Base field \(\Q(\zeta_{9})^+\)
Generator \(w\), with minimal polynomial \(x^{3} - 3x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[89,89,4w^{2} - 3w - 6]$ |
| Dimension: | $3$ |
| 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:
| \(x^{3} - 2x^{2} - 4x + 6\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w + 1]$ | $\phantom{-}e$ |
| 8 | $[8, 2, 2]$ | $-e^{2} + 3$ |
| 17 | $[17, 17, -2w^{2} + w + 3]$ | $\phantom{-}2e^{2} - 2e - 6$ |
| 17 | $[17, 17, -w^{2} - w + 3]$ | $-e$ |
| 17 | $[17, 17, -w^{2} + 2w + 3]$ | $-2e^{2} + 6$ |
| 19 | $[19, 19, -2w^{2} + 2w + 5]$ | $-2e^{2} + 8$ |
| 19 | $[19, 19, -2w^{2} + 3]$ | $\phantom{-}e^{2} + 2e - 4$ |
| 19 | $[19, 19, -2w + 1]$ | $\phantom{-}2e^{2} - 2e - 4$ |
| 37 | $[37, 37, -w^{2} + 3w + 3]$ | $-2e^{2} - e + 8$ |
| 37 | $[37, 37, 2w^{2} + w - 5]$ | $-2e + 2$ |
| 37 | $[37, 37, 3w^{2} - 2w - 5]$ | $-2e + 2$ |
| 53 | $[53, 53, -w - 4]$ | $\phantom{-}2e^{2} - 4e - 6$ |
| 53 | $[53, 53, -w^{2} + w - 2]$ | $\phantom{-}4e - 6$ |
| 53 | $[53, 53, w^{2} - 6]$ | $\phantom{-}e^{2} - 6$ |
| 71 | $[71, 71, w^{2} + w - 7]$ | $\phantom{-}2e^{2} - e$ |
| 71 | $[71, 71, w^{2} - 2w - 7]$ | $\phantom{-}4e^{2} + e - 18$ |
| 71 | $[71, 71, -2w^{2} + w - 1]$ | $-2e^{2} + 4e$ |
| 73 | $[73, 73, 3w^{2} - 3w - 8]$ | $-2e^{2} + e + 14$ |
| 73 | $[73, 73, 2w^{2} - 3w - 7]$ | $\phantom{-}2e^{2} - 5e - 4$ |
| 73 | $[73, 73, w^{2} + 2w - 5]$ | $-e^{2} + 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $89$ | $[89,89,4w^{2} - 3w - 6]$ | $-1$ |