  In this paper we use fractal geometry to investigate boundary aspects of the
first homology group for finite coverings of the modular surface. We obtain a
complete description of algebraically invisible parts of this homology group.
More precisely, we first show that for any modular subgroup the geodesic
forward dynamic on the associated surface admits a canonical symbolic
representation by a finitely irreducible shift space. We then use this
representation to derive an `almost complete' multifractal description of the
higher--dimensional level sets arising from Manin--Marcolli's limiting modular
symbols.
