## Hilbert Modular Forms and Modular Elliptic Curves

Information: In these tables, we tabulate some Hilbert modular forms for a number of totally real fields up to degree 6. For information on how this data was computed, see the paper Tables of Hilbert modular forms and elliptic curves over totally real fields (with Steve Donnelly, in preparation).

This data is intended for download and manipulation/importation as text files. To browse the data interactively, check out the LMFDB.

Each gzipped text file is formatted to load in Magma.

• COEFFS is a minimal polynomial for F with the convention:

[a[1],a[2],...,a[n+1]] corresponds to a[n+1]*x^n + ... + a[2]*x + a[1];

• n is the degree [F:Q];
• d is the discriminant of F;
• PRIMES is the list of primes (up to at least norm 1000), with the convention:

[N, n, alpha] corresponds to the ideal frakN of norm N generated by n and alpha, where n is the smallest positive integer in frakN;

• NEWFORMS is the list of newforms f, specified by the data
N, label, eigenvalues    or    N, label, g, eigenvalues
where:
• N is the level of f;
• label is an (arbitrary) label ("a", "b", ..., "z", "aa", ...);
• g is the minimal polynomial for the field H_f of Hecke eigenvalues, generated by e, absent if H_f = Q;
• eigenvalues is a list of eigenvalues with entries in H_f, each specified by a polynomial in e.

Only one representative of a level up to automorphisms of F appears. In particular, if F is Galois, then only one level up to the action of Galois is listed. The conjugate levels, by a theorem of Shimura, are obtained by applying the permutation of the list of primes induced by an automorphism to the list of eigenvalues.

The tables are cumulative and complete up to a given level norm, so if no entry appears in a given level then it has dimension zero. There is also a maximal level norm computed for each field.

The data is hosted by the NECC File Exchange.

UPDATE (June 2016)! There was a problem in labelling of the primes for certain cyclic degree 3 and degree 5 fields: for approximately 500 forms of squarefull level, the Hecke eigenvalues for a split prime were unfortunately permuted. The files affected are:
• Degree 3: 00049, 00081, 00169, 00361, 00961, 01369, 01849
• Degree 5: 0014641
This also affects the ecdata for degree 3 and 5. The files below are fixed, and the LMFDB has been updated accordingly.

fields

fields

fields

fields

fields