Base field 3.3.321.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 4x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[21, 21, -w^{2} + 2w + 3]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $3$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $\phantom{-}1$ |
| 3 | $[3, 3, w - 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w^{2} - 2]$ | $-1$ |
| 8 | $[8, 2, 2]$ | $-e + 1$ |
| 11 | $[11, 11, -w^{2} + w + 1]$ | $\phantom{-}e$ |
| 23 | $[23, 23, -w - 3]$ | $-8$ |
| 29 | $[29, 29, -w^{2} + 2w + 4]$ | $-e + 2$ |
| 31 | $[31, 31, 2w - 3]$ | $-2e$ |
| 41 | $[41, 41, -2w^{2} + 3w + 6]$ | $-2e - 6$ |
| 43 | $[43, 43, w^{2} - 3w + 3]$ | $-e$ |
| 47 | $[47, 47, w^{2} + w - 4]$ | $-3e + 4$ |
| 49 | $[49, 7, 2w^{2} - 3w - 3]$ | $-4e + 2$ |
| 53 | $[53, 53, w^{2} - 3w - 2]$ | $-e - 6$ |
| 59 | $[59, 59, 2w^{2} - w - 5]$ | $\phantom{-}2e + 4$ |
| 59 | $[59, 59, w^{2} - w - 7]$ | $\phantom{-}2e + 4$ |
| 59 | $[59, 59, -w^{2} - w + 7]$ | $-2e + 4$ |
| 67 | $[67, 67, 2w^{2} - 3w - 7]$ | $\phantom{-}4e + 4$ |
| 73 | $[73, 73, -w^{2} + 4w - 5]$ | $\phantom{-}2e + 2$ |
| 79 | $[79, 79, w^{2} - 8]$ | $-2e + 8$ |
| 79 | $[79, 79, w^{2} - 5w + 5]$ | $\phantom{-}e + 12$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 1]$ | $-1$ |
| $7$ | $[7, 7, w^{2} - 2]$ | $1$ |