Base field 3.3.1369.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 12x - 11\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[27, 3, 3]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $47$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} + x^{11} - 70x^{10} - 85x^{9} + 1624x^{8} + 1735x^{7} - 15545x^{6} - 9222x^{5} + 63494x^{4} + 4380x^{3} - 69592x^{2} - 5864x + 404\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 8 | $[8, 2, 2]$ | $...$ |
| 11 | $[11, 11, w]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -w^{2} + 3w + 7]$ | $...$ |
| 11 | $[11, 11, w^{2} - 2w - 8]$ | $...$ |
| 23 | $[23, 23, w^{2} - 2w - 7]$ | $...$ |
| 23 | $[23, 23, w^{2} - 3w - 8]$ | $...$ |
| 23 | $[23, 23, w - 1]$ | $...$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}1$ |
| 29 | $[29, 29, w^{2} - 2w - 5]$ | $...$ |
| 29 | $[29, 29, w^{2} - 3w - 10]$ | $...$ |
| 29 | $[29, 29, w - 3]$ | $...$ |
| 31 | $[31, 31, w^{2} - 2w - 6]$ | $...$ |
| 31 | $[31, 31, -w^{2} + 3w + 9]$ | $...$ |
| 31 | $[31, 31, w - 2]$ | $...$ |
| 37 | $[37, 37, -w^{2} + 4w + 7]$ | $...$ |
| 43 | $[43, 43, 2w^{2} - 6w - 13]$ | $...$ |
| 43 | $[43, 43, 2w^{2} - 4w - 17]$ | $...$ |
| 43 | $[43, 43, w^{2} - 2w - 12]$ | $...$ |
| 47 | $[47, 47, w^{2} - 4w - 4]$ | $...$ |
| 47 | $[47, 47, w^{2} - w - 5]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $27$ | $[27, 3, 3]$ | $-1$ |