Base field 4.4.14013.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} + 6x + 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[9, 3, w^{2} - 3]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
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 | $[3, 3, w]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w - 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w + 1]$ | $\phantom{-}e^{2} - 2$ |
| 7 | $[7, 7, -w^{3} + 5w - 2]$ | $-e$ |
| 13 | $[13, 13, -w^{3} + 5w + 1]$ | $\phantom{-}2e^{3} - 9e$ |
| 16 | $[16, 2, 2]$ | $-e^{2} + 3$ |
| 29 | $[29, 29, w^{3} + w^{2} - 5w - 1]$ | $\phantom{-}2e^{3} - 11e$ |
| 31 | $[31, 31, -w^{3} + 4w - 1]$ | $-2e^{3} + 10e$ |
| 41 | $[41, 41, w^{3} - 6w + 1]$ | $-e^{3} + 4e$ |
| 43 | $[43, 43, w^{3} + w^{2} - 6w - 1]$ | $\phantom{-}e^{3} - 5e$ |
| 47 | $[47, 47, -w^{3} + 2w^{2} + 5w - 11]$ | $\phantom{-}2e^{2} - 2$ |
| 49 | $[49, 7, w^{2} + w - 1]$ | $-3e^{3} + 20e$ |
| 59 | $[59, 59, w^{3} - w^{2} - 6w + 4]$ | $-2e^{3} + 11e$ |
| 59 | $[59, 59, w^{2} - w - 4]$ | $\phantom{-}3e^{2} - 6$ |
| 67 | $[67, 67, 2w^{3} + w^{2} - 9w - 2]$ | $-2e^{3} + 10e$ |
| 71 | $[71, 71, -3w^{3} - w^{2} + 16w + 5]$ | $\phantom{-}2e^{3} - 14e$ |
| 71 | $[71, 71, 2w - 1]$ | $\phantom{-}e^{3} - 7e$ |
| 73 | $[73, 73, w^{3} - 6w + 4]$ | $-7e$ |
| 83 | $[83, 83, w^{3} - w^{2} - 3w + 4]$ | $-e^{2} + 10$ |
| 103 | $[103, 103, w^{3} + w^{2} - 4w - 5]$ | $-4e^{2} + 12$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w]$ | $1$ |