Zagier duality and integrality for Fourier coefficients for weakly holomorphic modular forms

Abstract

In this note, we generalize the isomorphisms to the case when the discriminant form is not necessarily induced from real quadratic fields. In particular, this general setting includes all the subspaces with epsilon-conditions, only two spacial cases of which were treated before. With this established, we shall prove the Zagier duality for canonical bases. Finally, we raise a question on the integrality of the Fourier coefficients of these bases elements, or equivalently we concern the existence of a Miller-like basis for vector valued modular forms.

Worked out the isomorphisms for a general sign vector; proved Zagier duality for canonical bases; raise a question on integrality; 24 pages

References in corpus (2)

• An Isomorphism between Scalar-Valued Modular Forms and Modular Forms for Weil Representations
• Zagier duality for harmonic weak Maass forms of integral weight

Cited by in corpus (1)

• Divisibility properties for weakly holomorphic modular forms with sign vectors