Modular Symbols

A program for computing with modular symbols was developed by William Stein as part of his Ph.D. thesis, and redesigned and made part of Magma during a visit to the Magma group in 1999. Algorithmic details, research applications, and references can be found in the Stein's thesis [19] and subsequent work (see http://modular.fas.harvard.edu/papers).

• Construction of spaces of modular symbols of any character, level, and weight
• Computation of Hecke operators
• Decomposition into invariant subspaces
• Computation of certain invariants of the modular abelian varieties
• The intersection pairing on the integral homology of modular curves
• Special values of L-functions and computation of complex period lattices