RR:=RealField(20); ll:=Log(2,Pi(RR)); M := ModularForms(Gamma1(1),12); M; SetPrecision(M,2004); BB:=Basis(M); T12:=BB[1]; M2 := ModularForms(Gamma1(1),36); M; SetPrecision(M2,2004); BB2:=Basis(M2); T36:=BB2[1]; S1:=T12^30; S2:=T36^10; S:=S1; SS:=S2; // S:=S1^47; // SS:=S2^47; // print "Powers done"; // for n in [48..70] do for n in [2..48] do N:=360*n; // the dimension is 2*N S:=S*S1; XX1:=[]; br:=1; ober:=200+90*n; if ober ge 2000 then ober := 2000; end if; for r in [1..ober] do br:=br+Coefficient(S,r); xx:=N-Log(2,br)+N*Log(2,(r+1)/4); Append(~XX1,xx); end for; mm1,r1:=Maximum(XX1); SS:=SS*S2; XX2:=[]; br:=1; for r in [1..ober] do br:=br+Coefficient(SS,r); xx:=N-Log(2,br)+N*Log(2,(r+1)/4); Append(~XX2,xx); end for; mm2,r2:=Maximum(XX2); print 2*N,"&", RR ! mm1, "&", r1, "&", RR ! mm2, "&", r2, "&", RR ! Log(2,ZetaFunction(2*N))+Log(2,Factorial(N))-2*N+1-N*ll,"&", RR ! Log(2,ZetaFunction(2*N))+Log(2,Factorial(N))+Log(2,2*N-1)-2*N+1-N*ll,"\\\\ \%", ober; end for;