 103 | $[103, 103, -14w + 81]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11,11,-w + 1]$ | $1$ |