$p$-adic properties of certain half-integral weight modular forms

TL;DR

This paper investigates the $p$-adic properties of specific half-integral weight modular forms, extending the understanding of their behavior under Hecke operators in the context of Zagier's and Folsom-Ono's grids.

Contribution

It introduces a detailed analysis of $p$-adic properties of weakly holomorphic and mock modular forms of weights 3/2 and 1/2, expanding prior work on modular form grids.

Findings

Identifies $p$-adic behaviors of modular forms under Hecke operators.

Extends the understanding of Zagier's and Folsom-Ono's modular form grids.

Provides new insights into the structure of half-integral weight modular forms.

Abstract

In this paper, we study the parallel cases of Zagier's and Folsom-Ono's grids of weakly holomorphic (resp. weakly holomorphic and mock modular) forms of weights 3/2 and 1/2, investigating their $p$-adic properties under the action of Hecke operators.