Base field \(\Q(\sqrt{133}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 33\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[13, 13, w + 4]$ |
| Dimension: | $17$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $34$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{17} + 8x^{16} - 4x^{15} - 174x^{14} - 234x^{13} + 1418x^{12} + 3052x^{11} - 5278x^{10} - 15604x^{9} + 8184x^{8} + 39144x^{7} - 391x^{6} - 49076x^{5} - 11467x^{4} + 28548x^{3} + 9967x^{2} - 5795x - 2331\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 6]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w - 5]$ | $...$ |
| 4 | $[4, 2, 2]$ | $...$ |
| 7 | $[7, 7, 3w - 19]$ | $...$ |
| 11 | $[11, 11, -2w - 11]$ | $...$ |
| 11 | $[11, 11, -2w + 13]$ | $...$ |
| 13 | $[13, 13, w + 4]$ | $\phantom{-}1$ |
| 13 | $[13, 13, -w + 5]$ | $...$ |
| 19 | $[19, 19, 5w - 31]$ | $...$ |
| 23 | $[23, 23, -w - 7]$ | $...$ |
| 23 | $[23, 23, w - 8]$ | $...$ |
| 25 | $[25, 5, -5]$ | $...$ |
| 31 | $[31, 31, -w - 1]$ | $...$ |
| 31 | $[31, 31, w - 2]$ | $...$ |
| 41 | $[41, 41, 6w + 31]$ | $...$ |
| 41 | $[41, 41, 6w - 37]$ | $...$ |
| 43 | $[43, 43, -3w - 17]$ | $...$ |
| 43 | $[43, 43, -3w + 20]$ | $...$ |
| 59 | $[59, 59, 3w - 17]$ | $...$ |
| 59 | $[59, 59, 3w + 14]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, w + 4]$ | $-1$ |