Base field \(\Q(\sqrt{2}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[41, 41, 2w - 7]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $2$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -2w + 1]$ | $\phantom{-}e - 2$ |
| 7 | $[7, 7, -2w - 1]$ | $-2e$ |
| 9 | $[9, 3, 3]$ | $-2e + 2$ |
| 17 | $[17, 17, 3w + 1]$ | $\phantom{-}4$ |
| 17 | $[17, 17, 3w - 1]$ | $\phantom{-}2e - 2$ |
| 23 | $[23, 23, w + 5]$ | $-3e - 2$ |
| 23 | $[23, 23, -w + 5]$ | $\phantom{-}5e + 2$ |
| 25 | $[25, 5, 5]$ | $\phantom{-}4e$ |
| 31 | $[31, 31, 4w + 1]$ | $\phantom{-}3e + 2$ |
| 31 | $[31, 31, -4w + 1]$ | $\phantom{-}e - 6$ |
| 41 | $[41, 41, 2w - 7]$ | $-1$ |
| 41 | $[41, 41, -2w - 7]$ | $-4e - 2$ |
| 47 | $[47, 47, -w - 7]$ | $-4e + 4$ |
| 47 | $[47, 47, w - 7]$ | $-3e - 6$ |
| 71 | $[71, 71, -6w - 1]$ | $-e - 2$ |
| 71 | $[71, 71, 6w - 1]$ | $\phantom{-}2e - 4$ |
| 73 | $[73, 73, -7w - 5]$ | $\phantom{-}4e + 6$ |
| 73 | $[73, 73, 7w - 5]$ | $\phantom{-}4e - 8$ |
| 79 | $[79, 79, -w - 9]$ | $-6e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $41$ | $[41, 41, 2w - 7]$ | $1$ |