#17283: Changing the coefficient ring of a Dirichlet character gives a wrong
result
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Reporter: pbruin | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.4
Component: modular forms | Resolution:
Keywords: modular symbols dirichlet | Merged in:
character | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: |
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Changes (by pbruin):
* keywords: modular symbols dimension => modular symbols dirichlet
character
Old description:
> In the following example, two ways of computing the dimension of a space
> of modular symbols do not give the same result:
> {{{
> sage: k.<i> = QuadraticField(-1)
> sage: G = DirichletGroup(192)
> sage: chi = G([i,-1,-1])
> sage: M = ModularSymbols(chi);
> sage: M.cuspidal_submodule()
> AssertionError: According to dimension formulas the cuspidal subspace of
> "Modular Symbols space of dimension 0 and level 192, weight 2, character
> [zeta4, 1, -1], sign 0, over Cyclotomic Field of order 4 and degree 2"
> has dimension 40; however, computing it using modular symbols we obtained
> 0, so there is a bug (please report!).
> }}}
> The following problem is probably related (the conductor and the image of
> 133 are wrong in `M.character()`):
> {{{
> sage: chi
> Dirichlet character modulo 192 of conductor 48 mapping 127 |--> zeta16^4,
> 133 |--> -1, 65 |--> -1
> sage: M.character()
> Dirichlet character modulo 192 of conductor 24 mapping 127 |--> zeta4,
> 133 |--> 1, 65 |--> -1
> }}}
New description:
Changing the coefficient field of a Dirichlet character is broken in some
cases (the conductor and the image of 133 are wrong in `chi0`):
{{{
sage: k.<i> = CyclotomicField(4)
sage: G = DirichletGroup(192)
sage: G0 = DirichletGroup(192, k)
sage: chi = G([i,-1,-1]); chi
Dirichlet character modulo 192 of conductor 48 mapping 127 |--> zeta16^4,
133 |--> -1, 65 |--> -1
sage: chi0 = G0(chi); chi0
Dirichlet character modulo 192 of conductor 24 mapping 127 |--> i, 133
|--> 1, 65 |--> -1
}}}
This probably explains the following bug where two ways of computing the
dimension of a space of modular symbols do not give the same result:
{{{
sage: M = ModularSymbols(chi);
sage: M.cuspidal_submodule()
AssertionError: According to dimension formulas the cuspidal subspace of
"Modular Symbols space of dimension 0 and level 192, weight 2, character
[zeta4, 1, -1], sign 0, over Cyclotomic Field of order 4 and degree 2" has
dimension 40; however, computing it using modular symbols we obtained 0,
so there is a bug (please report!).
}}}
--
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Ticket URL: <http://trac.sagemath.org/ticket/17283#comment:2>
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