  In this note we describe a method to calculate the action of a particular
Fourier-Mukai transformation on a basis of brane charges on elliptically
fibered Calabi-Yau threefolds with and without a section. The Fourier-Mukai
kernel is the ideal sheaf of the relative diagonal and for fibrations that
admit a section this is essentially the Poincar\'e sheaf. We find that in this
case it induces an action of the modular group on the charges of 2-branes.
