  Cosmologists are taking a renewed interest in multiconnected spherical
3-manifolds (spherical spaceforms) as possible models for the physical
universe. To understand the formation of large scale structures in such a
universe, cosmologists express physical quantities, such as density
fluctuations in the primordial plasma, as linear combinations of the eigenmodes
of the Laplacian, which can then be integrated forward in time. This need for
explicit eigenmodes contrasts sharply with previous mathematical
investigations, which have focused on questions of isospectrality rather than
eigenmodes. The present article provides explicit orthonormal bases for the
eigenmodes of lens and prism spaces. As a corollary it extends known results on
spectra from homogeneous lens spaces L(p,1) [Ikeda 1995] to arbitrary lens
spaces L(p,q).
