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Details regarding the construction of the database of classical modular forms can be found in the paper Computing Classical Modular Forms [arXiv:2002.04717 ] by Alex J. Best, Jonathan Bober, Andrew R. Booker, Edgar Costa, John Cremona, Maarten Derickx, David Lowry-Duda, Min Lee, David Roe, Andrew V. Sutherland, and John Voight. In particular, the classical modular forms data in the LMFDB comes from three sources:

For newforms of weight $k=1$ the projective fields cut out by the kernel of the projective Galois representation associated to the newform come from four sources:

Additional acknowledgments

Initial page design and coding was done by Fredrik Strömberg and Stephan Ehlen.

David Lowry-Duda provided the code used to generate the graphical presentations of classical modular forms that appear in the properties box, based on [arXiv:2002.05234 ].