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HILBERT MODULAR FORMS

 
Acknowledgements
 
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
 
Basic Properties
 
Elements
 
Operators
 
Creation of Subspaces
 
Eigenspace Decomposition and Eigenforms
 
Further Examples
 
Bibliography







DETAILS

 
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 (H137E1)

 
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 (H137E2)

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

 
Operators
      HeckeOperator(M, P) : ModFrmHil, RngOrdIdl -> Mtrx
      Example ModFrmHil_hecke (H137E3)
      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 (H137E4)
      Example ModFrmHil_newsubspace-example2 (H137E5)

 
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 (H137E6)

 
Further Examples
      Example ModFrmHil_integral-hecke (H137E7)
      Example ModFrmHil_classical-example (H137E8)

 
Bibliography

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Version: V2.19 of Mon Dec 17 14:40:36 EST 2012