Base field 3.3.568.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x - 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[22, 22, -2w^{2} + 3w + 9]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $5$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} - 2x - 1\) |
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| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w^{2} - w - 7]$ | $-e + 1$ |
| 11 | $[11, 11, -w^{2} + w + 1]$ | $-1$ |
| 17 | $[17, 17, -w^{2} + w + 3]$ | $\phantom{-}2e + 2$ |
| 25 | $[25, 5, -w^{2} - w - 1]$ | $\phantom{-}4e$ |
| 27 | $[27, 3, 3]$ | $-2e + 4$ |
| 29 | $[29, 29, -w^{2} + 3w - 1]$ | $-4e + 6$ |
| 37 | $[37, 37, 3w^{2} - 5w - 13]$ | $-5e + 5$ |
| 41 | $[41, 41, 2w - 1]$ | $-4e + 8$ |
| 53 | $[53, 53, 5w^{2} - 9w - 21]$ | $-3e + 1$ |
| 53 | $[53, 53, 3w^{2} - 5w - 15]$ | $\phantom{-}6e - 8$ |
| 53 | $[53, 53, w^{2} - 3w - 7]$ | $-e - 1$ |
| 59 | $[59, 59, w^{2} - 3w - 5]$ | $-2e - 4$ |
| 61 | $[61, 61, 2w^{2} - 4w - 9]$ | $\phantom{-}6e - 4$ |
| 61 | $[61, 61, 2w - 7]$ | $-5e - 1$ |
| 61 | $[61, 61, 2w - 5]$ | $-4e - 2$ |
| 67 | $[67, 67, -w^{2} + w - 1]$ | $\phantom{-}2e - 12$ |
| 71 | $[71, 71, -2w - 5]$ | $-2e + 2$ |
| 71 | $[71, 71, 3w^{2} - 3w - 19]$ | $-e + 11$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w + 1]$ | $-1$ |
| $11$ | $[11, 11, -w^{2} + w + 1]$ | $1$ |