  We employ a multipole-Taylor expansion to investigate how tightly the
gravitational potential of the quadruple-image lens MG J0414+0534 is
constrained by recent VLBI observations. These observations revealed that each
of the four images of the background radio source contains four distinct
components, thereby providing more numerous and more precise constraints on the
lens potential than were previously available. We expand the two-dimensional
lens potential using multipoles for the angular coordinate and a modified
Taylor series for the radial coordinate. After discussing the physical
significance of each term, we compute models of MG J0414+0534 using only VLBI
positions as constraints. The best-fit model has both interior and exterior
quadrupole moments as well as exterior m=3 and m=4 multipole moments. The
deflector centroid in the models matches the optical galaxy position, and the
quadrupoles are aligned with the optical isophotes. The radial distribution of
mass could not be well constrained. We discuss the implications of these models
for the deflector mass distribution and for the predicted time delays between
lensed components.
