Chiral de Rham Complex on the Upper Half Plane and Modular Forms

Abstract For any congruence subgroup $\Gamma $, we study the vertex operator algebra $\Omega ^{ch}(\mathbb H,\Gamma )$ constructed from $-invariant global sections of chiral de Rham complex on upper half plane, which are holomorphic at all cusps. We construct a basis in terms modular forms $ and compute its character. show that operations determined by modification Rankin–Cohen brackets forms.