Base field 3.3.985.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[8, 2, 2]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 21x^{6} + 145x^{4} - 405x^{2} + 392\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w + 1]$ | $\phantom{-}\frac{1}{2}e^{6} - 9e^{4} + \frac{91}{2}e^{2} - 66$ |
| 5 | $[5, 5, w - 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w + 2]$ | $-\frac{2}{7}e^{7} + 5e^{5} - \frac{171}{7}e^{3} + \frac{250}{7}e$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -w^{2} + 2w + 2]$ | $-\frac{1}{14}e^{7} + \frac{3}{2}e^{5} - \frac{131}{14}e^{3} + \frac{223}{14}e$ |
| 17 | $[17, 17, -w - 3]$ | $-\frac{1}{2}e^{6} + 8e^{4} - \frac{65}{2}e^{2} + 36$ |
| 17 | $[17, 17, -w^{2} + 2w + 1]$ | $-\frac{1}{14}e^{7} + \frac{3}{2}e^{5} - \frac{131}{14}e^{3} + \frac{237}{14}e$ |
| 17 | $[17, 17, -w^{2} + w + 4]$ | $\phantom{-}\frac{1}{2}e^{7} - \frac{17}{2}e^{5} + \frac{77}{2}e^{3} - \frac{97}{2}e$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $-\frac{1}{14}e^{7} + e^{5} - \frac{33}{14}e^{3} - \frac{18}{7}e$ |
| 27 | $[27, 3, -3]$ | $-\frac{1}{2}e^{6} + 9e^{4} - \frac{89}{2}e^{2} + 64$ |
| 29 | $[29, 29, w^{2} - w - 8]$ | $\phantom{-}e^{2} - 6$ |
| 29 | $[29, 29, w^{2} - w - 3]$ | $-\frac{1}{14}e^{7} + e^{5} - \frac{33}{14}e^{3} - \frac{11}{7}e$ |
| 29 | $[29, 29, w^{2} - w - 1]$ | $\phantom{-}\frac{1}{2}e^{7} - 9e^{5} + \frac{91}{2}e^{3} - 67e$ |
| 31 | $[31, 31, w^{2} - 2]$ | $-\frac{3}{7}e^{7} + 8e^{5} - \frac{302}{7}e^{3} + \frac{473}{7}e$ |
| 37 | $[37, 37, 2w - 5]$ | $-\frac{5}{14}e^{7} + 6e^{5} - \frac{375}{14}e^{3} + \frac{239}{7}e$ |
| 43 | $[43, 43, w^{2} - 2w - 5]$ | $-\frac{3}{2}e^{6} + 26e^{4} - \frac{245}{2}e^{2} + 170$ |
| 47 | $[47, 47, w^{2} - 3w - 2]$ | $\phantom{-}\frac{3}{2}e^{6} - 27e^{4} + \frac{275}{2}e^{2} - 204$ |
| 49 | $[49, 7, w^{2} + w - 4]$ | $-\frac{5}{14}e^{7} + \frac{13}{2}e^{5} - \frac{473}{14}e^{3} + \frac{793}{14}e$ |
| 53 | $[53, 53, w^{2} - 2w - 6]$ | $\phantom{-}\frac{1}{2}e^{6} - 8e^{4} + \frac{63}{2}e^{2} - 26$ |
| 71 | $[71, 71, w - 5]$ | $\phantom{-}e^{6} - 18e^{4} + 93e^{2} - 144$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $8$ | $[8, 2, 2]$ | $-1$ |