Sharedwww / tables / artin / 6176.mOpen in CoCalc
Author: William A. Stein
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N := 2^5*193;
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bound := 3000;
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F<alp> := GF(25);
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G<a2,b2,c>:=DirichletGroup(N, F);
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assert Order(a2) mod 2 eq 0;
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assert Order(c) mod 3 eq 0;
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// This doesn't work: space has dimension 0.
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// eps := a2^(Order(a2) div 2) * (c^(Order(c) div 3));
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// This doesn't work -- it's not odd.
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// eps := b2^(Order(b2) div 2) * (c^(Order(c) div 3));
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eps := a2^(Order(a2) div 2) * b2^(Order(b2) div 2) * (c^(Order(c) div 3));
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time M := ModularSymbols(eps,5,+1);
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"Created M = ", M;
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R<x>:= PolynomialRing(F);
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I := [<17,x>, <53,x>, <59,x>, <71, x>, <73, x>, <97, x>];
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time V := Kernel(I, M);
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"Created V = ", V;
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save "6176.space";
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if Dimension(V) ne 2 then
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error "Dimension of V is not 2.";
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end if;
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printf "Computing T_2, T_3, T_5, ..., T_%o.\n", PreviousPrime(bound+1);
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time T := [DualHeckeOperator(V,p) : p in [2..bound] | IsPrime(p)];
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file := Open(IntegerToString(N) cat ".Tp", "w");
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fprintf file, "F<alp> := GF(%o);\n", #F;
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fprintf file, "T%o := \n %m;\n", N, T;
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print "All done!";
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