Base field 3.3.1016.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[8, 8, -2w^{2} + w + 13]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 12x^{4} + 35x^{2} - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w - 3]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w^{2} - w - 5]$ | $-\frac{1}{2}e^{3} + \frac{7}{2}e$ |
| 9 | $[9, 3, w^{2} + w - 1]$ | $-\frac{1}{2}e^{5} + 5e^{3} - \frac{21}{2}e$ |
| 13 | $[13, 13, 2w^{2} - 2w - 11]$ | $\phantom{-}e^{3} - 5e$ |
| 29 | $[29, 29, -w^{2} - 3w - 1]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{11}{2}e^{3} + 14e$ |
| 29 | $[29, 29, -w^{2} + w + 3]$ | $-2e$ |
| 29 | $[29, 29, 2w - 5]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{11}{2}e^{2} + 10$ |
| 31 | $[31, 31, -w^{2} + w + 1]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + 5e$ |
| 37 | $[37, 37, -2w - 1]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{13}{2}e^{3} + 21e$ |
| 43 | $[43, 43, -2w - 3]$ | $-\frac{1}{2}e^{5} + 5e^{3} - \frac{17}{2}e$ |
| 47 | $[47, 47, 2w - 3]$ | $\phantom{-}4$ |
| 59 | $[59, 59, 4w^{2} + 8w - 1]$ | $\phantom{-}e^{4} - 9e^{2} + 14$ |
| 61 | $[61, 61, -w^{2} - w - 1]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{3}{2}e^{2} - 10$ |
| 67 | $[67, 67, w^{2} + w - 5]$ | $\phantom{-}\frac{3}{2}e^{4} - \frac{21}{2}e^{2} + 10$ |
| 71 | $[71, 71, w^{2} - w - 9]$ | $-\frac{3}{2}e^{4} + \frac{17}{2}e^{2} + 4$ |
| 73 | $[73, 73, -2w^{2} + 2w + 9]$ | $\phantom{-}\frac{1}{2}e^{5} - 6e^{3} + \frac{35}{2}e$ |
| 73 | $[73, 73, 6w^{2} + 10w - 7]$ | $\phantom{-}e^{4} - 9e^{2} + 8$ |
| 73 | $[73, 73, 3w^{2} - 3w - 17]$ | $\phantom{-}e^{5} - \frac{19}{2}e^{3} + \frac{31}{2}e$ |
| 79 | $[79, 79, -2w^{2} + 2w + 15]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{11}{2}e^{2} + 8$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w - 3]$ | $-1$ |