  We study the stability of coherent structures in plane Couette flow against
long-wavelength perturbations in wide domains that cover several pairs of
coherent structures. For one and two pairs of vortices, the states retain the
stability properties of the small domains, but for three pairs new unstable
modes are found. They are shown to be connected to bifurcations that break the
translational symmetry and drive the coherent structures from the spanwise
extended state to a modulated one that is a precursor to spanwise localized
states. Tracking the stability of the orbits as functions of the spanwise wave
length reveals a rich variety of additional bifurcations.
