modular abelian quotient -- something goes wrong

[williamstein]

This isn't right:

sage: J = J0(43)
sage: G,_ = J[0].intersection(J[1])
sage: J[1]/G
Simple abelian subvariety 43b(1,43) of dimension 2 of J0(43)

This is

sage: J[0]/G

(Abelian variety factor of dimension 1 of J0(43),
 Abelian variety morphism:
  From: Simple abelian subvariety 43a(1,43) of dimension 1 of J0(43)
  To:   Abelian variety factor of dimension 1 of J0(43))

For some reason J[1]/G isn't even creating the right output (i.e., pair (abvar, map)).

CC: @koffie

Component: modular forms

Stopgaps: todo

Author: Kevin Lui

Branch/Commit: 0bc6f5a

Reviewer: Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/6392

[koffie]

comment:1

G is strictly speaking not a subgroup of J[1] in this example it's a subgroup of J[0]. What happens if you travel down the code is equivalent to this:

G=J[1].finite_subgroup(G) #This should raise an error since J[0] and J[1] have empty intersection
J[1]._quotient_by_finite_subgroup(G):

Now the source code of _quotient_by_finite_subgroup is

def _quotient_by_finite_subgroup(self, G):
    if G.order() == 1:
        return self
    L = self.lattice() + G.lattice()
    A = ModularAbelianVariety(self.groups(), L, G.field_of_definition())
    M = L.coordinate_module(self.lattice()).basis_matrix()
    phi = self.Hom(A)(M)
    return A, phi

So i guess it should instead return

return self, self.Hom(self).identity()

There is also a problem with the is_subgroup code:
sage: G.is_subgroup(J[1])
True
This error is caused by the intersection code:
sage: G.intersection(J[1])
Finite subgroup with invariants [2, 2] over QQ of Simple abelian subvariety 43b(1,43) of dimension 2 of J0(43)

Maybe I'm a bit confused but is the intersection of abelian varieties defined in an other way than just the set theoretic one. Because by reading the source code I really get the feeling that it does. The errors certainly seem to come from different assumtions about this in different parts of the code.

[koffie]

comment:2

My confusion mainly comes from the following:

sage: J[1].finite_subgroup(G)
Finite subgroup with invariants [] over QQ of Simple abelian subvariety
43b(1,43) of dimension 2 of J0(43)
J[1].intersection(G)
Finite subgroup with invariants [2, 2] over QQ of Simple abelian
subvariety 43b(1,43) of dimension 2 of J0(43)