Base field 4.4.19664.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 2x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[8, 4, -w^{3} + 2w^{2} + 4w]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 14x^{6} + 59x^{4} - 70x^{2} + 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}0$ |
| 2 | $[2, 2, -w - 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w^{3} + 2w^{2} + 5w - 1]$ | $-\frac{1}{2}e^{4} + \frac{7}{2}e^{2} - 1$ |
| 7 | $[7, 7, -w^{3} + 2w^{2} + 5w - 3]$ | $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} - 8e$ |
| 29 | $[29, 29, -w^{2} + w + 3]$ | $-\frac{1}{2}e^{6} + 6e^{4} - \frac{37}{2}e^{2} + 11$ |
| 29 | $[29, 29, 2w^{3} - 5w^{2} - 7w + 9]$ | $\phantom{-}\frac{1}{2}e^{4} - \frac{7}{2}e^{2} + 5$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 5w + 1]$ | $\phantom{-}e^{5} - 9e^{3} + 16e$ |
| 41 | $[41, 41, -w^{3} + 4w^{2} - w - 3]$ | $\phantom{-}\frac{1}{2}e^{6} - 5e^{4} + \frac{19}{2}e^{2} + 5$ |
| 43 | $[43, 43, -w^{3} + 3w^{2} + 2w - 5]$ | $\phantom{-}\frac{1}{2}e^{7} - 7e^{5} + \frac{57}{2}e^{3} - 26e$ |
| 47 | $[47, 47, w^{2} - 3w - 3]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{5}{2}e^{3} - 2e$ |
| 53 | $[53, 53, w^{3} - 2w^{2} - 3w + 1]$ | $-\frac{1}{2}e^{6} + 5e^{4} - \frac{23}{2}e^{2} + 5$ |
| 59 | $[59, 59, w^{2} - w - 5]$ | $-e^{7} + 13e^{5} - 48e^{3} + 40e$ |
| 61 | $[61, 61, 5w^{3} - 12w^{2} - 19w + 17]$ | $\phantom{-}e^{6} - \frac{21}{2}e^{4} + \frac{53}{2}e^{2} - 7$ |
| 67 | $[67, 67, 2w^{3} - 5w^{2} - 7w + 5]$ | $\phantom{-}\frac{1}{2}e^{7} - \frac{15}{2}e^{5} + 33e^{3} - 34e$ |
| 67 | $[67, 67, w^{3} - 4w^{2} + w + 5]$ | $\phantom{-}\frac{1}{2}e^{7} - \frac{13}{2}e^{5} + 26e^{3} - 36e$ |
| 67 | $[67, 67, 3w^{3} - 7w^{2} - 12w + 11]$ | $-\frac{1}{2}e^{7} + \frac{13}{2}e^{5} - 24e^{3} + 18e$ |
| 67 | $[67, 67, -2w^{3} + 4w^{2} + 8w - 5]$ | $-\frac{1}{2}e^{7} + 8e^{5} - \frac{71}{2}e^{3} + 32e$ |
| 71 | $[71, 71, -3w^{3} + 8w^{2} + 9w - 9]$ | $-2e^{3} + 10e$ |
| 71 | $[71, 71, -w^{3} + 3w^{2} + 2w - 7]$ | $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + 8e$ |
| 79 | $[79, 79, 3w^{3} - 7w^{2} - 14w + 15]$ | $-\frac{1}{2}e^{7} + 7e^{5} - \frac{61}{2}e^{3} + 40e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $1$ |