# Admissible Representations of ${\operatorname{GL}}_2({\mathbb{Q}}_p)$

- [Introduction](introduction.md)

  - [Motivation](introduction.md#motivation)

  - [Definitions](introduction.md#definitions)

  - [The Principal Series](introduction.md#the-principal-series)

  - [Supercuspidal Representations](introduction.md#supercuspidal-representations)

  - [The Local Langlands Correspondence](introduction.md#the-local-langlands-correspondence)

  - [Connection with Modular Forms](introduction.md#connection-with-modular-forms)

  - [Category](introduction.md#category)

  - [Verbose Output](introduction.md#verbose-output)

- [Creation of Admissible Representations](creation.md)

  - [`LocalComponent(M, p): ModSym, RngIntElt → RepLoc`](creation.md#function-localcomponent-modsym-rngintelt)

  - [`Example: Creation Example`](creation.md#example-ex-7bb24b)

- [Attributes of Admissible Representations](attributes.md)

  - [`CentralCharacter(pi): RepLoc → GrpDrchElt`](attributes.md#function-centralcharacter-reploc)

  - [`Conductor(pi): RepLoc → RngIntElt`](attributes.md#function-conductor-reploc)

  - [`DefiningModularSymbolsSpace(pi): RepLoc → ModSym`](attributes.md#function-definingmodularsymbolsspace-reploc)

  - [`IsMinimal(pi): RepLoc → BoolElt, GrpDrchElt, RepLoc`](attributes.md#function-isminimal-reploc)

  - [`Example: Attributes Example`](attributes.md#example-ex-ad405c)

- [Structure of Admissible Representations](structure.md)

  - [`IsPrincipalSeries(pi): RepLoc → BoolElt`](structure.md#function-isprincipalseries-reploc)

  - [`IsSupercuspidal(pi): RepLoc → BoolElt`](structure.md#function-issupercuspidal-reploc)

  - [`PrincipalSeriesParameters(pi): RepLoc → GrpDrchElt, GrpDrchElt`](structure.md#function-principalseriesparameters-reploc)

  - [`CuspidalInducingDatum(pi): RepLoc → ModGrp`](structure.md#function-cuspidalinducingdatum-reploc)

- [Local Galois Representations](galois.md)

  - [`GaloisRepresentation(pi): RepLoc → GalRep`](galois.md#function-galoisrepresentation-reploc)

  - [`WeilRepresentation(pi): RepLoc → GalRep`](galois.md#function-weilrepresentation-reploc)

  - [`AdmissiblePair(pi): RepLoc → RngPad, Map`](galois.md#function-admissiblepair-reploc)

- [Examples](examples.md)

  - [`Example: example1`](examples.md#example-ex-e326da)

  - [`Example: example2`](examples.md#example-ex-298b2e)

  - [`Example: example3`](examples.md#example-ex-3e3aa7)