Differential automorphisms for modular forms on Γ0(4)

Abstract

If k ∈ 1 2 N, then let M k ( 0 (4)) be the usual space of half integral weight modular forms. Ono constructed differential endomorphisms of M k ( 0 (4)) by using the usual differential operator. Here we construct a similar set of differential endomorphisms using a linear combination of the differential operator and the quasi-modular forms E 2 , E 2 |V 2 , and E 2 |V 4 . We compute a full set of eigenforms with eigenvalues, and we prove that these endomorphisms are in fact automorphisms.