This is a space of vector valued Siegel modular forms with real representation $\mathrm{Det}^{ 16}\otimes\mathrm{Sym}^{ 0 }$. The following table gives the dimensions of various subspaces of $M_{16, 0}(\mathrm{Sp}(4, \mathbb{Z}))$.

Total4
Eisenstein1
Klingen1
Maass2
Interesting0

The following samples live in this space.

16_E   16_Klingen   16_Maass