The database contains 368,356 Hilbert newforms over 400 totally real number fields of degree up to 6.
For each field for which forms are presented, the data is complete up to a given level norm.
For each form, the Hecke eigenvalue data is complete up to a bound, but this bound depends on the form (so e.g. for forms of large dimension, there may be fewer Hecke eigenvalues than for others of the same level). However, we do ensure that if there is a Hecke eigenvalue with prime of given norm, then all Hecke eigenvalues of that norm (or smaller) are in the database.
When the base field does not have narrow class number 1, the forms over that field may have nontrivial central character (coming from the narrow class group).