  We give a vanishing and classification result for holomorphic differential
forms on smooth projective models of the moduli spaces of pointed K3 surfaces.
We prove that there is no nonzero holomorphic k-form for 0<k<10 and for even
k>19. In the remaining cases, we give an isomorphism between the space of
holomorphic k-forms with that of vector-valued modular forms (9<k<19) or
scalar-valued cusp forms (odd k>18) for the modular group. These results are in
fact proved in the generality of lattice-polarization.
