  Cosmological models where spatial sections are the Poincar\'e dodecahedral
space D have been recently invoked to give an account of the lower modes of the
angular anisotropies of the cosmic microwave background. Further explorations
of this possibility require the knowledge of the eigenmodes of the Laplacian of
D. Only the first modes have been calculated numerically. Here we give an
explicit form for these modes up to arbitrary order, in term of eigenvectors of
a small rank matrix, very easy to calculate numerically. As an illustration we
give the first modes, up to the eigenvalue $-k (k+2)$ for $k=62$. These results
are obtained by application of a more general method (presented in a previous
work) which allows to express the properties of any eigenfunction of the
Laplacian of the three sphere under an arbitrary rotation of SO(4).
