Base field \(\Q(\sqrt{185}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 46\); narrow class number \(2\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[2, 2, w]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} + 3x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}1$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 2]$ | $-e - 2$ |
| 9 | $[9, 3, 3]$ | $-e - 3$ |
| 11 | $[11, 11, 2w + 13]$ | $\phantom{-}2e + 1$ |
| 11 | $[11, 11, -2w + 15]$ | $\phantom{-}e + 4$ |
| 13 | $[13, 13, w + 4]$ | $-3e - 5$ |
| 13 | $[13, 13, w + 8]$ | $\phantom{-}2e - 1$ |
| 17 | $[17, 17, w + 3]$ | $-3$ |
| 17 | $[17, 17, w + 13]$ | $\phantom{-}4e + 4$ |
| 23 | $[23, 23, w]$ | $-e - 3$ |
| 23 | $[23, 23, w + 22]$ | $-2e$ |
| 37 | $[37, 37, w + 18]$ | $\phantom{-}6e + 5$ |
| 41 | $[41, 41, -2w + 13]$ | $-4e - 11$ |
| 41 | $[41, 41, -2w - 11]$ | $\phantom{-}3e + 6$ |
| 43 | $[43, 43, w + 11]$ | $-9e - 14$ |
| 43 | $[43, 43, w + 31]$ | $-3$ |
| 49 | $[49, 7, -7]$ | $-3e - 10$ |
| 71 | $[71, 71, -2w + 17]$ | $\phantom{-}5e + 6$ |
| 71 | $[71, 71, -2w - 15]$ | $-e + 5$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-1$ |