Base field \(\Q(\sqrt{5}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[139, 139, 2w - 13]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $2$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 2x - 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, 2]$ | $\phantom{-}e$ |
5 | $[5, 5, -2w + 1]$ | $-2e + 2$ |
9 | $[9, 3, 3]$ | $\phantom{-}e - 2$ |
11 | $[11, 11, -3w + 2]$ | $\phantom{-}2e - 5$ |
11 | $[11, 11, -3w + 1]$ | $-2$ |
19 | $[19, 19, -4w + 3]$ | $-4e + 5$ |
19 | $[19, 19, -4w + 1]$ | $-e + 4$ |
29 | $[29, 29, w + 5]$ | $-4e + 1$ |
29 | $[29, 29, -w + 6]$ | $\phantom{-}6e - 7$ |
31 | $[31, 31, -5w + 2]$ | $\phantom{-}e + 6$ |
31 | $[31, 31, -5w + 3]$ | $-2e$ |
41 | $[41, 41, -6w + 5]$ | $-5e + 4$ |
41 | $[41, 41, w - 7]$ | $\phantom{-}2e - 10$ |
49 | $[49, 7, -7]$ | $\phantom{-}4e + 2$ |
59 | $[59, 59, 2w - 9]$ | $-4e + 10$ |
59 | $[59, 59, 7w - 5]$ | $\phantom{-}2e + 8$ |
61 | $[61, 61, 3w - 10]$ | $-3e$ |
61 | $[61, 61, -3w - 7]$ | $\phantom{-}8e - 6$ |
71 | $[71, 71, -8w + 7]$ | $-6e + 4$ |
71 | $[71, 71, w - 9]$ | $\phantom{-}8e - 10$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$139$ | $[139, 139, 2w - 13]$ | $1$ |