Base field \(\Q(\sqrt{377}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 94\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[2,2,-w + 1]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} + x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}1$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}e - 2$ |
| 11 | $[11, 11, w + 2]$ | $-5$ |
| 11 | $[11, 11, w + 8]$ | $\phantom{-}e + 3$ |
| 13 | $[13, 13, 4w - 41]$ | $\phantom{-}e + 2$ |
| 19 | $[19, 19, w + 7]$ | $-5e - 1$ |
| 19 | $[19, 19, w + 11]$ | $-e - 2$ |
| 23 | $[23, 23, -2w + 21]$ | $\phantom{-}2e + 5$ |
| 23 | $[23, 23, -2w - 19]$ | $\phantom{-}e - 3$ |
| 25 | $[25, 5, -5]$ | $-4e - 1$ |
| 29 | $[29, 29, 6w - 61]$ | $\phantom{-}2e + 1$ |
| 31 | $[31, 31, w + 12]$ | $-4e - 2$ |
| 31 | $[31, 31, w + 18]$ | $\phantom{-}3e - 1$ |
| 37 | $[37, 37, w + 4]$ | $-4e - 5$ |
| 37 | $[37, 37, w + 32]$ | $\phantom{-}2e - 1$ |
| 41 | $[41, 41, w + 3]$ | $\phantom{-}e - 7$ |
| 41 | $[41, 41, w + 37]$ | $\phantom{-}2e + 1$ |
| 47 | $[47, 47, w]$ | $-2e - 9$ |
| 47 | $[47, 47, w + 46]$ | $-2e + 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-w + 1]$ | $-1$ |