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- Title
Families of φ-congruence subgroups of the modular group.
- Authors
Babe, Angelica; Fiori, Andrew; Franc, Cameron
- Abstract
We introduce and study families of finite index subgroups of the modular group that generalize the congruence subgroups. Such groups, termed φ-congruence subgroups, are obtained by reducing homomorphisms φ from the modular group into a linear algebraic group modulo integers. In particular, we examine two families of examples, arising on the one hand from a map into a quasi-unipotent group, and on the other hand from maps into symplectic groups of degree four. In the quasiunipotent case, we also provide a detailed discussion of the corresponding modular forms, using the fact that the tower of curves in this case contains the tower of isogenies over the elliptic curve y² = x³ - 1728 defined by the commutator subgroup of the modular group.
- Subjects
LINEAR algebraic groups; COMMUTATORS (Operator theory); SYMPLECTIC groups; GEOMETRIC congruences; MODULAR forms; MODULAR groups; ELLIPTIC curves
- Publication
Mathematika, 2023, Vol 69, Issue 4, p1104
- ISSN
0025-5793
- Publication type
Article
- DOI
10.1112/mtk.12218