Algorithms and the Jacquet-Lang-lands Correspondence
Algorithm I (Using Definite Quaternion Orders)
Algorithm II (Using Indefinite Quaternion Orders)
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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Wed Apr 24 15:09:57 EST 2013