Base field 4.4.16317.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 5x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[9, 3, w^{3} - w^{2} - 4w]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 16x^{2} + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}\frac{1}{2}e^{3} - 8e$ |
| 7 | $[7, 7, -w^{2} + 2w + 1]$ | $\phantom{-}\frac{1}{2}e^{2} - 3$ |
| 7 | $[7, 7, -w^{2} + 2]$ | $-\frac{1}{2}e^{2} + 5$ |
| 9 | $[9, 3, w^{3} - w^{2} - 4w]$ | $-1$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -w^{3} + 2w^{2} + 3w - 2]$ | $-\frac{1}{2}e^{3} + 9e$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 4w - 2]$ | $\phantom{-}\frac{1}{2}e^{3} - 9e$ |
| 25 | $[25, 5, w^{2} - w - 3]$ | $\phantom{-}4$ |
| 37 | $[37, 37, 2w - 1]$ | $\phantom{-}6$ |
| 43 | $[43, 43, -w^{3} + 2w^{2} + 2w - 2]$ | $\phantom{-}\frac{1}{2}e^{2} - 3$ |
| 43 | $[43, 43, w^{3} - w^{2} - 3w + 1]$ | $-\frac{1}{2}e^{2} + 5$ |
| 59 | $[59, 59, 2w - 5]$ | $\phantom{-}\frac{1}{2}e^{3} - 11e$ |
| 59 | $[59, 59, -2w - 3]$ | $-\frac{3}{2}e^{3} + 25e$ |
| 79 | $[79, 79, -w^{3} + 2w^{2} + 5w - 4]$ | $\phantom{-}e^{2} - 6$ |
| 79 | $[79, 79, -w^{3} + w^{2} + 6w - 2]$ | $-e^{2} + 10$ |
| 83 | $[83, 83, -w^{3} + 7w]$ | $-\frac{3}{2}e^{3} + 23e$ |
| 83 | $[83, 83, -w^{3} + 2w^{2} + 4w - 2]$ | $-\frac{1}{2}e^{3} + 9e$ |
| 83 | $[83, 83, -w^{3} + w^{2} + 5w - 3]$ | $\phantom{-}\frac{1}{2}e^{3} - 9e$ |
| 83 | $[83, 83, w^{2} - 2w - 6]$ | $-\frac{1}{2}e^{3} + 5e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9, 3, w^{3} - w^{2} - 4w]$ | $1$ |