Explicit Computation of Cusp forms via Hecke Action on Cohomology and its Complexity

2009/05/18 by Jonas B. Rasmussen, Rasmussen, Jonas B.
Mathematics · #11F11 #11Y16 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0905.2887

openalex publication_date 2009/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the literature, the standard approach to finding bases of spaces of modular forms is via modular symbols and the homology of modular curves. By using the Eichler-Shimura isomorphism, a work by Wang shows how one can use a cohomological viewpoint to determine bases of spaces of cusp forms on Γ₀(N) of weight k ≥ 2 and character χ. It is interesting to look at the complexity of this alternative approach, and we do this for an explicit implementation of the algorithm suggested by Wang.

Related

• Computing actions on cusp forms
• A Hecke-equivariant decomposition of spaces of Drinfeld cusp forms via representation theory, and an investigation of its subfactors
• Hecke eigenforms for meromorphic cusp forms
• Computing bases of modular forms using the graded algebra structure
• Explicit formulas for Hecke operators on cusp forms, Dedekind symbols and period polynomials