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Author: William A. Stein
Compute Environment: Ubuntu 18.04 (Deprecated)
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/* This is for ex:new_old in chapter on dimension formulas... */
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intrinsic new_old()
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{}
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M := ModularForms(45, 2);
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M15 := ModularForms(15,2);
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M9 := ModularForms(9,2);
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V := VectorSpace(RationalField(),Dimension(M));
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B15 := [];
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for b in Basis(M15) do
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f := PowerSeries(b, 40);
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q := Parent(f).1;
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g := Evaluate(f, q^3) + O(q^40);
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Append(~B15, V!Eltseq(M!f));
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Append(~B15, V!Eltseq(M!g));
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end for;
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W15 := sub<V | B15>;
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print W15;
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B9 := [];
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for b in Basis(M9) do
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f := PowerSeries(b, 40);
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q := Parent(f).1;
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g := Evaluate(f, q^5) + O(q^40);
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Append(~B9, V!Eltseq(M!f));
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Append(~B9, V!Eltseq(M!g));
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end for;
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W9 := sub<V | B9>;
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print W9;
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print W15 meet W9;
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print W15 + W9;
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end intrinsic;
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