Base field \(\Q(\sqrt{14}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 14\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[26, 26, 3w + 10]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} + 5x + 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w - 4]$ | $\phantom{-}1$ |
5 | $[5, 5, -w + 3]$ | $-1$ |
5 | $[5, 5, w + 3]$ | $-1$ |
7 | $[7, 7, -2w - 7]$ | $\phantom{-}e$ |
9 | $[9, 3, 3]$ | $-e - 3$ |
11 | $[11, 11, w + 5]$ | $\phantom{-}2e + 3$ |
11 | $[11, 11, -w + 5]$ | $-e - 1$ |
13 | $[13, 13, -w - 1]$ | $-2e - 5$ |
13 | $[13, 13, -w + 1]$ | $-1$ |
31 | $[31, 31, 2w - 5]$ | $\phantom{-}e - 4$ |
31 | $[31, 31, -2w - 5]$ | $-2e - 8$ |
43 | $[43, 43, 7w + 27]$ | $\phantom{-}2e$ |
43 | $[43, 43, 3w + 13]$ | $-e - 4$ |
47 | $[47, 47, 2w - 3]$ | $\phantom{-}4e + 9$ |
47 | $[47, 47, -2w - 3]$ | $-2e + 1$ |
61 | $[61, 61, 7w + 25]$ | $-2e - 13$ |
61 | $[61, 61, -5w - 17]$ | $\phantom{-}2e + 4$ |
67 | $[67, 67, -w - 9]$ | $\phantom{-}3e + 2$ |
67 | $[67, 67, w - 9]$ | $\phantom{-}4e + 15$ |
101 | $[101, 101, 3w - 5]$ | $\phantom{-}2e + 9$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w - 4]$ | $-1$ |
$13$ | $[13, 13, -w + 1]$ | $1$ |