On some free algebras of orthogonal modular forms II

In this paper we construct 16 free algebras of modular forms on type IV symmetric domains for some reflection groups related to the eight rescaled root lattices $$A_1(2)$$ , $$A_1(3)$$ $$A_1(4)$$ $$2A_1(2)$$ $$A_2(2)$$ $$A_2(3)$$ $$A_3(2)$$ $$D_4(2)$$ . As a corollary, prove modularity formal Fourier–Jacobi expansions these groups.