Modular Forms over Imaginary Quadratic Fields

• Introduction
  • Algorithms
  • Categories
  • Verbose Output
• Creation
  • BianchiCuspForms(F, N): FldNum, RngOrdIdl → ModFrmBianchi
• Attributes
  • BaseField(M): ModFrmBianchi → FldNum
  • BaseRing(M): ModFrmBianchi → FldNum
  • CoefficientField(M): ModFrmBianchi → FldNum
  • CoefficientRing(M): ModFrmBianchi → FldNum
  • Level(M): ModFrmBianchi → RngOrdIdl
  • Dimension(M): ModFrmBianchi → RngIntElt
  • VoronoiData(M): ModFrmBianchi → Rec
  • Example: Spaces of Bianchi Modular Forms
• Hecke Operators
  • HeckeOperator(M, P): ModFrmBianchi, RngOrdIdl → Mtrx
  • Example: Hecke Operators on Bianchi Cusp Forms
• New Spaces and Newforms
  • NewSubspace(M): ModFrmBianchi → ModFrmBianchi
  • NewformDecomposition(M): ModFrmBianchi → List
  • Eigenform(M): ModFrmBianchi → ModFrmBianchiElt
• Bibliography