Base field \(\Q(\sqrt{10}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 10\); narrow class number \(2\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[13,13,-w + 6]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} + x^{2} - 4x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e^{2} + e - 3$ |
| 3 | $[3, 3, w + 2]$ | $-e^{2} - e + 2$ |
| 5 | $[5, 5, w]$ | $-e - 2$ |
| 13 | $[13, 13, w + 6]$ | $-e - 3$ |
| 13 | $[13, 13, w + 7]$ | $\phantom{-}1$ |
| 31 | $[31, 31, -2w + 3]$ | $-e^{2} - 4e + 1$ |
| 31 | $[31, 31, 2w + 3]$ | $\phantom{-}e - 7$ |
| 37 | $[37, 37, w + 11]$ | $\phantom{-}2e^{2} + e - 11$ |
| 37 | $[37, 37, w + 26]$ | $\phantom{-}2e^{2} + 4e - 9$ |
| 41 | $[41, 41, 3w + 7]$ | $\phantom{-}e^{2} - e - 5$ |
| 41 | $[41, 41, -3w + 7]$ | $\phantom{-}3e^{2} + 4e - 8$ |
| 43 | $[43, 43, w + 15]$ | $-2e - 1$ |
| 43 | $[43, 43, w + 28]$ | $-2e^{2} + 2e + 8$ |
| 49 | $[49, 7, -7]$ | $-2e^{2} + 5$ |
| 53 | $[53, 53, w + 13]$ | $-e^{2} + 5e + 5$ |
| 53 | $[53, 53, w + 40]$ | $-e^{2} - 4e - 1$ |
| 67 | $[67, 67, w + 12]$ | $-e^{2} + 2e + 10$ |
| 67 | $[67, 67, w + 55]$ | $\phantom{-}2e^{2} + 3e - 7$ |
| 71 | $[71, 71, -w - 9]$ | $\phantom{-}4e^{2} + e - 10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13,13,-w + 6]$ | $-1$ |