Angelica Babei - A family of $\phi$-congruence subgroups of the modular group
Angelica Babei, Fanny Bastien · HAL (Le Centre pour la Communication Scientifique Directe) · 2022
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.