# Modular Arithmetic Geometry

Modular CurvesModular curve creation and attributes.

[Modular Curves](ModularCurves/index-modular-curves.md)Small Modular CurvesExplicit models, projections and automorphisms of small modular curves.

[Small Modular Curves](SmallModularCurves/index-small-modular-curves.md)Congruence Subgroups of PSL2(R)Congruence subgroups, their structure and group elements.

[Congruence Subgroups of {\operatorname{PSL}}_2({\mathbb{R}})](CongruenceSubgroupsOfPSL2R/index-congruence-subgroups-of-psl2-r.md)Arithmetic Fuchsian Groups and Shimura CurvesFuchsian groups, fundamental domains and triangle groups.

[Arithmetic Fuchsian Groups and Shimura Curves](ArithmeticFuchsianGroupsAndShimuraCurves/index-arithmetic-fuchsian-groups-and-shimura-curves.md)Modular FormsSpaces of modular forms, bases and q-expansions.

[Modular Forms](ModularForms/index-modular-forms.md)Modular SymbolsModular symbols spaces, creation and bases.

[Modular Symbols](ModularSymbols/index-modular-symbols.md)Brandt ModulesBrandt modules, subspaces and Hecke operators.

[Brandt Modules](BrandtModules/index-brandt-modules.md)Supersingular Divisors on Modular CurvesSupersingular divisors: creation, basis and properties.

[Supersingular Divisors on Modular Curves](SupersingularDivisorsOnModularCurves/index-supersingular-divisors-on-modular-curves.md)Modular Abelian VarietiesModular abelian varieties, homology and morphisms.

[Modular Abelian Varieties](ModularAbelianVarieties/index-modular-abelian-varieties.md)Hilbert Modular FormsHilbert modular forms: creation and basic properties.

[Hilbert Modular Forms](HilbertModularForms/index-hilbert-modular-forms.md)Modular Forms over Imaginary Quadratic FieldsBianchi modular forms, basic properties and Hecke operators.

[Modular Forms over Imaginary Quadratic Fields](ModularFormsOverImaginaryQuadraticFields/index-modular-forms-over-imaginary-quadratic-fields.md)Algebraic Modular FormsAlgebraic modular forms: creation, properties and elements.

[Algebraic Modular Forms](AlgebraicModularForms/index-algebraic-modular-forms.md)Representations of Local FieldsAdmissible representations of GL\ :sub:`2`\ (Q\ :sub:`p`\ ) and local Langlands.

[Admissible Representations of {\operatorname{GL}}_2({\mathbb{Q}}_p)](RepresentationsOfLocalFields/index-representations-of-local-fields.md)