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.

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: This also affects the ecdata for degree 3 and 5. The files below are fixed, and the LMFDB has been updated accordingly.

Elliptic Curve Data

Degree 2

Degree 3

Degree 4

Degree 5

Degree 6

Degree 2

fields

0005 0008 0012 0013 0017 0021 0024 0028 0029 0033 0037 0040 0041 0044 0053 0056 0057 0060 0061 0065 0069 0073 0076 0077 0085 0088 0089 0092 0093 0097 0101 0104 0105 0109 0113 0120 0124 0129 0133 0136 0137 0140 0141 0145 0149 0152 0156 0157 0161 0165 0168 0172 0173 0177 0181 0184 0185 0188 0193 0197 0201 0204 0205 0209 0213 0232 0233 0236 0237 0241 0248 0249 0265 0268 0269 0273 0277 0280 0281 0284 0285 0293 0296 0301 0305 0313 0316 0317 0321 0328 0329 0332 0337 0341 0344 0345 0348 0349 0353 0357 0364 0365 0373 0376 0377 0380 0381 0385 0389 0393 0397 0401 0408 0409 0412 0413 0417 0421 0424 0428 0429 0433 0437 0440 0444 0445 0449 0453 0456 0457 0460 0461 0465 0469 0472 0473 0476 0481 0485 0488 0489 0492 0493 0497

Degree 3

fields

00049 00081 00148 00169 00229 00257 00316 00321 00361 00404 00469 00473 00564 00568 00621 00697 00733 00756 00761 00785 00788 00837 00892 00940 00961 00985 00993 01016 01076 01101 01129 01229 01257 01300 01304 01345 01369 01373 01384 01396 01425 01436 01489 01492 01509 01524 01556 01573 01593 01620 01708 01765 01772 01825 01849 01901 01929 01937 01940 01944 01957

Degree 4

fields

000725 001125 001600 001957 002000 002048 002225 002304 002525 002624 002777 003600 003981 004205 004225 004352 004400 004525 004752 004913 005125 005225 005725 005744 006125 006224 006809 007053 007056 007168 007225 007232 007488 007537 007600 007625 008000 008069 008112 008468 008525 008725 008768 008789 008957 009225 009248 009301 009792 009909 010025 010273 010304 010309 010512 010816 010889 011025 011197 011324 011344 011348 011525 011661 012197 012357 012400 012544 012725 013025 013068 013448 013525 013625 013676 013725 013768 013824 013888 013968 014013 014197 014272 014336 014400 014656 014725 015125 015188 015317 015529 015952 016225 016317 016357 016400 016448.1 016448.2 016609 016997 017069 017417 017424 017428 017600 017609 017725 017989 018097 018432 018496 018625 018688 018736 019025 019225 019429 019525 019600 019664 019773 019796 019821

Degree 5

fields

0014641 0024217 0036497 0038569 0065657 0070601 0081509 0081589 0089417 0101833 0106069 0117688 0122821 0124817 0126032 0135076 0138136 0138917 0144209 0147109 0149169 0153424 0157457 0160801 0161121 0170701 0173513 0176281 0176684 0179024 0180769 0181057 0186037 0195829

Degree 6

fields

00300125 00371293 00434581 00453789 00485125 00592661 00703493 00722000 00810448 00820125 00905177 00966125 00980125 01075648 01081856 01134389 01202933 01229312 01241125 01259712 01279733 01292517 01312625 01387029 01397493 01416125 01528713 01541581 01683101 01767625 01868969 01922000 01995125 01997632