Calculating Modular Forms Using the Graded Algebra Structure

main.sage: Code for Sagemath for computing a basis for M_k(Gamma_0(N)) when the level N graded algebra of modular forms is generated at weight two
INSTRUCTIONS.txt: Instructions for using the above code
sage_v_our_algorithm_data.xls: Speed and memory comparisons between Sage's internal algorithm and our own. Our experiments were run on a 24-core AMD Opteron 6344 server with 64GB of RAM running Sage 6.4.1 in CentOS 6.8.