Base field 4.4.14336.1
Generator \(w\), with minimal polynomial \(x^{4} - 8x^{2} + 14\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 2, 2]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 32x^{6} + 264x^{4} - 784x^{2} + 768\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^{3} + w^{2} + 5w - 6]$ | $\phantom{-}0$ |
| 7 | $[7, 7, w^{3} - w^{2} - 5w + 7]$ | $\phantom{-}\frac{3}{8}e^{6} - 11e^{4} + 70e^{2} - 112$ |
| 7 | $[7, 7, -w - 1]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w - 1]$ | $\phantom{-}e$ |
| 17 | $[17, 17, w^{2} - w - 5]$ | $\phantom{-}\frac{3}{32}e^{7} - \frac{11}{4}e^{5} + \frac{69}{4}e^{3} - \frac{49}{2}e$ |
| 17 | $[17, 17, w^{2} + w - 5]$ | $\phantom{-}\frac{3}{32}e^{7} - \frac{11}{4}e^{5} + \frac{69}{4}e^{3} - \frac{49}{2}e$ |
| 23 | $[23, 23, -w - 3]$ | $-\frac{1}{8}e^{6} + \frac{7}{2}e^{4} - 19e^{2} + 24$ |
| 23 | $[23, 23, w - 3]$ | $-\frac{1}{8}e^{6} + \frac{7}{2}e^{4} - 19e^{2} + 24$ |
| 25 | $[25, 5, -w^{3} + w^{2} + 4w - 3]$ | $-\frac{7}{32}e^{7} + \frac{13}{2}e^{5} - \frac{171}{4}e^{3} + \frac{143}{2}e$ |
| 25 | $[25, 5, -w^{3} - w^{2} + 4w + 3]$ | $-\frac{7}{32}e^{7} + \frac{13}{2}e^{5} - \frac{171}{4}e^{3} + \frac{143}{2}e$ |
| 41 | $[41, 41, w^{3} - 4w - 1]$ | $-\frac{7}{32}e^{7} + \frac{13}{2}e^{5} - \frac{171}{4}e^{3} + \frac{139}{2}e$ |
| 41 | $[41, 41, -w^{3} + 4w - 1]$ | $-\frac{7}{32}e^{7} + \frac{13}{2}e^{5} - \frac{171}{4}e^{3} + \frac{139}{2}e$ |
| 71 | $[71, 71, -w^{3} + 2w^{2} + 4w - 9]$ | $-\frac{3}{8}e^{7} + 11e^{5} - 70e^{3} + 113e$ |
| 71 | $[71, 71, w^{3} + 2w^{2} - 4w - 9]$ | $-\frac{3}{8}e^{7} + 11e^{5} - 70e^{3} + 113e$ |
| 73 | $[73, 73, w^{3} - w^{2} - 5w + 3]$ | $\phantom{-}\frac{1}{2}e^{6} - 15e^{4} + 101e^{2} - 170$ |
| 73 | $[73, 73, w^{3} + w^{2} - 5w - 3]$ | $\phantom{-}\frac{1}{2}e^{6} - 15e^{4} + 101e^{2} - 170$ |
| 79 | $[79, 79, 2w^{2} - 2w - 9]$ | $-\frac{3}{8}e^{7} + 11e^{5} - 70e^{3} + 114e$ |
| 79 | $[79, 79, -2w^{3} + 8w + 5]$ | $-\frac{3}{8}e^{7} + 11e^{5} - 70e^{3} + 114e$ |
| 81 | $[81, 3, -3]$ | $-\frac{3}{4}e^{6} + 22e^{4} - 139e^{2} + 226$ |
| 89 | $[89, 89, -w^{3} - 2w^{2} + 6w + 13]$ | $-\frac{1}{4}e^{6} + 7e^{4} - 39e^{2} + 54$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-w^{3}+w^{2}+5w-6]$ | $1$ |