Base field 4.4.13824.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} + 6\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[9, 3, -w^{2} + 3]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $11$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 16x^{6} + 82x^{4} - 152x^{2} + 72\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^{2} + w + 2]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w^{2} - w - 3]$ | $\phantom{-}0$ |
| 11 | $[11, 11, -w^{2} + w + 1]$ | $-\frac{1}{4}e^{7} + \frac{7}{2}e^{5} - \frac{27}{2}e^{3} + 13e$ |
| 11 | $[11, 11, -w^{2} - w + 1]$ | $-\frac{1}{4}e^{7} + \frac{7}{2}e^{5} - \frac{27}{2}e^{3} + 13e$ |
| 13 | $[13, 13, w^{3} - 4w + 1]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{7}{2}e^{4} + \frac{25}{2}e^{2} - 7$ |
| 13 | $[13, 13, -w^{3} + 4w + 1]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{7}{2}e^{4} + \frac{25}{2}e^{2} - 7$ |
| 25 | $[25, 5, -w^{2} - 2w + 1]$ | $-\frac{3}{4}e^{6} + \frac{19}{2}e^{4} - \frac{63}{2}e^{2} + 23$ |
| 25 | $[25, 5, w^{2} - 2w - 1]$ | $-\frac{3}{4}e^{6} + \frac{19}{2}e^{4} - \frac{63}{2}e^{2} + 23$ |
| 37 | $[37, 37, w^{3} - 3w - 1]$ | $-2e^{2} + 8$ |
| 37 | $[37, 37, w^{3} - 3w + 1]$ | $-2e^{2} + 8$ |
| 59 | $[59, 59, w^{2} - w - 5]$ | $\phantom{-}\frac{1}{2}e^{7} - 6e^{5} + 17e^{3} - 4e$ |
| 59 | $[59, 59, -w^{2} - w + 5]$ | $\phantom{-}\frac{1}{2}e^{7} - 6e^{5} + 17e^{3} - 4e$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 4w - 7]$ | $-\frac{1}{2}e^{6} + 5e^{4} - 9e^{2} - 4$ |
| 61 | $[61, 61, w^{3} - 3w^{2} - 6w + 11]$ | $-\frac{1}{2}e^{6} + 5e^{4} - 9e^{2} - 4$ |
| 73 | $[73, 73, 2w^{2} - w - 5]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{5}{2}e^{4} + \frac{5}{2}e^{2} + 11$ |
| 73 | $[73, 73, 2w - 1]$ | $\phantom{-}\frac{3}{4}e^{6} - \frac{19}{2}e^{4} + \frac{63}{2}e^{2} - 19$ |
| 73 | $[73, 73, -2w - 1]$ | $\phantom{-}\frac{3}{4}e^{6} - \frac{19}{2}e^{4} + \frac{63}{2}e^{2} - 19$ |
| 73 | $[73, 73, 2w^{2} + w - 5]$ | $\phantom{-}\frac{1}{4}e^{6} - \frac{5}{2}e^{4} + \frac{5}{2}e^{2} + 11$ |
| 83 | $[83, 83, 2w^{3} + w^{2} - 9w - 7]$ | $-\frac{1}{4}e^{7} + \frac{5}{2}e^{5} - \frac{3}{2}e^{3} - 17e$ |
| 83 | $[83, 83, -2w^{3} + w^{2} + 7w + 1]$ | $-\frac{1}{4}e^{7} + \frac{5}{2}e^{5} - \frac{3}{2}e^{3} - 17e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3,3,w^{2}-w-3]$ | $1$ |