  We show that low-lying eigenmodes of the Laplace operator are suitable to
represent properties of the underlying SU(2) lattice configurations. We study
this for the case of finite temperature background fields, yet in the
confinement phase. For calorons as classical solutions put on the lattice, the
lowest mode localizes one of the constituent monopoles by a maximum and the
other one by a minimum, respectively. We introduce adjustable phase boundary
conditions in the time direction, under which the role of the monopoles in the
mode localization is interchanged. Similar hopping phenomena are observed for
thermalized configurations. We also investigate periodic and antiperiodic modes
of the adjoint Laplacian for comparison.
  In the second part we introduce a new Fourier-like low-pass filter method. It
provides link variables by truncating a sum involving the Laplacian eigenmodes.
The filter not only reproduces classical structures, but also preserves the
confining potential for thermalized ensembles. We give a first characterization
of the structures emerging from this procedure.
