Base field \(\Q(\zeta_{9})^+\)
Generator \(w\), with minimal polynomial \(x^{3} - 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[111,111,w^{2} - 4w - 6]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $3$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 5\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w + 1]$ | $\phantom{-}1$ |
8 | $[8, 2, 2]$ | $\phantom{-}e$ |
17 | $[17, 17, -2w^{2} + w + 3]$ | $-2e - 2$ |
17 | $[17, 17, -w^{2} - w + 3]$ | $\phantom{-}2e$ |
17 | $[17, 17, -w^{2} + 2w + 3]$ | $-2e - 2$ |
19 | $[19, 19, -2w^{2} + 2w + 5]$ | $\phantom{-}2e + 2$ |
19 | $[19, 19, -2w^{2} + 3]$ | $-2e$ |
19 | $[19, 19, -2w + 1]$ | $-2e$ |
37 | $[37, 37, -w^{2} + 3w + 3]$ | $\phantom{-}4e + 2$ |
37 | $[37, 37, 2w^{2} + w - 5]$ | $-1$ |
37 | $[37, 37, 3w^{2} - 2w - 5]$ | $\phantom{-}0$ |
53 | $[53, 53, -w - 4]$ | $-2e - 4$ |
53 | $[53, 53, -w^{2} + w - 2]$ | $-2e - 4$ |
53 | $[53, 53, w^{2} - 6]$ | $\phantom{-}2e - 2$ |
71 | $[71, 71, w^{2} + w - 7]$ | $-4$ |
71 | $[71, 71, w^{2} - 2w - 7]$ | $-4$ |
71 | $[71, 71, -2w^{2} + w - 1]$ | $-4$ |
73 | $[73, 73, 3w^{2} - 3w - 8]$ | $\phantom{-}4e$ |
73 | $[73, 73, 2w^{2} - 3w - 7]$ | $-2$ |
73 | $[73, 73, w^{2} + 2w - 5]$ | $-2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3,3,w^{2} - 1]$ | $-1$ |
$37$ | $[37,37,-2w^{2} - w + 5]$ | $1$ |