Hilbert Modular Forms
- Introduction
- Creation of Full Cuspidal Spaces
- Caching Spaces of Modular Forms
- Basic Properties
BaseField(M): ModFrmHilBaseRing(M): ModFrmHilCoefficientField(M): ModFrmHilCoefficientRing(M): ModFrmHilWeight(M): ModFrmHil → SeqEnum[RngIntElt]CentralCharacter(M): ModFrmHil → RngIntEltLevel(M): ModFrmHil → RngOrdIdlDirichletCharacter(M): ModFrmHil → GrpDrchNFEltIsCuspidal(M): ModFrmHil → BoolEltIsNew(M): ModFrmHil → BoolEltNewLevel(M): ModFrmHil → RngOrdIdlDimension(M): ModFrmHil → RngIntEltQuaternionOrder(M): ModFrmHil → AlgAssVOrdIsDefinite(M): ModFrmHil → BoolElt- Example: Level and Weight of a Hilbert Space
- Elements
- Operators
HeckeOperator(M, P): ModFrmHil, RngOrdIdl → Mtrx- Example: Hecke Operators on Hilbert Forms
AtkinLehnerOperator(M, P): ModFrmHil, RngOrdIdl → MtrxDegeneracyOperator(M, P, Q): ModFrmHil, RngOrdIdl, RngOrdIdl → MtrxDeleteHeckePrecomputation(O): AlgAssVOrdDeleteHeckePrecomputation(O, P): AlgAssVOrd, RngOrdIdl
- Creation of Subspaces
- Eigenspace Decomposition and Eigenforms
HeckeEigenvalueBound(M, P): ModFrmHil, RngOrdIdl → RngIntEltNewformDecomposition(M): ModFrmHil → ListNewformsOfDegree1(M): ModFrmHil → ListEigenform(M): ModFrmHil → ModFrmHilEltEigenforms(M): ModFrmHil → ListHeckeEigenvalueField(M): ModFrmHil → FldHeckeEigenvalue(f, P): ModFrmHilElt, RngOrdIdl → FldAlgElt- Example: Newforms for Elliptic Curves of Conductor 11
- Further Examples
- Bibliography