ModularCurve function #29
Description
(From Angelos Koutsianas)
I run the following code in Magma V2.28-11 version.
AttachSpec("../ModFrmGL2/ModFrmGL2/ModFrmGL2.spec");
SetVerbose("ModularCurves", 1);
P<x,y,z,u,v,w> := ProjectiveSpace(Rationals(),5);
gens := [[4,0,0,3], [0,1,1,0], [2,0,0,2]];
N := 11;
H_N := sub<GL(2, Integers(N)) | gens>;
H := PSL2Subgroup(H_N);
M := ModularSymbols(H, 2, Rationals(), 0);
S := CuspidalSubspace(M);
XD10nred<[x]>, basisD10 := ModularCurve(H);
The same code worked well in a version of the code I had a year ago. I used to take a genus 6 modular curve! However, the current version of the code says that the curve should be hyperelliptic which is not! I get the following error/message
[PC] While attempting to compile /cecm/home/akoutsia/Programming/Magma/ModFrmGL
[PC] 2/ModFrmGL2/ModSymA/ModelsAndMaps.m (Data file non-existent):
[PC] Can't open input file /cecm/home/akoutsia/Programming/Magma/ModFrmGL2/ModF
[PC] rmGL2/ModSymA/ModelsAndMaps.m (No such file or directory)
Computing genus of curve...
Done.
Curve is Hyperelliptic. Returned scheme is not the Curve!
In order to get a model and check that the q-expansion computation is still ok, I used the basis above and the code below.
A := [];
mons := [];
for i in [1..6] do
f1 := basisD10[i];
for j in [i..6] do
f2 := basisD10[j];
fij := f1f2;
Append(~A, Coefficients(fij)[1..200]);
Append(~mons, P.iP.j);
end for;
end for;
A := Matrix(A);
ker := Basis(Kernel(A));
polys := [];
for v0 in ker do
poly := &+[mons[i] * Rationals()!(v0[i]) : i in [1..#mons]];
Append(~polys, poly);
end for;
C := Curve(P, polys);
The final curve C is the one I used to get.