Base field \(\Q(\zeta_{20})^+\)
Generator \(w\), with minimal polynomial \(x^{4} - 5x^{2} + 5\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[81, 3, -3]$ |
Dimension: | $2$ |
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:
\(x^{2} - 32\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -w^{3} - w^{2} + 3w + 4]$ | $\phantom{-}0$ |
5 | $[5, 5, w]$ | $\phantom{-}4$ |
19 | $[19, 19, -w^{2} + w + 4]$ | $-e$ |
19 | $[19, 19, w^{3} - w^{2} - 3w + 1]$ | $\phantom{-}e$ |
19 | $[19, 19, -w^{3} - w^{2} + 3w + 1]$ | $\phantom{-}e$ |
19 | $[19, 19, -w^{2} - w + 4]$ | $-e$ |
41 | $[41, 41, w + 3]$ | $\phantom{-}0$ |
41 | $[41, 41, -w^{3} + 3w + 3]$ | $\phantom{-}0$ |
41 | $[41, 41, -w^{3} + 3w - 3]$ | $\phantom{-}0$ |
41 | $[41, 41, w - 3]$ | $\phantom{-}0$ |
59 | $[59, 59, 2w^{2} + w - 7]$ | $-2e$ |
59 | $[59, 59, -w^{3} - 2w^{2} + 3w + 3]$ | $\phantom{-}2e$ |
59 | $[59, 59, 2w^{3} - w^{2} - 7w + 2]$ | $\phantom{-}2e$ |
59 | $[59, 59, w^{3} - w^{2} - w + 3]$ | $-2e$ |
61 | $[61, 61, 3w^{2} - w - 8]$ | $-4$ |
61 | $[61, 61, w^{3} + 3w^{2} - 3w - 7]$ | $-4$ |
61 | $[61, 61, -w^{3} + 3w^{2} + 3w - 7]$ | $-4$ |
61 | $[61, 61, -3w^{2} - w + 8]$ | $-4$ |
79 | $[79, 79, -w^{3} + 2w^{2} + 2w - 6]$ | $\phantom{-}e$ |
79 | $[79, 79, w^{3} + 2w^{2} - 4w - 4]$ | $-e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$81$ | $[81, 3, -3]$ | $1$ |