Base field \(\Q(\sqrt{3}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 3\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[59, 59, 5w - 4]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $4$ |
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 |
---|---|---|
2 | $[2, 2, -w + 1]$ | $\phantom{-}e$ |
3 | $[3, 3, w]$ | $-e + 2$ |
11 | $[11, 11, -2w + 1]$ | $\phantom{-}e + 4$ |
11 | $[11, 11, 2w + 1]$ | $\phantom{-}2e + 1$ |
13 | $[13, 13, w + 4]$ | $-3e - 2$ |
13 | $[13, 13, -w + 4]$ | $\phantom{-}4e - 3$ |
23 | $[23, 23, -3w + 2]$ | $-3e + 3$ |
23 | $[23, 23, 3w + 2]$ | $-4e + 1$ |
25 | $[25, 5, 5]$ | $\phantom{-}2e - 5$ |
37 | $[37, 37, 2w - 7]$ | $-6e + 1$ |
37 | $[37, 37, -2w - 7]$ | $\phantom{-}3e - 6$ |
47 | $[47, 47, -4w - 1]$ | $\phantom{-}4e - 9$ |
47 | $[47, 47, 4w - 1]$ | $\phantom{-}7e - 3$ |
49 | $[49, 7, -7]$ | $\phantom{-}e + 2$ |
59 | $[59, 59, 5w - 4]$ | $-1$ |
59 | $[59, 59, -5w - 4]$ | $-4e - 3$ |
61 | $[61, 61, -w - 8]$ | $\phantom{-}6e - 6$ |
61 | $[61, 61, w - 8]$ | $-e$ |
71 | $[71, 71, 5w - 2]$ | $-5e + 12$ |
71 | $[71, 71, -5w - 2]$ | $\phantom{-}10e - 8$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$59$ | $[59, 59, 5w - 4]$ | $1$ |