K := pAdicField(2);
K`DefaultPrecision := 100;
q_prec := 30;

procedure Basis(k)
   M := ModularForms(1,k);        // S_128(SL_2(Z))
   S := CuspidalSubspace(M);
   N := Newforms(S)[1][1];
   F := pAdicEmbeddings(N,2);
   for orbit in F do
      for f in orbit do
         PowerSeries(f,q_prec);
      end for;
   end for;
end procedure;

print "\n\n// k = 64";
time Basis(64);

print "\n\n// k = 128";
time Basis(128);

print "\n\n// k = 256";
time Basis(256);

