Base field 3.3.1425.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x - 3\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[9, 3, w^{2} - w - 8]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $11$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 12x^{2} + 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $-1$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w^{2} - w - 7]$ | $\phantom{-}e$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{7}{2}e$ |
| 11 | $[11, 11, w - 1]$ | $-\frac{1}{4}e^{3} + \frac{7}{2}e$ |
| 13 | $[13, 13, w^{2} - 2w - 8]$ | $-\frac{3}{4}e^{3} + \frac{15}{2}e$ |
| 17 | $[17, 17, w^{2} - 2w - 7]$ | $-\frac{3}{2}e^{2} + 9$ |
| 19 | $[19, 19, -w^{2} + 2w + 4]$ | $\phantom{-}\frac{1}{2}e^{2} - 8$ |
| 19 | $[19, 19, -2w^{2} + 3w + 16]$ | $\phantom{-}\frac{1}{2}e^{3} - 6e$ |
| 23 | $[23, 23, -w^{2} + 2w + 2]$ | $\phantom{-}e^{3} - 9e$ |
| 31 | $[31, 31, 2w^{2} - 3w - 13]$ | $-\frac{1}{2}e^{3} + 3e$ |
| 37 | $[37, 37, w^{2} - w - 10]$ | $-\frac{1}{2}e^{3} + 6e$ |
| 43 | $[43, 43, 3w^{2} - 5w - 19]$ | $\phantom{-}\frac{1}{2}e^{3} - 6e$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{9}{2}e$ |
| 43 | $[43, 43, 2w^{2} - 2w - 17]$ | $\phantom{-}e^{2} - 10$ |
| 47 | $[47, 47, w^{2} - 2]$ | $\phantom{-}\frac{3}{2}e^{2} - 3$ |
| 67 | $[67, 67, w^{2} - 3w - 5]$ | $\phantom{-}2e^{2} - 14$ |
| 79 | $[79, 79, -w^{2} + 3w - 1]$ | $-\frac{1}{4}e^{3} - \frac{3}{2}e$ |
| 83 | $[83, 83, w^{2} + w - 4]$ | $-\frac{3}{2}e^{2} + 3$ |
| 97 | $[97, 97, w^{2} - 11]$ | $\phantom{-}\frac{1}{2}e^{2} - 8$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 1]$ | $1$ |