Base field 3.3.1940.1
Generator \(w\), with minimal polynomial \(x^{3} - 8x - 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[9, 9, w - 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 10x^{2} + 7\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}\frac{1}{3}e^{2} - \frac{2}{3}$ |
| 3 | $[3, 3, w^{2} - 7]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w - 3]$ | $\phantom{-}\frac{2}{3}e^{2} - \frac{7}{3}$ |
| 9 | $[9, 3, w^{2} - 2w - 1]$ | $-\frac{2}{3}e^{3} + \frac{16}{3}e$ |
| 17 | $[17, 17, -2w^{2} + 15]$ | $\phantom{-}\frac{2}{3}e^{2} - \frac{16}{3}$ |
| 17 | $[17, 17, 3w + 1]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{11}{3}e$ |
| 17 | $[17, 17, -w^{2} + w + 5]$ | $-2e$ |
| 19 | $[19, 19, -2w^{2} + w + 15]$ | $-\frac{2}{3}e^{3} + \frac{19}{3}e$ |
| 29 | $[29, 29, w^{2} - w - 1]$ | $\phantom{-}\frac{2}{3}e^{3} - \frac{10}{3}e$ |
| 41 | $[41, 41, w^{2} - 5]$ | $\phantom{-}e^{3} - 7e$ |
| 43 | $[43, 43, w^{2} + w - 3]$ | $-\frac{4}{3}e^{3} + \frac{26}{3}e$ |
| 47 | $[47, 47, 2w - 1]$ | $-e^{2} + 8$ |
| 53 | $[53, 53, -2w - 3]$ | $-\frac{4}{3}e^{3} + \frac{32}{3}e$ |
| 59 | $[59, 59, w^{2} - w - 11]$ | $\phantom{-}\frac{4}{3}e^{2} - \frac{44}{3}$ |
| 71 | $[71, 71, w^{2} - 3]$ | $-\frac{5}{3}e^{3} + \frac{58}{3}e$ |
| 73 | $[73, 73, 6w^{2} - 2w - 47]$ | $\phantom{-}e^{3} - 12e$ |
| 83 | $[83, 83, w^{2} - 4w + 1]$ | $-2e^{2} + 9$ |
| 83 | $[83, 83, 3w^{2} - 25]$ | $\phantom{-}\frac{8}{3}e^{2} - \frac{43}{3}$ |
| 83 | $[83, 83, w - 5]$ | $\phantom{-}2e^{2} - 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w^{2} - 7]$ | $-1$ |