Base field \(\Q(\sqrt{21}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 5\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[60,30,-2w + 10]$ |
Dimension: | $2$ |
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:
\(x^{2} - 3x - 6\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w + 1]$ | $\phantom{-}1$ |
4 | $[4, 2, 2]$ | $\phantom{-}1$ |
5 | $[5, 5, w]$ | $-1$ |
5 | $[5, 5, w - 1]$ | $\phantom{-}e$ |
7 | $[7, 7, -w - 3]$ | $-e + 2$ |
17 | $[17, 17, -2w + 3]$ | $-e$ |
17 | $[17, 17, -2w - 1]$ | $-e$ |
37 | $[37, 37, w + 6]$ | $\phantom{-}2e + 2$ |
37 | $[37, 37, -w + 7]$ | $\phantom{-}e - 4$ |
41 | $[41, 41, 3w + 1]$ | $-4e + 6$ |
41 | $[41, 41, -3w + 4]$ | $\phantom{-}2e - 6$ |
43 | $[43, 43, 3w + 8]$ | $\phantom{-}e + 2$ |
43 | $[43, 43, 3w - 11]$ | $-4$ |
47 | $[47, 47, 3w - 2]$ | $\phantom{-}e + 6$ |
47 | $[47, 47, 3w - 1]$ | $\phantom{-}0$ |
59 | $[59, 59, -5w - 6]$ | $-2e$ |
59 | $[59, 59, -4w - 3]$ | $-2e$ |
67 | $[67, 67, -w - 8]$ | $-3e + 2$ |
67 | $[67, 67, w - 9]$ | $\phantom{-}3e - 10$ |
79 | $[79, 79, 2w - 11]$ | $-4e + 8$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3,3,-w + 2]$ | $-1$ |
$4$ | $[4,2,2]$ | $-1$ |
$5$ | $[5,5,-w]$ | $1$ |