  Using group theoretical and numerical methods we have calculated the exact
energy spectrum of the two-dimensional Hubbard model on square lattices with
four electrons for a wide range of the interaction strength. All known
symmetries, i.e.\ the full space group symmetry, the SU(2) spin symmetry, and,
in case of a bipartite lattice, the SU(2) pseudospin symmetry, have been taken
explicitly into account. But, quite remarkably, a large amount of residual
degeneracies remains giving strong evidence for the existence of a yet unknown
symmetry. The level spacing distribution and the spectral rigidity are found to
be in close to but not exact agreement with random matrix theory. In contrast,
the level velocity correlation function presents an unexpected exponential
decay qualitatively different from random matrix behavior.
