Reliability of Hilbert modular form data (reviewed)

All Hilbert modular form eigenform data has been computed using rigorous algorithms.

• When “is base change” says no, we have certified that the form is not a base change; when yes, there is strong evidence of a base change (Hecke eigenvalues seem to match their conjugates under a nontrivial subgroup of automorphisms) but this has not been rigorously established.
• When “is cm” says no, we have certified that the form is not a CM form; when yes, there is strong evidence that the form has complex multiplication (the form seems to match its twist by a CM character) but this has not been rigorously established.

Wherever possible (specifically, when there is a prime $\mathfrak{p} \parallel \mathfrak{N}$ exactly dividing the level), we computed the forms using both definite and indefinite algorithms (see the description in Donnelly-Voight [arXiv:1605.02637]) and got the same answer.