A trace formula for vector-valued modular forms

A Simple Trace Formula for Algebraic Modular Forms

We derive an elementary formula for the trace of a Hecke operator acting on a space of algebraic modular forms, as a sum of character values. We describe explicit computations in the case of the unitary group U(4), allowing the determination of the eigenvalues of a certain Hecke operator. This produces numerical evidence for a U(2, 2) analogue of Harder’s conjecture, on congruences between Heck...

Vector valued hermitian and quaternionic modular forms

Construction of Vector Valued Modular Forms from Jacobi Forms

We give a geometrical construction of the canonical automorphic factor for the Jacobi group and construct new vector valued modular forms from Jacobi forms by differentiating them with respect to toroidal variables and then evaluating at zero.

Vector-valued modular forms associated to linear ordinary differential equations

We consider a class of linear ordinary differential equations determined by a modular form of weight one, and construct vector-valued modular forms of weight two by using solutions of such differential equations.

Structure of the module of vector-valued modular forms

Let V be a representation of the modular group Γ of dimension p. We show that the Z-graded space H(V ) of holomorphic vector-valued modular forms associated to V is a free module of rank p over the algebra M of classical holomorphic modular forms. We study the nature of H considered as a functor from Γ-modules to graded M-lattices and give some applications, including the calculation of the Hil...