#17283: Check consistency when constructing Dirichlet characters
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Reporter: pbruin | Owner:
Type: defect | Status: new
Priority: minor | Milestone: sage-6.4
Component: modular forms | Resolution:
Keywords: dirichlet character | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Changes (by pbruin):
* priority: critical => minor
* keywords: modular symbols dirichlet character => dirichlet character
Old description:
> Evaluating Dirichlet characters is broken in some cases (the image of 133
> is wrong in this example):
> {{{
> sage: k.<i> = CyclotomicField(4)
> sage: G = DirichletGroup(192)
> sage: chi = G([i,-1,-1]); chi
> Dirichlet character modulo 192 of conductor 48 mapping 127 |--> zeta16^4,
> 133 |--> -1, 65 |--> -1
> sage: chi(133)
> 1
> }}}
> Because of this, changing the coefficient field of `chi` is broken as
> well:
> {{{
> sage: G0 = DirichletGroup(192, k)
> 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!).
> }}}
New description:
It is too easy to construct Dirichlet characters with inconsistent values:
{{{
sage: k.<i> = CyclotomicField(4)
sage: G = DirichletGroup(192)
sage: chi = G([i,-1,-1]); chi # should raise an error since 127 only has
order 2
Dirichlet character modulo 192 of conductor 48 mapping 127 |--> zeta16^4,
133 |--> -1, 65 |--> -1
sage: chi(133) # no surprise that this gives an inconsistent answer
1
}}}
The `check` option (`True` by default) should verify that the images of
the generators have the correct orders.
--
Comment:
The previous inconsistencies reported on this ticket were just because
there does not exist a Dirichlet character with the values as in the
example...
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Ticket URL: <http://trac.sagemath.org/ticket/17283#comment:4>
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