  We compute the de Rham cohomology of the weak stable foliation of the
geodesic flow of a connected orientable closed hyperbolic surface with various
coefficients. For most of the coefficients, we also give certain "Hodge
decompositions" of the corresponding de Rham complexes, which are not obtained
by the usual Hodge theory of foliations. These results are based on unitary
representation theory of $\mathrm{PSL}(2,\mathbb{R})$. As an application we
obtain an answer to a problem considered by Haefliger and Li around 1980.
