This is a space of vector valued Siegel modular forms with real representation $\mathrm{Det}^{ 12}\otimes\mathrm{Sym}^{ 10 }$. The following table gives the dimensions of various subspaces of $M_{12, 10}(\mathrm{Sp}(4, \mathbb{Z}))$.
Total | 4 |
Non cusp | 1 |
Cusp | 3 |