  We compute the Hodge polynomials for the moduli space of representations of
an elliptic curve with two marked points into SL(2,C). When we fix the
conjugacy classes of the representations around the marked points to be
diagonal and of modulus one, the character variety is diffeomorphic to the
moduli space of strongly parabolic Higgs bundles, whose Betti numbers are
known. In that case we can recover some of the Hodge numbers of the character
variety. We extend this result to the moduli space of doubly periodic
instantons.
