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: | $[121, 11, 11]$ |
Dimension: | $2$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $3$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - x - 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, 2]$ | $\phantom{-}e$ |
5 | $[5, 5, -2w + 1]$ | $-e - 1$ |
9 | $[9, 3, 3]$ | $-e + 3$ |
11 | $[11, 11, -3w + 2]$ | $-1$ |
11 | $[11, 11, -3w + 1]$ | $-1$ |
19 | $[19, 19, -4w + 3]$ | $-4$ |
19 | $[19, 19, -4w + 1]$ | $-4$ |
29 | $[29, 29, w + 5]$ | $\phantom{-}2e - 4$ |
29 | $[29, 29, -w + 6]$ | $\phantom{-}2e - 4$ |
31 | $[31, 31, -5w + 2]$ | $-e + 1$ |
31 | $[31, 31, -5w + 3]$ | $-e + 1$ |
41 | $[41, 41, -6w + 5]$ | $-2e + 4$ |
41 | $[41, 41, w - 7]$ | $-2e + 4$ |
49 | $[49, 7, -7]$ | $\phantom{-}2$ |
59 | $[59, 59, 2w - 9]$ | $-e + 5$ |
59 | $[59, 59, 7w - 5]$ | $-e + 5$ |
61 | $[61, 61, 3w - 10]$ | $\phantom{-}2e + 4$ |
61 | $[61, 61, -3w - 7]$ | $\phantom{-}2e + 4$ |
71 | $[71, 71, -8w + 7]$ | $\phantom{-}3e - 3$ |
71 | $[71, 71, w - 9]$ | $\phantom{-}3e - 3$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$11$ | $[11, 11, -3w + 2]$ | $1$ |
$11$ | $[11, 11, -3w + 1]$ | $1$ |