Arithmetic Subgroups of ${\mathrm{SL}}_2(\mathbf{Z})$

This chapter describes the basic functionality for finite index subgroups of the modular group ${\mathrm{SL}}_2(\mathbf{Z})$.

• Arithmetic subgroups, finite index subgroups of ${\mathrm{SL}}_2(\mathbf{Z})$
• Arithmetic subgroups defined by permutations of cosets
• Elements of arithmetic subgroups
• Congruence arithmetic subgroups of ${\mathrm{SL}}_2(\mathbf{Z})$
• Congruence subgroup ${\mathrm{\Gamma }}_H(N)$
• Congruence subgroup ${\mathrm{\Gamma }}_1(N)$
• Congruence subgroup ${\mathrm{\Gamma }}_0(N)$
• Congruence subgroup $\mathrm{\Gamma }(N)$
• The modular group ${\mathrm{SL}}_2(\mathbf{Z})$
• Farey symbol for arithmetic subgroups of ${\mathrm{PSL}}_2(\mathbf{Z})$
• Helper functions for congruence subgroups

Indices and Tables

• Index

• Module Index

• Search Page