Base field 3.3.761.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[9, 3, -w^{2} + 2w + 4]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - 2x^{2} - 4x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 1]$ | $\phantom{-}\frac{1}{2}e^{2}$ |
| 8 | $[8, 2, 2]$ | $-e^{2} + e + 1$ |
| 9 | $[9, 3, -w^{2} + 2w + 4]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -w^{2} + 2w + 2]$ | $\phantom{-}e^{2} - e$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $\phantom{-}\frac{1}{2}e^{2} - e$ |
| 19 | $[19, 19, w + 3]$ | $-\frac{1}{2}e^{2} + 2e$ |
| 19 | $[19, 19, -w^{2} + 2w + 5]$ | $-e^{2} + 6$ |
| 19 | $[19, 19, -w^{2} + 3w + 2]$ | $-2e^{2} + e + 8$ |
| 23 | $[23, 23, w^{2} - w - 3]$ | $-\frac{1}{2}e^{2} + 3e$ |
| 23 | $[23, 23, -w^{2} + 2]$ | $\phantom{-}\frac{1}{2}e^{2} - 3e - 2$ |
| 23 | $[23, 23, -w + 4]$ | $-e - 2$ |
| 31 | $[31, 31, w^{2} - 5]$ | $-2e$ |
| 43 | $[43, 43, w^{2} - 3w - 3]$ | $-\frac{5}{2}e^{2} + e + 10$ |
| 49 | $[49, 7, w^{2} - 6]$ | $-\frac{1}{2}e^{2} - 4e + 4$ |
| 53 | $[53, 53, 2w - 5]$ | $\phantom{-}\frac{1}{2}e^{2} - 4$ |
| 61 | $[61, 61, 2w^{2} - 2w - 9]$ | $\phantom{-}e^{2} + 6$ |
| 71 | $[71, 71, 2w - 3]$ | $-2e^{2} + 4$ |
| 73 | $[73, 73, 2w^{2} - 5w - 5]$ | $\phantom{-}e^{2} - e + 2$ |
| 83 | $[83, 83, w^{2} - w - 9]$ | $-e^{2} + 2e + 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9, 3, -w^{2} + 2w + 4]$ | $-1$ |