Details regarding the construction of the database of paramodular forms can be found in the paper A database of paramodular forms from quinary orthogonal modular forms [preprint] by Eran Assaf, Watson Ladd, Gustavo Rama, Gonzalo Tornaría and John Voight. In particular, the Siegel paramodular forms data in the LMFDB come from two sources:

For paramodular newforms of weight $(k,j) = (3,0)$ and level $N < 1000$ such that there exists a prime $p \parallel N$ data was computed by Eran Assaf using software available at [https://github.com/assaferan/omf5].

For paramodular newforms of weight $(k,j) = (3,2), (4,0)$ and level $N < 1000$ such that there exists a prime $p \parallel N$ data was computed by Gustavo Rama using software available at [https://gitlab.fing.edu.uy/grama/quinary].
 Review status: beta
 Last edited by Eran Assaf on 20230624 19:59:30
Not referenced anywhere at the moment.
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