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