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The database of Hilbert modular forms was computed by Steve Donnelly and John Voight using algorithms implemented in [Magma] by Lassina Dembele, Steve Donnelly, Markus Kirschmer, and John Voight; the computational effort is described in Dembele-Voight [arXiv:1605.02637] . A detailed overview and mathematical description of these algorithms can be found in a survey by Dembélé-Voight [arXiv:1010.5727] .

Further extensions, including adding Galois conjugate levels, were provided by John Cremona and Aurel Page.