Computing bases of modular forms using the graded algebra structure [article]

Michael Lam, Noah McClelland, Matthew Petty, John Webb
2017 arXiv   pre-print
We develop a new algorithm to compute a basis for M_k(Γ_0(N)), the space of weight k holomorphic modular forms on Γ_0(N), in the case when the graded algebra of modular forms over Γ_0(N) is generated at weight two. Our tests show that this algorithm significantly outperforms a commonly used algorithm which relies more heavily on modular symbols.
arXiv:1709.07475v1 fatcat:qctj7wndw5gd7beczdn4lyhtte