Base field \(\Q(\sqrt{2}, \sqrt{3})\)
Generator \(w\), with minimal polynomial \(x^{4} - 4x^{2} + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[49,7,-2w^{3} + 6w - 1]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 14x^{4} + 53x^{2} - 32\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{3} - 4w + 1]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w^{2} + 2]$ | $-e^{4} + 7e^{2} - 2$ |
| 23 | $[23, 23, w^{3} - w^{2} - 4w + 1]$ | $-2e$ |
| 23 | $[23, 23, w^{2} - w - 3]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + 8e$ |
| 23 | $[23, 23, -w^{2} - w + 3]$ | $-2e$ |
| 23 | $[23, 23, -w^{3} - w^{2} + 4w + 1]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + 8e$ |
| 25 | $[25, 5, w^{3} - 5w + 1]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{9}{2}e^{2} + 6$ |
| 25 | $[25, 5, w^{3} - 5w - 1]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{9}{2}e^{2} + 6$ |
| 47 | $[47, 47, -3w^{3} + 2w^{2} + 12w - 8]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + 6e$ |
| 47 | $[47, 47, -2w^{3} - w^{2} + 6w]$ | $-e^{5} + 9e^{3} - 14e$ |
| 47 | $[47, 47, 2w^{3} - w^{2} - 6w]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + 6e$ |
| 47 | $[47, 47, w^{2} + w - 5]$ | $-e^{5} + 9e^{3} - 14e$ |
| 49 | $[49, 7, 2w^{3} - 6w - 1]$ | $-e^{4} + 11e^{2} - 18$ |
| 49 | $[49, 7, -2w^{3} + 6w - 1]$ | $-1$ |
| 71 | $[71, 71, 2w^{3} - w^{2} - 7w + 1]$ | $\phantom{-}2e^{3} - 14e$ |
| 71 | $[71, 71, 3w^{3} - w^{2} - 11w + 2]$ | $-2e^{3} + 12e$ |
| 71 | $[71, 71, 4w^{3} - 2w^{2} - 14w + 5]$ | $\phantom{-}2e^{3} - 14e$ |
| 71 | $[71, 71, -3w^{3} + 2w^{2} + 10w - 4]$ | $-2e^{3} + 12e$ |
| 73 | $[73, 73, -w^{3} - 2w^{2} + 3w + 5]$ | $-2e^{2} + 2$ |
| 73 | $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ | $-2e^{2} + 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $49$ | $[49,7,-2w^{3} + 6w - 1]$ | $1$ |