Introduction

      Definitions and Background

      Algorithms and Supported Groups

      Orthogonal Modular Forms

      Unitary Modular Forms

      Categories

      Verbose Output

 
Creation of Spaces of Algebraic Modular Forms
      AlgebraicModularForms(G) : GrpRed -> ModFrmAlg
      AlgebraicModularForms(data) : List -> ModFrmAlg
      OrthogonalModularForms(Q, W) : AlgMatElt, GrpRep -> ModFrmAlg
      OrthogonalModularForms(F, Q, W, p) : Fld, AlgMatElt, [RngIntElt], RngIntElt -> ModFrmAlg
      OrthogonalModularForms(L) : Lat -> ModFrmAlg
      Example ModFrmAlg_creation-example (H151E1)
      UnitaryModularForms(Q, W) : AlgMatElt, GrpRep -> ModFrmAlg
      UnitaryModularForms(F, Q, W, p) : Fld, AlgMatElt, [RngIntElt], RngIntElt -> ModFrmAlg

 
Basic Properties
      BaseRing(M) : ModFrmAlg -> Rng
      FieldOfDefinition(M) : ModFrmAlg -> FldOrd
      InnerForm(M) : ModFrmAlg -> AlgMatElt
      Weight(M) : ModFrmAlg -> GrpRep
      Level(M) : ModFrmAlg -> LatNF
      IsOrthogonal(M) : ModFrmAlg -> BoolElt
      IsSpecialOrthogonal(M) : ModFrmAlg -> BoolElt
      Dimension(M) : ModFrmAlg -> RngIntElt
      VectorSpace(M) : ModFrmAlg -> ModTupFld
      Example ModFrmAlg_basic-example (H151E2)
      Genus(M) : ModFrmAlg -> SymGen
      GenusReps(M) : ModFrmAlg -> [ Lat ]
      SetGenus(M, reps) : ModFrmAlg, [ Lat ] ->
      AutomorphismGroups(M) : ModFrmAlg -> [GrpMat]
      SetAutomorphismGroups(M, groups) : ModFrmAlg, [GrpMat] ->

 
Elements
      Parent(f) : ModFrmAlgElt -> ModFrmAlg
      BaseField(f) : ModFrmAlgElt -> Fld
      IsCuspidal(f) : ModFrmAlgElt -> BoolElt
      IsEisenstein(f) : ModFrmAlgElt -> BoolElt

 
Operators
      HeckeOperator(M, P, k) : ModFrmHil, RngOrdIdl, RngIntElt -> AlgMatElt
      Example ModFrmAlg_hecke (H151E3)
      HeckeOperator(M, P, k) : ModFrmHil, RngOrdIdl, RngIntElt -> AlgMatElt
      PerestroikaOperator(M, P) : ModFrmHil, RngOrdIdl -> AlgMatElt
      PlusOperator(M, P) : ModFrmHil, RngOrdIdl -> AlgMatElt
      HeckeOperators(M, k) : ModFrmAlg, RngIntElt -> [ AlgMatElt ], [ RngOrdIdl ]
      SetHeckeOperator(M, T, P, k) : ModFrmAlg, AlgMatElt, RngOrdIdl, RngIntElt ->
      HeckeImages(M, i, n, k) : ModFrmAlg, RngIntElt, RngIntElt, RngIntElt -> Assoc

 
Creation of Subspaces
      CuspidalSubspace(M) : ModFrmAlg -> ModMatFld

 
Eigenspace Decomposition and Eigenforms
      Decomposition(M, B) : ModFrmAlg, RngIntElt -> [ ModTupFld ], BoolElt
      HeckeEigenforms(M) : ModFrmAlg -> [ ModFrmAlgElt ]
      EisensteinSeries(M) : ModFrmAlg -> [ ModFrmAlgElt ]
      HeckeEigenform(M, data) : ModFrmAlg, Tup -> ModFrmAlgElt
      HeckeEigenvalue(f, P) : ModFrmAlgElt, RngOrdIdl -> FldElt
      HeckeEigenvalues(f, P) : ModFrmAlgElt, RngOrdIdl -> [ FldElt ]
      HeckeEigensystems(M, k) : ModFrmAlg, RngIntElt -> List, [ RngOrdIdl ]
      DisplayHeckeEigensystem(f) : ModFrmAlgElt ->
      HeckeEigensystem(f, k) : ModFrmAlgElt, RngIntElt -> [ FldElt ], [ RngOrdIdl ]
      LPolynomial(f, P, d) : ModFrmAlgElt, RngOrdIdl, RngIntElt -> RngSerPowElt
      LPolynomials(f) : ModFrmAlgElt -> [ RngUPolElt ]
      SatakePolynomialUnramified(M) : ModFrmAlg -> RngUPolElt
      SatakePolynomial(f, p) : ModFrmAlgElt, RngIntElt -> RngSerPowElt
      SatakePolynomialBallot(r, a) : RngIntElt, RngIntElt -> RngUPolElt
      Example ModFrmAlg_eigenform-examples (H151E4)

 
Relation to Other Modular Forms
      ModularForm(f) : ModFrmAlgElt -> ModFrmElt
      ThetaSeries(f) : ModFrmAlgElt -> RngSerPowElt
      ThetaSiegel(f, g) : ModFrmAlgElt, RngIntElt -> Assoc
      ShimuraLift(f, k, N) : RngSerPowElt, RngIntElt, RngIntElt -> RngSerPowElt
      Example ModFrmAlg_shimura_lift (H151E5)

 
Further Examples
      Example ModFrmAlg_orthogonal_rank4_disc193 (H151E6)
      Example ModFrmAlg_unitary_rank3_discm7-example (H151E7)

 
Bibliography

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