Sharedwww / tables / hecke-magma-faq / 1.txtOpen in CoCalc
Author: William A. Stein
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For this to work, you'll have to make the following two modifications:
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1) In dirichlet.m (in the modsym distribution):
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In this intrinsic:
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intrinsic DirichletGroup(m::RngIntElt,R::Rng,z::RngElt,r::RngIntElt) ->
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GrpDrch
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{The group of Dirichlet characters mod m with image in the order-r cyclic
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subgroup of R generated by the root of unity z.}
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//...
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modify the require statement like this:
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if not (Type(R) in {FldLoc, FldPr}) then
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require z^r eq R!1 : "Argument 3 must have order equal to argument 4.";
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end if;
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Now you can happily create characters of giagantic degree, and you don't
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have to bother with cyclotomic polynomials.
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2) In dims.m, replace DimensionCuspForms by the following:
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intrinsic DimensionCuspForms(eps::GrpDrchElt, k::RngIntElt) -> RngElt
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{Compute the dimension of the space of cusp forms of weight k and
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character eps.}
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require Characteristic(BaseRing(eps)) eq 0 :
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"The base ring of argument 1 must be of characteristic 0.";
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requirege k,2;
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N := Modulus(eps);
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if IsTrivial(eps) then
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return S0(N,k);
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end if;
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if (IsOdd(eps) and IsEven(k)) or (IsEven(eps) and IsOdd(k)) then
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return 0;
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end if;
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ans := idxG0(N) * (k-1)/12 + CohenOesterle(eps,k);
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if Type(ans) in {FldRatElt, FldCycElt} then
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return Integers()!ans;
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end if;
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return ans;
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end intrinsic;
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