Apparaît dans la collection : Summer School 2022 - Cohomology, Geometry and Explicit number theory (COGENT)

In this talk, we introduce families of subgroups of finite index in the modular group, generalizing the congruence subgroups. One source of such families is studying homomorphisms of the modular group into linear algebraic groups over finite fields. In particular, we examine a family of noncongruence subgroups arising from a map into a quasi-unipotent group. Using the fact that the tower of curves in this case contains the tower of isogenies over the elliptic curve $y^2=x^3-1728$ defined by the commutator subgroup of the modular group, we provide a detailed discussion of the corresponding modular forms.