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: | $[76,38,-w^{3} + 3w^{2} + 3w - 8]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} - 3x^{2} - 5x + 12\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -w^{3} - w^{2} + 3w + 4]$ | $\phantom{-}1$ |
5 | $[5, 5, w]$ | $\phantom{-}e$ |
19 | $[19, 19, -w^{2} + w + 4]$ | $-e^{2} + e + 5$ |
19 | $[19, 19, w^{3} - w^{2} - 3w + 1]$ | $-e^{2} + e + 5$ |
19 | $[19, 19, -w^{3} - w^{2} + 3w + 1]$ | $\phantom{-}1$ |
19 | $[19, 19, -w^{2} - w + 4]$ | $\phantom{-}e^{2} - 2e - 4$ |
41 | $[41, 41, w + 3]$ | $-2e^{2} + 2e + 12$ |
41 | $[41, 41, -w^{3} + 3w + 3]$ | $-2e^{2} + 2e + 12$ |
41 | $[41, 41, -w^{3} + 3w - 3]$ | $-e + 3$ |
41 | $[41, 41, w - 3]$ | $\phantom{-}2e^{2} - 4e - 6$ |
59 | $[59, 59, 2w^{2} + w - 7]$ | $\phantom{-}2e^{2} + e - 18$ |
59 | $[59, 59, -w^{3} - 2w^{2} + 3w + 3]$ | $-e^{2} + 6$ |
59 | $[59, 59, 2w^{3} - w^{2} - 7w + 2]$ | $\phantom{-}2e^{2} + e - 18$ |
59 | $[59, 59, w^{3} - w^{2} - w + 3]$ | $\phantom{-}3e^{2} - 6e - 12$ |
61 | $[61, 61, 3w^{2} - w - 8]$ | $-3e^{2} + 3e + 17$ |
61 | $[61, 61, w^{3} + 3w^{2} - 3w - 7]$ | $\phantom{-}2e^{2} + e - 16$ |
61 | $[61, 61, -w^{3} + 3w^{2} + 3w - 7]$ | $\phantom{-}e^{2} - 3e - 1$ |
61 | $[61, 61, -3w^{2} - w + 8]$ | $-e^{2} + 8$ |
79 | $[79, 79, -w^{3} + 2w^{2} + 2w - 6]$ | $\phantom{-}e^{2} + 2e - 13$ |
79 | $[79, 79, w^{3} + 2w^{2} - 4w - 4]$ | $-2e^{2} + e + 11$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4,2,w^{2} + w - 1]$ | $-1$ |
$19$ | $[19,19,w^{3} + w^{2} - 3w - 1]$ | $-1$ |