Base field \(\Q(\sqrt{42}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 42\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[7, 7, w - 7]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $52$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 7x^{2} + 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w]$ | $-\frac{1}{2}e^{3} - \frac{3}{2}e$ |
| 7 | $[7, 7, w - 7]$ | $-1$ |
| 11 | $[11, 11, w + 3]$ | $-e^{3} - 5e$ |
| 11 | $[11, 11, w + 8]$ | $-e^{3} - 5e$ |
| 13 | $[13, 13, w + 4]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{7}{2}e$ |
| 13 | $[13, 13, w + 9]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{7}{2}e$ |
| 17 | $[17, 17, -w - 5]$ | $-2$ |
| 17 | $[17, 17, -w + 5]$ | $-2$ |
| 19 | $[19, 19, w + 2]$ | $-\frac{1}{2}e^{3} - \frac{3}{2}e$ |
| 19 | $[19, 19, w + 17]$ | $-\frac{1}{2}e^{3} - \frac{3}{2}e$ |
| 25 | $[25, 5, 5]$ | $-2e^{2} - 4$ |
| 29 | $[29, 29, w + 10]$ | $-e^{3} - 3e$ |
| 29 | $[29, 29, w + 19]$ | $-e^{3} - 3e$ |
| 41 | $[41, 41, -w - 1]$ | $\phantom{-}4e^{2} + 18$ |
| 41 | $[41, 41, w - 1]$ | $\phantom{-}4e^{2} + 18$ |
| 47 | $[47, 47, -2w + 11]$ | $\phantom{-}0$ |
| 47 | $[47, 47, 4w - 25]$ | $\phantom{-}0$ |
| 53 | $[53, 53, w + 25]$ | $-2e^{3} - 10e$ |
| 53 | $[53, 53, w + 28]$ | $-2e^{3} - 10e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w - 7]$ | $1$ |