  For certain subgroups of $M_{24}$, we give vertex operator algebraic module
constructions whose associated trace functions are meromorphic Jacobi forms.
These meromorphic Jacobi forms are canonically associated to the mock modular
forms of Mathieu moonshine. The construction is related to the Conway moonshine
module and employs a technique introduced by Anagiannis--Cheng--Harrison. With
this construction we are able to give concrete vertex algebraic realizations of
certain cuspidal Hecke eigenforms of weight two. In particular, we give
explicit realizations of trace functions whose integralities are equivalent to
divisibility conditions on the number of $\mathbb{F}_p$ points on the Jacobians
of modular curves.
