CoCalc Public Fileswww / tables / artin / 6176.m
Author: William A. Stein
1N := 2^5*193;
2bound := 3000;
3
4   F<alp> := GF(25);
5   G<a2,b2,c>:=DirichletGroup(N, F);
6   assert Order(a2) mod 2 eq 0;
7   assert Order(c) mod 3 eq 0;
8
9// This doesn't work: space has dimension 0.
10//   eps := a2^(Order(a2) div 2) * (c^(Order(c) div 3));
11// This doesn't work -- it's not odd.
12//   eps := b2^(Order(b2) div 2) * (c^(Order(c) div 3));
13   eps := a2^(Order(a2) div 2) * b2^(Order(b2) div 2) * (c^(Order(c) div 3));
14
15   time M := ModularSymbols(eps,5,+1);
16   "Created M = ", M;
17
18   R<x>:= PolynomialRing(F);
19   I := [<17,x>, <53,x>, <59,x>, <71, x>, <73, x>, <97, x>];
20   time V := Kernel(I, M);
21   "Created V = ", V;
22   save "6176.space";
23
24   if Dimension(V) ne 2 then
25      error "Dimension of V is not 2.";
26   end if;
27
28printf "Computing T_2, T_3, T_5, ..., T_%o.\n", PreviousPrime(bound+1);
29time T := [DualHeckeOperator(V,p) : p in [2..bound] | IsPrime(p)];
30
31file := Open(IntegerToString(N) cat ".Tp", "w");
32fprintf file, "F<alp> := GF(%o);\n", #F;
33fprintf file, "T%o := \n %m;\n", N, T;
34
35print "All done!";
36