Base field 3.3.961.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x + 8\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[16,8,-w - 2]$ |
| 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:
| \(x^{3} - 4x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, \frac{1}{2}w^{2} - \frac{1}{2}w - 4]$ | $-1$ |
| 2 | $[2, 2, \frac{1}{2}w^{2} + \frac{1}{2}w - 3]$ | $\phantom{-}0$ |
| 2 | $[2, 2, -w + 1]$ | $\phantom{-}e$ |
| 23 | $[23, 23, -w^{2} + w + 7]$ | $-e^{2} + e - 2$ |
| 23 | $[23, 23, w^{2} + w - 7]$ | $\phantom{-}4e^{2} + 2e - 10$ |
| 23 | $[23, 23, -2w + 1]$ | $-3e^{2} + e + 8$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}e^{2} + 3e - 6$ |
| 29 | $[29, 29, -w^{2} - 3w + 1]$ | $-2e^{2} - 4e + 4$ |
| 29 | $[29, 29, w^{2} - 3w + 1]$ | $-e^{2} - e - 2$ |
| 29 | $[29, 29, -2w^{2} + 21]$ | $-e^{2} - 3e + 4$ |
| 31 | $[31, 31, -3w^{2} + w + 31]$ | $-2e - 2$ |
| 47 | $[47, 47, 2w - 3]$ | $-4e^{2} - 6e + 14$ |
| 47 | $[47, 47, w^{2} + w - 5]$ | $-e^{2} - e + 4$ |
| 47 | $[47, 47, w^{2} - w - 9]$ | $\phantom{-}e^{2} - 3e - 8$ |
| 61 | $[61, 61, w^{2} - w - 11]$ | $\phantom{-}5e^{2} - 3e - 14$ |
| 61 | $[61, 61, -w^{2} - w + 3]$ | $\phantom{-}2e - 4$ |
| 61 | $[61, 61, -2w + 5]$ | $\phantom{-}4e^{2} - 10$ |
| 89 | $[89, 89, w^{2} - w - 1]$ | $\phantom{-}2e^{2} - 2e - 6$ |
| 89 | $[89, 89, w^{2} + w - 13]$ | $\phantom{-}4e^{2} + 2e - 16$ |
| 89 | $[89, 89, -2w - 5]$ | $\phantom{-}e^{2} + e - 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-\frac{1}{2}w^{2} - \frac{1}{2}w + 3]$ | $1$ |
| $2$ | $[2,2,-\frac{1}{2}w^{2} + \frac{1}{2}w + 4]$ | $1$ |