Base field \(\Q(\sqrt{2}, \sqrt{5})\)
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} + 4\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[81, 3, 3]$ |
Dimension: | $3$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $5$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} - x^{2} - 12x + 16\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, \frac{1}{2}w^{3} - 2w]$ | $\phantom{-}e$ |
9 | $[9, 3, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 2w - 3]$ | $\phantom{-}1$ |
9 | $[9, 3, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 2w - 3]$ | $\phantom{-}1$ |
25 | $[25, 5, w^{2} - 3]$ | $-e^{2} - 3e + 10$ |
31 | $[31, 31, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 3w]$ | $-e^{2} - e + 6$ |
31 | $[31, 31, -\frac{1}{2}w^{2} - w + 3]$ | $-e^{2} - e + 6$ |
31 | $[31, 31, -\frac{1}{2}w^{2} + w + 3]$ | $-e^{2} - e + 6$ |
31 | $[31, 31, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w]$ | $-e^{2} - e + 6$ |
41 | $[41, 41, \frac{1}{2}w^{3} - w^{2} - w + 3]$ | $\phantom{-}2e^{2} + 2e - 18$ |
41 | $[41, 41, w^{3} + w^{2} - 5w - 3]$ | $\phantom{-}2e^{2} + 2e - 18$ |
41 | $[41, 41, -\frac{3}{2}w^{2} - w + 5]$ | $\phantom{-}2e^{2} + 2e - 18$ |
41 | $[41, 41, -\frac{1}{2}w^{3} - w^{2} + w + 3]$ | $\phantom{-}2e^{2} + 2e - 18$ |
49 | $[49, 7, -\frac{1}{2}w^{3} + 2w - 3]$ | $-e^{2} + e + 14$ |
49 | $[49, 7, \frac{1}{2}w^{3} - 2w - 3]$ | $-e^{2} + e + 14$ |
71 | $[71, 71, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 2w - 5]$ | $-2e^{2} - 2e + 20$ |
71 | $[71, 71, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - 3w - 5]$ | $-2e^{2} - 2e + 20$ |
71 | $[71, 71, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 3w + 5]$ | $-2e^{2} - 2e + 20$ |
71 | $[71, 71, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 2w - 5]$ | $-2e^{2} - 2e + 20$ |
79 | $[79, 79, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - 2w - 4]$ | $\phantom{-}e^{2} + e - 6$ |
79 | $[79, 79, -w^{3} - \frac{1}{2}w^{2} + 6w]$ | $\phantom{-}e^{2} + e - 6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$9$ | $[9,3,-\frac{1}{2}w^{3}+\frac{1}{2}w^{2}+2w-3]$ | $-1$ |
$9$ | $[9,3,\frac{1}{2}w^{3}+\frac{1}{2}w^{2}-2w-3]$ | $-1$ |