The Bruinier--Funke pairing and the orthogonal complement of unary theta functions

Abstract

We describe an algorithm for computing the inner product between a holomorphic modular form and a unary theta function, in order to determine whether the form is orthogonal to unary theta functions without needing a basis of the entire space of modular forms and without needing to use linear algebra to decompose this space completely.

Conference proceedings in Springer for L-functions and automorphic forms, held at the University of Heidelberg, February 22-26, 2016