2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/132049In 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.20 pages, 1 figureGeometric TopologyK-Theory and HomologyNumber Theory11F06, 20H05, 37F35text