  Using that the overpartition rank function is the holomorphic part of a
harmonic Maass form, we deduce formulas for the rank differences modulo 7. To
do so we make improvements on the current state of the overpartition rank
function in terms of harmonic Maass forms by giving simple formulas for the
transformations under $\mbox{SL}_2(\mathbb{Z})$ as well as formulas for orders
at cusps.
