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 Donnelly-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].
Galois conjugate levels were added by John Cremona and Aurel Page.
Thanks to Dan Yasaki for fixing an issue with Hecke eigenvalues that had inadvertently been cyclically permuted.
Coding for pages was done by John Cremona and John Voight.