Base field \(\Q(\sqrt{2}, \sqrt{3})\)
Generator \(w\), with minimal polynomial \(x^4 - 4 x^2 + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[47,47,-2 w^2 + 3 w]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $2$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^3 - 4 w + 1]$ | $-2$ |
| 9 | $[9, 3, -w^2 + 2]$ | $-2$ |
| 23 | $[23, 23, w^3 - w^2 - 4 w + 1]$ | $-4$ |
| 23 | $[23, 23, w^2 - w - 3]$ | $-8$ |
| 23 | $[23, 23, -w^2 - w + 3]$ | $\phantom{-}0$ |
| 23 | $[23, 23, -w^3 - w^2 + 4 w + 1]$ | $-4$ |
| 25 | $[25, 5, w^3 - 5 w + 1]$ | $-2$ |
| 25 | $[25, 5, w^3 - 5 w - 1]$ | $\phantom{-}2$ |
| 47 | $[47, 47, -3 w^3 + 2 w^2 + 12 w - 8]$ | $\phantom{-}0$ |
| 47 | $[47, 47, -2 w^3 - w^2 + 6 w]$ | $\phantom{-}1$ |
| 47 | $[47, 47, 2 w^3 - w^2 - 6 w]$ | $-8$ |
| 47 | $[47, 47, w^2 + w - 5]$ | $\phantom{-}4$ |
| 49 | $[49, 7, 2 w^3 - 6 w - 1]$ | $-6$ |
| 49 | $[49, 7, -2 w^3 + 6 w - 1]$ | $\phantom{-}2$ |
| 71 | $[71, 71, 2 w^3 - w^2 - 7 w + 1]$ | $-8$ |
| 71 | $[71, 71, 3 w^3 - w^2 - 11 w + 2]$ | $\phantom{-}0$ |
| 71 | $[71, 71, 4 w^3 - 2 w^2 - 14 w + 5]$ | $-8$ |
| 71 | $[71, 71, -3 w^3 + 2 w^2 + 10 w - 4]$ | $\phantom{-}0$ |
| 73 | $[73, 73, -w^3 - 2 w^2 + 3 w + 5]$ | $\phantom{-}6$ |
| 73 | $[73, 73, -w^3 + 2 w^2 + 3 w - 3]$ | $-2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $47$ | $[47,47,-2 w^2 + 3 w]$ | $-1$ |