Transverse stability of the drive beam is critical to plasma wakefield accelerators. A long, relativistic particle beam propagating in an overdense plasma is subject to beam envelope modulation and centroid displacement (hosing) instabilities. Coupled equations for the beam centroid and envelope are derived and solved. It is shown that the hosing growth rate is comparable to self-modulation, and coupling of the self-modulation enhances beam hosing and induces harmonic content. Large amounts of hosing significantly alters the structure of the plasma wakefields.