Kronecker limit formula for Fermat curves

We will consider the n-th Fermat curve together with a cover of projective space. There is a (non congruence) subgroup of the full modular group associated to this cover for which the modular forms are known. We will describe a connection of non-holomorphic Eisenstein series and certain modular forms. From that we can derive the scattering constants that have some applications in Arakelov theory.