Base field \(\Q(\sqrt{7}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 7\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[27,27,-2w - 1]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} + x - 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 3]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w - 2]$ | $\phantom{-}e + 1$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}0$ |
| 7 | $[7, 7, w]$ | $-e + 2$ |
| 19 | $[19, 19, 2w - 3]$ | $\phantom{-}2e + 5$ |
| 19 | $[19, 19, 2w + 3]$ | $-e + 5$ |
| 25 | $[25, 5, 5]$ | $\phantom{-}e - 4$ |
| 29 | $[29, 29, -w - 6]$ | $-e - 3$ |
| 29 | $[29, 29, w - 6]$ | $-4e - 3$ |
| 31 | $[31, 31, 4w + 9]$ | $\phantom{-}2e - 1$ |
| 31 | $[31, 31, -4w + 9]$ | $-4e - 1$ |
| 37 | $[37, 37, -3w + 10]$ | $-e - 4$ |
| 37 | $[37, 37, -6w + 17]$ | $\phantom{-}2e + 5$ |
| 47 | $[47, 47, -3w - 4]$ | $\phantom{-}3$ |
| 47 | $[47, 47, 3w - 4]$ | $-3e - 6$ |
| 53 | $[53, 53, 2w - 9]$ | $\phantom{-}e - 3$ |
| 53 | $[53, 53, 2w + 9]$ | $\phantom{-}e - 3$ |
| 59 | $[59, 59, 3w - 2]$ | $\phantom{-}6e + 6$ |
| 59 | $[59, 59, -3w - 2]$ | $-3$ |
| 83 | $[83, 83, -6w - 13]$ | $-6e + 3$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3,3,-w - 2]$ | $1$ |