Base field 4.4.8112.1
Generator \(w\), with minimal polynomial \(x^4 - 5 x^2 + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[9, 3, -w^2 + 3]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^2 - 18\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}0$ |
| 4 | $[4, 2, w^2 - w - 1]$ | $\phantom{-}0$ |
| 9 | $[9, 3, -w^2 + 2]$ | $-4$ |
| 13 | $[13, 13, w^3 - 4 w + 2]$ | $\phantom{-}e$ |
| 13 | $[13, 13, -w^3 + 4 w + 2]$ | $-e$ |
| 17 | $[17, 17, w^3 - 3 w - 1]$ | $\phantom{-}e$ |
| 17 | $[17, 17, -w^3 + 3 w - 1]$ | $-e$ |
| 29 | $[29, 29, w^3 + w^2 - 4 w - 2]$ | $-e$ |
| 29 | $[29, 29, w^3 - w^2 - 4 w + 2]$ | $\phantom{-}e$ |
| 43 | $[43, 43, w^2 + w - 4]$ | $-8$ |
| 43 | $[43, 43, w^2 - w - 4]$ | $-8$ |
| 53 | $[53, 53, w^3 - 2 w - 2]$ | $-12$ |
| 53 | $[53, 53, -w^3 + 2 w - 2]$ | $-12$ |
| 79 | $[79, 79, w^3 - w^2 - 4 w + 1]$ | $\phantom{-}2 e$ |
| 79 | $[79, 79, -w^3 - w^2 + 4 w + 1]$ | $-2 e$ |
| 101 | $[101, 101, -w^3 + w^2 + 3 w - 5]$ | $\phantom{-}6$ |
| 101 | $[101, 101, w^3 + w^2 - 3 w - 5]$ | $\phantom{-}6$ |
| 103 | $[103, 103, 2 w^2 - w - 4]$ | $-4$ |
| 103 | $[103, 103, 2 w^2 + w - 4]$ | $-4$ |
| 107 | $[107, 107, 2 w^2 + w - 5]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w]$ | $-1$ |