Base field \(\Q(\sqrt{3}, \sqrt{7})\)
Generator \(w\), with minimal polynomial \(x^{4} - 5x^{2} + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[9, 3, w^{3} - 4w]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} - x - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w^{3} + 5w + 1]$ | $-1$ |
| 3 | $[3, 3, w - 1]$ | $-1$ |
| 4 | $[4, 2, -w^{3} + 4w - 1]$ | $\phantom{-}e$ |
| 25 | $[25, 5, w^{2} - 3]$ | $-2e + 4$ |
| 25 | $[25, 5, w^{2} - 2]$ | $-2e + 4$ |
| 37 | $[37, 37, w + 3]$ | $\phantom{-}2e - 4$ |
| 37 | $[37, 37, w^{3} - 5w + 3]$ | $\phantom{-}2e - 4$ |
| 37 | $[37, 37, -w^{3} + 5w + 3]$ | $\phantom{-}2e - 4$ |
| 37 | $[37, 37, -w + 3]$ | $\phantom{-}2e - 4$ |
| 47 | $[47, 47, w^{3} - 3w - 3]$ | $\phantom{-}4e - 4$ |
| 47 | $[47, 47, w^{3} + w^{2} - 6w - 1]$ | $\phantom{-}4e - 4$ |
| 47 | $[47, 47, w^{3} - w^{2} - 6w + 1]$ | $\phantom{-}4e - 4$ |
| 47 | $[47, 47, -w^{3} - w^{2} + 6w + 4]$ | $\phantom{-}4e - 4$ |
| 49 | $[49, 7, w^{3} - 6w]$ | $-4e + 6$ |
| 59 | $[59, 59, -w^{3} + w^{2} + 4w - 5]$ | $\phantom{-}4$ |
| 59 | $[59, 59, -w^{3} + w^{2} + 4w]$ | $\phantom{-}4$ |
| 59 | $[59, 59, w^{3} + w^{2} - 4w]$ | $\phantom{-}4$ |
| 59 | $[59, 59, w^{3} + w^{2} - 4w - 5]$ | $\phantom{-}4$ |
| 83 | $[83, 83, -3w + 2]$ | $-4e$ |
| 83 | $[83, 83, -w^{3} + w^{2} + 7w + 1]$ | $-4e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3,3,-w^{3}+5w+1]$ | $1$ |
| $3$ | $[3,3,w-1]$ | $1$ |