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Magma
Computer • algebra
Documentation
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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 (H146E1)
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 (H146E2)
Elements
Parent(f) : ModFrmHilElt -> ModFrmHil
BaseField(f) : ModFrmHilElt -> Fld
Operators
HeckeOperator(M, P) : ModFrmHil, RngOrdIdl -> Mtrx
Example
ModFrmHil_hecke (H146E3)
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 (H146E4)
Example
ModFrmHil_newsubspace-example2 (H146E5)
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 (H146E6)
Further Examples
Example
ModFrmHil_integral-hecke (H146E7)
Example
ModFrmHil_classical-example (H146E8)
Bibliography
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V2.28, 13 July 2023