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 ${\mathrm{PSL}}_2(\mathbf{Z})$
• Cython helper functions for congruence subgroups

Indices and Tables

• Index

• Module Index

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