Chiral de Rham complex on the upper half plane and modular forms.
For any congruence subgroup \Gamma$ we study the vertex operator algebra \Omega^{ch}\mathbb H,\Gamma) constructed from the \Gamma$ invariant global sections of the chiral de Rham complex on the upper half plane, which are holomorphic at all the cusps. We introduce an $SL(2,\mathbb R) invariant filtration on the global sections and show that the \Gamma$ invariants on the graded algebra is isomorphic to certain copies of modular forms. We also give an explicit formula for the lifting of modular forms to \Omega^{ch}\mathbb H,\Gamma) and compute the character formula of \Omega^{ch}\mathbb H,\Gamma) Furthermore, we show that the vertex algebra structure modifies the Rankin Cohen bracket, and the modified bracket becomes non zero between constant modular forms involving the Eisenstein series.