Base field \(\Q(\sqrt{65}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 16\); narrow class number \(2\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[9, 3, 3]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 7x^{2} + 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $-e$ |
2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
5 | $[5, 5, w + 2]$ | $\phantom{-}0$ |
7 | $[7, 7, w + 1]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{7}{2}e$ |
7 | $[7, 7, w + 5]$ | $-\frac{1}{2}e^{3} - \frac{7}{2}e$ |
9 | $[9, 3, 3]$ | $-1$ |
13 | $[13, 13, w + 6]$ | $\phantom{-}0$ |
29 | $[29, 29, -2w + 7]$ | $-2e^{2} - 4$ |
29 | $[29, 29, 2w + 5]$ | $-2e^{2} - 4$ |
37 | $[37, 37, w + 9]$ | $\phantom{-}\frac{1}{2}e^{3} + \frac{11}{2}e$ |
37 | $[37, 37, w + 27]$ | $-\frac{1}{2}e^{3} - \frac{11}{2}e$ |
47 | $[47, 47, w + 10]$ | $\phantom{-}2e$ |
47 | $[47, 47, w + 36]$ | $-2e$ |
61 | $[61, 61, 2w - 3]$ | $-e^{2} - 9$ |
61 | $[61, 61, -2w - 1]$ | $-e^{2} - 9$ |
67 | $[67, 67, w + 23]$ | $-e^{3} - e$ |
67 | $[67, 67, w + 43]$ | $\phantom{-}e^{3} + e$ |
73 | $[73, 73, w + 24]$ | $-2e^{3} - 10e$ |
73 | $[73, 73, w + 48]$ | $\phantom{-}2e^{3} + 10e$ |
79 | $[79, 79, 2w - 13]$ | $-e^{2} - 3$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$9$ | $[9, 3, 3]$ | $1$ |