The study of Fourier coefficients of modular forms has a long and rich history, from Ramanujan’s conjectures to the modularity theorem relating modular forms to elliptic curves. In this talk, we first present the arithmetic–geometric viewpoint on modular forms provided by modular curves, and use it to study certain congruences. These may first appear as numerical coincidences, but in fact hide structures arising from the geometry and cohomology of modular curves in p-adic setting. this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006)