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: | $[25,5,-w^{2} + 2]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 9x^{2} + 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w^{3} + 5w + 1]$ | $\phantom{-}e$ |
3 | $[3, 3, w - 1]$ | $-e^{3} + 9e$ |
4 | $[4, 2, -w^{3} + 4w - 1]$ | $-1$ |
25 | $[25, 5, w^{2} - 3]$ | $-4$ |
25 | $[25, 5, w^{2} - 2]$ | $-1$ |
37 | $[37, 37, w + 3]$ | $-e^{2} + 12$ |
37 | $[37, 37, w^{3} - 5w + 3]$ | $-e^{2} + 1$ |
37 | $[37, 37, -w^{3} + 5w + 3]$ | $\phantom{-}e^{2} - 8$ |
37 | $[37, 37, -w + 3]$ | $\phantom{-}e^{2} + 3$ |
47 | $[47, 47, w^{3} - 3w - 3]$ | $-2e^{3} + 20e$ |
47 | $[47, 47, w^{3} + w^{2} - 6w - 1]$ | $-2e^{3} + 20e$ |
47 | $[47, 47, w^{3} - w^{2} - 6w + 1]$ | $-2e^{3} + 20e$ |
47 | $[47, 47, -w^{3} - w^{2} + 6w + 4]$ | $-2e^{3} + 20e$ |
49 | $[49, 7, w^{3} - 6w]$ | $-8$ |
59 | $[59, 59, -w^{3} + w^{2} + 4w - 5]$ | $\phantom{-}4e^{3} - 32e$ |
59 | $[59, 59, -w^{3} + w^{2} + 4w]$ | $-4e^{3} + 37e$ |
59 | $[59, 59, w^{3} + w^{2} - 4w]$ | $-e^{3} + 13e$ |
59 | $[59, 59, w^{3} + w^{2} - 4w - 5]$ | $-4e^{3} + 32e$ |
83 | $[83, 83, -3w + 2]$ | $-6e^{3} + 52e$ |
83 | $[83, 83, -w^{3} + w^{2} + 7w + 1]$ | $-4e^{3} + 32e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$25$ | $[25,5,-w^{2} + 2]$ | $1$ |