Lifting of Modular Forms

Abstract

The existence and construction of vector-valued modular forms (vvmf) for any arbitrary Fuchsian group G , for any representation ρ : G ⟶ GL d ( ℂ ) of finite image can be established by lifting scalar-valued modular forms of the finite index subgroup ker ( ρ ) of G . In this article vvmf are explicitly constructed for any admissible multiplier (representation) ρ , see Section 3 for the definition of admissible multiplier. In other words, the following question has been partially answered: For which representations ρ of a given G , is there a vvmf with at least one nonzero component?