Base field 3.3.316.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 4x + 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[29, 29, 2w + 1]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $9$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} + 2x^{2} - 5x - 9\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w - 1]$ | $-e^{2} + 5$ |
| 11 | $[11, 11, w^{2} - w - 1]$ | $\phantom{-}e^{2} - 4$ |
| 17 | $[17, 17, -w^{2} - w + 3]$ | $\phantom{-}e^{2} - e - 2$ |
| 19 | $[19, 19, w^{2} - w + 1]$ | $\phantom{-}e + 3$ |
| 23 | $[23, 23, 2w - 3]$ | $-2e^{2} - e + 10$ |
| 27 | $[27, 3, 3]$ | $\phantom{-}e^{2} + e + 2$ |
| 29 | $[29, 29, 2w + 1]$ | $\phantom{-}1$ |
| 31 | $[31, 31, 2w^{2} - 2w - 9]$ | $-2e^{2} + 3e + 13$ |
| 37 | $[37, 37, 2w^{2} - 2w - 5]$ | $\phantom{-}e^{2} - e - 3$ |
| 41 | $[41, 41, 2w^{2} - 9]$ | $\phantom{-}e^{2} + e - 12$ |
| 43 | $[43, 43, w^{2} + w - 5]$ | $\phantom{-}4e^{2} - e - 24$ |
| 43 | $[43, 43, -3w^{2} + w + 15]$ | $\phantom{-}2e^{2} - 2$ |
| 43 | $[43, 43, -2w^{2} + 2w + 11]$ | $\phantom{-}2e^{2} - e - 13$ |
| 53 | $[53, 53, w^{2} - w - 7]$ | $-4e^{2} - 2e + 19$ |
| 61 | $[61, 61, 4w^{2} - 2w - 15]$ | $\phantom{-}4e^{2} + e - 12$ |
| 67 | $[67, 67, -5w^{2} + 3w + 23]$ | $-5e^{2} - 3e + 17$ |
| 73 | $[73, 73, 2w^{2} - 3]$ | $-4e^{2} - 3e + 14$ |
| 73 | $[73, 73, -3w^{2} - w + 7]$ | $-5e^{2} - 2e + 20$ |
| 73 | $[73, 73, -6w^{2} + 4w + 25]$ | $\phantom{-}5e^{2} - 27$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, 2w + 1]$ | $-1$ |