Base field \(\Q(\sqrt{7}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 7\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[21, 21, -2w + 7]$ |
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:
\(x^{3} - x^{2} - 4x + 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w - 3]$ | $\phantom{-}e$ |
3 | $[3, 3, w - 2]$ | $\phantom{-}1$ |
3 | $[3, 3, w + 2]$ | $-e^{2} + e + 2$ |
7 | $[7, 7, w]$ | $\phantom{-}1$ |
19 | $[19, 19, 2w - 3]$ | $\phantom{-}2e^{2} - 2e - 8$ |
19 | $[19, 19, 2w + 3]$ | $-2e^{2} + 6$ |
25 | $[25, 5, 5]$ | $\phantom{-}e^{2} - e - 4$ |
29 | $[29, 29, -w - 6]$ | $-2$ |
29 | $[29, 29, w - 6]$ | $-e^{2} - 3e + 8$ |
31 | $[31, 31, 4w + 9]$ | $-e^{2} + e - 2$ |
31 | $[31, 31, -4w + 9]$ | $\phantom{-}2e^{2} + 2e - 8$ |
37 | $[37, 37, -3w + 10]$ | $\phantom{-}e^{2} + 3e - 4$ |
37 | $[37, 37, -6w + 17]$ | $-3e^{2} - e + 12$ |
47 | $[47, 47, -3w - 4]$ | $\phantom{-}e^{2} - 5e - 2$ |
47 | $[47, 47, 3w - 4]$ | $\phantom{-}2e^{2} - 2$ |
53 | $[53, 53, 2w - 9]$ | $-2e^{2} + 6e + 6$ |
53 | $[53, 53, 2w + 9]$ | $\phantom{-}4e^{2} - 6e - 12$ |
59 | $[59, 59, 3w - 2]$ | $\phantom{-}2e^{2} - 2e$ |
59 | $[59, 59, -3w - 2]$ | $\phantom{-}4e^{2} - 8$ |
83 | $[83, 83, -6w - 13]$ | $-2e^{2} + 6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w - 2]$ | $-1$ |
$7$ | $[7, 7, w]$ | $-1$ |