Base field 3.3.1556.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 11\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[2, 2, w - 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 10x^{2} + 18\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 1]$ | $\phantom{-}1$ |
| 3 | $[3, 3, w - 2]$ | $\phantom{-}e$ |
| 9 | $[9, 3, w^{2} + w - 7]$ | $-\frac{2}{3}e^{3} + \frac{11}{3}e$ |
| 11 | $[11, 11, w]$ | $\phantom{-}e^{2} - 4$ |
| 11 | $[11, 11, -2w + 3]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{7}{3}e$ |
| 11 | $[11, 11, -w^{2} + 3w - 1]$ | $\phantom{-}\frac{1}{3}e^{3} - \frac{7}{3}e$ |
| 17 | $[17, 17, w + 2]$ | $-2e^{2} + 12$ |
| 17 | $[17, 17, -2w + 5]$ | $-\frac{2}{3}e^{3} + \frac{17}{3}e$ |
| 17 | $[17, 17, -w^{2} - w + 5]$ | $-\frac{1}{3}e^{3} + \frac{1}{3}e$ |
| 23 | $[23, 23, w - 4]$ | $\phantom{-}2e^{2} - 8$ |
| 29 | $[29, 29, w^{2} - 6]$ | $-2e$ |
| 31 | $[31, 31, w^{2} - w - 1]$ | $\phantom{-}\frac{2}{3}e^{3} - \frac{8}{3}e$ |
| 37 | $[37, 37, -w^{2} - 2w + 6]$ | $\phantom{-}0$ |
| 43 | $[43, 43, w^{2} - 3w + 3]$ | $-3e^{2} + 16$ |
| 47 | $[47, 47, 3w^{2} - 28]$ | $-2e^{2} + 4$ |
| 53 | $[53, 53, w^{2} - w - 3]$ | $\phantom{-}\frac{2}{3}e^{3} - \frac{20}{3}e$ |
| 61 | $[61, 61, -5w + 6]$ | $-2e^{2} + 18$ |
| 71 | $[71, 71, w^{2} - w - 7]$ | $-4$ |
| 83 | $[83, 83, -2w^{2} - w + 14]$ | $\phantom{-}\frac{7}{3}e^{3} - \frac{49}{3}e$ |
| 89 | $[89, 89, w^{2} + 3w - 3]$ | $\phantom{-}14$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w - 1]$ | $-1$ |