It is well known that the first Kronecker limit theorem gives the Laurent expansion of the Eisenstein series $E(z,s)$ over $SL(2,Z)$ at $s=1$; see, for example, Serge Lang's book Elliptic Curves, Section 20.4. 

My question is, is there an analogous formula for the Eisenstein series over congruence subgroups? This seems a natural question and I believe that it must be hidden somewhere in the literature, but I cannot find a reference. 

Any help will be appreciated. Thanks!