When understand the specific reason why my code is not working properly, I
managed to pin it down to the following mysterious behaviour of q_eigenform.
First run the following code in sage.
G=DirichletGroup(80);
chi=G[22];
D=ModularSymbols(chi,2,-1).cuspidal_subspace().new_subspace().decomposition();
for f in D:
elt=f.q_eigenform(10,'alpha')[3];
N=elt.parent().absolute_field('a');
fact=N.factor(2);
for P,e in fact:
res_field=N.residue_field(P);
print res_field(elt);
It will print
0
0
0
0
which, I think, is the 'right' answer.
Now *close* your sage session entirely. Open a new session and then run the
following *silly* code:
G=DirichletGroup(80);
for chi in G:
D=ModularSymbols(chi,2,-1).cuspidal_subspace().new_subspace().decomposition();
for f in D:
elt=f.q_eigenform(10,'alpha')[3];
if not elt.parent()==QQ:
K=elt.parent().absolute_field('b');
if chi==G[22]:
fact=K.factor(2);
for P,e in fact:
res_field=K.residue_field(P);
print res_field(elt);
It will print:
0
0
1
0
As far as I understand the theory, this cannot happen. If you let sage
print the alpha^3 coefficient of you see that in both cases it picks a
different q_eigenform in f, the Galois conjugacy class of newforms.
Although this can be a bit annoying, in theory it is fine. But I am pretty
sure that when your reduce this coefficient modulo some prime P, any two
elements of the same Galois conjugacy class can differ at most by some
automorphism of the residue field (and obviously 1 and 0 do not satisfy
this criterion).
To make matters worse: if you run a single sage session and you run the
'good' code first and the 'bad' code second, then suddenly the 'bad' code
is fixed and printing only 0s. If you run the 'bad' code first and the
'good' code second, then they are both 'bad' and the 'good' code suddenly
prints 0,0,1,0 as well.
By trying I found out that this is because somehow q_eigenform picks the
same q_eigenform as whichever code that ran first and somehow these choices
are not compatible! I don't know the inner workings of q_eigenform, but
this behaviour seems strange to me.
Can anyone explain what is going on here? Is it a bug?
Thanks!
--
You received this message because you are subscribed to the Google Groups
"sage-support" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at https://groups.google.com/group/sage-support.
For more options, visit https://groups.google.com/d/optout.
