Base field \(\Q(\sqrt{13}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 3\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[69, 69, -w - 8]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $5$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - x - 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w]$ | $\phantom{-}e$ |
3 | $[3, 3, -w + 1]$ | $\phantom{-}1$ |
4 | $[4, 2, 2]$ | $-2e + 2$ |
13 | $[13, 13, -2w + 1]$ | $\phantom{-}4e - 2$ |
17 | $[17, 17, w + 4]$ | $\phantom{-}e + 3$ |
17 | $[17, 17, -w + 5]$ | $\phantom{-}3e - 5$ |
23 | $[23, 23, 3w + 1]$ | $\phantom{-}1$ |
23 | $[23, 23, -3w + 4]$ | $-5e$ |
25 | $[25, 5, 5]$ | $-3e + 5$ |
29 | $[29, 29, 3w - 2]$ | $\phantom{-}3e - 4$ |
29 | $[29, 29, -3w + 1]$ | $-2e - 6$ |
43 | $[43, 43, -4w - 1]$ | $-6e + 2$ |
43 | $[43, 43, 4w - 5]$ | $\phantom{-}7e - 6$ |
49 | $[49, 7, -7]$ | $\phantom{-}8e - 4$ |
53 | $[53, 53, -w - 7]$ | $-7e + 5$ |
53 | $[53, 53, w - 8]$ | $\phantom{-}9e - 4$ |
61 | $[61, 61, -3w - 8]$ | $\phantom{-}3e + 6$ |
61 | $[61, 61, 3w - 11]$ | $-6e - 2$ |
79 | $[79, 79, 5w - 4]$ | $-8e + 2$ |
79 | $[79, 79, 5w - 1]$ | $-5e + 1$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, -w + 1]$ | $-1$ |
$23$ | $[23, 23, 3w + 1]$ | $-1$ |