Base field 4.4.11661.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 5x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[9, 3, -w^{2} + w + 2]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 6x^{2} + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w - 2]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w - 1]$ | $-e$ |
| 16 | $[16, 2, 2]$ | $-e^{2} - 1$ |
| 23 | $[23, 23, -w^{3} + 4w + 1]$ | $-2e^{2} + 2$ |
| 25 | $[25, 5, w^{3} - 2w^{2} - 2w + 2]$ | $\phantom{-}3e^{3} - 14e$ |
| 25 | $[25, 5, w^{3} - w^{2} - 3w + 1]$ | $-3e^{3} + 14e$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 4w + 4]$ | $-2e^{3} + 11e$ |
| 29 | $[29, 29, w^{3} - w^{2} - 5w + 1]$ | $\phantom{-}2e^{3} - 11e$ |
| 43 | $[43, 43, -w^{3} + 2w^{2} + 3w - 2]$ | $\phantom{-}e^{2} - 6$ |
| 43 | $[43, 43, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}e^{2} - 6$ |
| 61 | $[61, 61, -w^{2} + 2w + 4]$ | $\phantom{-}2e$ |
| 61 | $[61, 61, w^{2} - 5]$ | $-2e$ |
| 79 | $[79, 79, 3w^{3} - 7w^{2} - 8w + 16]$ | $-e^{3} + 9e$ |
| 79 | $[79, 79, -w^{3} + w^{2} + 6w - 4]$ | $\phantom{-}e^{3} - 9e$ |
| 101 | $[101, 101, -w^{3} + 3w^{2} + w - 7]$ | $-4e^{3} + 22e$ |
| 101 | $[101, 101, w^{3} - 4w - 4]$ | $\phantom{-}4e^{3} - 22e$ |
| 103 | $[103, 103, 2w^{3} - w^{2} - 8w - 1]$ | $\phantom{-}e^{2} - 12$ |
| 103 | $[103, 103, 2w^{3} - 5w^{2} - 4w + 8]$ | $\phantom{-}e^{2} - 12$ |
| 107 | $[107, 107, 2w^{2} - 3w - 4]$ | $\phantom{-}4e^{2} - 10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w - 2]$ | $-1$ |