Introduction

      Definitions and Background

      Algorithms and the Jacquet-Lang-lands Correspondence

      Algorithm I (Using Definite Quaternion Orders)

      Algorithm II (Using Indefinite Quaternion Orders)

      Categories

      Verbose Output

 
Creation of Full Cuspidal Spaces
      HilbertCuspForms(F, N, k) : FldNum, RngOrdIdl, SeqEnum -> ModFrmHil
      Example ModFrmHil_creation-example (H149E1)

 
Caching Spaces of Modular Forms
      SetStoreModularForms(F, v) : Fld, BoolElt ->
      ClearStoredModularForms(F) : Fld ->

 
Basic Properties
      BaseField(M) : ModFrmHil ->
      Weight(M) : ModFrmHil -> SeqEnum[RngIntElt]
      CentralCharacter(M) : ModFrmHil -> RngIntElt
      Level(M) : ModFrmHil -> RngOrdIdl
      DirichletCharacter(M) : ModFrmHil -> GrpDrchNFElt
      IsCuspidal(M) : ModFrmHil -> BoolElt
      IsNew(M) : ModFrmHil -> BoolElt
      NewLevel(M) : ModFrmHil -> RngOrdIdl
      Dimension(M) : ModFrmHil -> RngIntElt
      QuaternionOrder(M) : ModFrmHil -> AlgAssVOrd
      IsDefinite(M) : ModFrmHil -> BoolElt
      Example ModFrmHil_basic-example (H149E2)

 
Elements
      Parent(f) : ModFrmHilElt -> ModFrmHil
      BaseField(f) : ModFrmHilElt -> Fld

 
Operators
      HeckeOperator(M, P) : ModFrmHil, RngOrdIdl -> Mtrx
      Example ModFrmHil_hecke (H149E3)
      AtkinLehnerOperator(M, P) : ModFrmHil, RngOrdIdl -> Mtrx
      DegeneracyOperator(M, P, Q) : ModFrmHil, RngOrdIdl, RngOrdIdl -> Mtrx
      DeleteHeckePrecomputation(O) : AlgAssVOrd ->

 
Creation of Subspaces
      NewSubspace(M) : ModFrmHil -> ModFrmHil
      SetRationalBasis(M) : ModFrmHil ->
      Example ModFrmHil_newsubspace-example1 (H149E4)
      Example ModFrmHil_newsubspace-example2 (H149E5)

 
Eigenspace Decomposition and Eigenforms
      HeckeEigenvalueBound(M, P) : ModFrmHil, RngOrdIdl -> RngIntElt
      NewformDecomposition(M) : ModFrmHil -> List
      NewformsOfDegree1(M) : ModFrmHil -> List
      Eigenform(M) : ModFrmHil -> ModFrmHilElt
      Eigenforms(M) : ModFrmHil -> List
      HeckeEigenvalueField(M) : ModFrmHil -> Fld
      HeckeEigenvalue(f, P) : ModFrmHilElt, RngOrdIdl -> FldAlgElt
      Example ModFrmHil_eigenform-examples (H149E6)

 
Further Examples
      Example ModFrmHil_integral-hecke (H149E7)
      Example ModFrmHil_classical-example (H149E8)

 
Bibliography

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