Code and data for structure of mixed weight Hilbert modular forms (K = Q(sqrt(5)))

Fourier coefficients of generators

In directories "./forms_csv/A*", Fourier coefficients of generators are stored as csv files. Each generator corresponds to each csv file. We fixed an order of generators. For example, A1 has 3 generators. The first generator is of weight (7, 9) and some of its Fourier coefficients are stored in "./forms_csv/A1/gen0_wt_7_9.csv". The second generator is of weight (8, 10) and the third generator is of weight (11, 13). Note that this order may not be the ascending order with respect to weights of generators. In fact, the weights of generators of A7 is ordered so that (5, 19), (4, 18), (7, 21), (8, 22).

In each csv file, x = sqrt{5}. We normalized generators in a certain way. The first line and the second line of each csv file show the numerator and the denominator of a constant. The remaining lines of the csv file show Fourier coefficients of a generator. a(v, u) is corresponding to c(v, u) (in our paper) divided by the constant. For example, for "./forms_csv/A1/gen0_wt_7_9.csv", c(1, 1) is equal to 1 times (-x + 1)/4 and c(2, 2) is equal to -200 times (-x + 1)/4.

Relations

In "./relations", relations of generators are stored as text files. For example, relations of generators of A7 is stored in "./relations/a7_rel". Each line in this file corresponds to each relation among generators. In this case, there are two relations. The first line is [-1496880000*g5, 43200*g6 + 29*g2^3, 0, -g2] and this shows coefficients of generators. We use the order of generators explained above. Let F5, F4, F7 and F8 be the generators of A7 of weight (5, 19), (4, 18), (7, 21), (8, 22) respectively. Then it satisfies -1496880000*g5 * F5 + (43200*g6 + 29*g2^3) * F4 - g2 * F8 = 0.