Basic properties
| Space: | $M_{16}\left(\textrm{Sp}(8,\mathbb{Z})\right)$ |
| Type: | cusp form |
| Weight: | 16 |
| Hecke eigenform: | yes |
| Integral Fourier coefficients: | unknown |
Coefficient field
| Field: | \(\Q(\sqrt{18209}) \) |
| Degree: | 2 |
| Discriminant: | $131 \cdot 139$ |
| Signature: | $(2, 0)$ |
| Is Galois: | True |
| Field polynomial: |
$x^{2} - 18209$ |
| Field generator: | $a$ |
Selected eigenvalues $\lambda(l)$ of $T(l)$
| $l$ | $\lambda(l)$ |
|---|
| $2$ | $-132710400 a - 25111756800$ |
Selected Fourier coefficients $c(F)$
| \(\det(F)\) | \(F\) | $c(F)$ |
|---|
| 5 |
(2, 2, 2, 2, 1, 0, 0, 1, 0, 1) | $45 a - 2835$ |
| 8 |
(2, 2, 2, 2, 0, 0, 0, 1, 1, 0) | $72 a + 29640$ |
| 9 |
(2, 2, 2, 2, 1, 0, 0, 0, 0, 1) | $1782 a - 112266$ |
| 12 |
(2, 2, 2, 2, 0, 0, 0, 1, 0, 0) | $11664 a - 734832$ |
| 16 |
(2, 2, 2, 2, 0, 0, 0, 0, 0, 0) | $-34560 a + 10151680$ |
Select different
$\lambda(l)$ and $c(F)$ to display or specify a modulus $\mathfrak{m}$ to reduce them by
| $\lambda(l)$ available for $l$ in: |
2
|
| $c(F)$ available for $\det(F)$ in: |
4
5
8
9
12
16
64
|
Download
(json file containing all available data)
