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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