- Introduction
- 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
- Elements
- 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
- 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
- Further Examples
- Bibliography
V2.29, 21 October 2025