Base field \(\Q(\sqrt{30}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 30\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[8, 4, 2w]$ |
| 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:
| \(x^{2} - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w]$ | $\phantom{-}2$ |
| 5 | $[5, 5, -w + 5]$ | $\phantom{-}0$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w + 4]$ | $-e$ |
| 13 | $[13, 13, w + 2]$ | $\phantom{-}0$ |
| 13 | $[13, 13, w + 11]$ | $\phantom{-}0$ |
| 17 | $[17, 17, w + 8]$ | $\phantom{-}4$ |
| 17 | $[17, 17, w + 9]$ | $\phantom{-}4$ |
| 19 | $[19, 19, w + 7]$ | $\phantom{-}4$ |
| 19 | $[19, 19, -w + 7]$ | $\phantom{-}4$ |
| 29 | $[29, 29, -w - 1]$ | $\phantom{-}2e$ |
| 29 | $[29, 29, w - 1]$ | $-2e$ |
| 37 | $[37, 37, w + 17]$ | $\phantom{-}4e$ |
| 37 | $[37, 37, w + 20]$ | $-4e$ |
| 71 | $[71, 71, 2w - 7]$ | $-4e$ |
| 71 | $[71, 71, -2w - 7]$ | $\phantom{-}4e$ |
| 83 | $[83, 83, w + 14]$ | $\phantom{-}14$ |
| 83 | $[83, 83, w + 69]$ | $\phantom{-}14$ |
| 101 | $[101, 101, -7w + 37]$ | $-2e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $1$ |