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
.
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
.