Base field 3.3.1076.1
Generator \(w\), with minimal polynomial \(x^{3} - 8x - 6\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[9, 9, -w - 3]$ |
| Dimension: | $3$ |
| 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:
| \(x^{3} - 2x^{2} - 5x + 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 2]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w^{2} + 2w + 3]$ | $\phantom{-}0$ |
| 7 | $[7, 7, -2w^{2} + 5w + 5]$ | $-e^{2} + e + 4$ |
| 9 | $[9, 3, -w^{2} + 5]$ | $\phantom{-}e^{2} - e - 2$ |
| 13 | $[13, 13, -w^{2} + 3w + 1]$ | $-2e^{2} + 10$ |
| 13 | $[13, 13, 2w + 5]$ | $-2e + 2$ |
| 13 | $[13, 13, w - 1]$ | $\phantom{-}e^{2} - e - 4$ |
| 17 | $[17, 17, w^{2} - w - 5]$ | $\phantom{-}2e + 2$ |
| 19 | $[19, 19, w^{2} - 2w - 5]$ | $\phantom{-}2$ |
| 29 | $[29, 29, w^{2} - 7]$ | $-8$ |
| 31 | $[31, 31, 2w^{2} - 3w - 11]$ | $-2e + 6$ |
| 49 | $[49, 7, -2w^{2} - 4w + 1]$ | $-4e + 4$ |
| 59 | $[59, 59, w^{2} - 2w - 11]$ | $\phantom{-}6$ |
| 71 | $[71, 71, -2w + 7]$ | $-2e^{2} - 4e + 12$ |
| 73 | $[73, 73, w^{2} - 3w - 13]$ | $-4e^{2} + 22$ |
| 73 | $[73, 73, 2w^{2} - 2w - 17]$ | $-4e^{2} + 4e + 18$ |
| 73 | $[73, 73, -w^{2} - 4w - 5]$ | $\phantom{-}2e - 2$ |
| 79 | $[79, 79, 2w - 1]$ | $-e^{2} - 3e + 8$ |
| 79 | $[79, 79, w^{2} + w - 5]$ | $\phantom{-}3e^{2} - e - 16$ |
| 79 | $[79, 79, w - 5]$ | $-4e^{2} + 22$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -w^{2} + 2w + 3]$ | $-1$ |