Let $\Gamma$ denote a cofinite Fuchsian subgroup. In the context of Arakelov theory, the canonical Green’s function associated with $\Gamma$ is a fundamental analytic object. It plays an important role in the study of arithmetic invariants of modular curves. In particular, effective bounds for the canonical Green’s function are essential for establishing asymptotic formulas for Arakelov invariants, such as the Arakelov self-intersection number of the relative dualizing sheaf, associated with modular curves corresponding to congruence subgroups of level $N$, where $N$ is a positive integer. In this talk, I will present an approach to obtaining effective bounds for the canonical Green’s function, following ideas inspired by the work of Jorgenson and Kramer. I will then briefly discuss how these bounds are applied in Arakelov theory to derive asymptotic estimates for arithmetic invariants of modular curves.