Bounds for automorphic L-functions. II.
We give explicit upper bounds for the coefficients of arbitrary weight k, level 2 cusp forms, making Deligne’s well-known bound precise. We also derive asymptotic formulas and explicit upper bounds for the coefficients of certain level 2 modular functions.
We construct a family of modular forms from harmonic Maass Jacobi forms by considering their Taylor expansion and using the method of holomorphic projection. As an application we present a certain type Hurwitz class relations which can be viewed as a generalization of Mertens' result in M. H. Mertens (2016).