Local components bug finding minimal twist

[davidloeffler]

The following is from an email of François Brunault:

I got the following error when trying to compute minimal twists in Sage. Here f is the newform attached to the elliptic curve 256a1, and the minimal twist of f has level 64.

Best, François

sage: f=Newforms(256,names='a')[0]
sage: T=TypeSpace(f,2)
sage: T.is_minimal()
False
sage: T.minimal_twist()
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)

/Users/francoisbrunault/<ipython console> in <module>()

/Users/francoisbrunault/Documents/SAGE/sage-5.0.beta13/local/lib/python2.7/site-packages/sage/modular/local_comp/type_space.pyc in minimal_twist(self)
   383             D._set_sign(D.star_eigenvalues()[0])
   384         M = ModularForms(D.group(), D.weight())
--> 385         ff = Newform(M, D, names='a')
   386         return ff
   387

/Users/francoisbrunault/Documents/SAGE/sage-5.0.beta13/local/lib/python2.7/site-packages/sage/modular/modform/element.pyc in __init__(self, parent, component, names, check)
   636                 raise ValueError, "component must be cuspidal"
   637             if not component.is_simple():
--> 638                 raise ValueError, "component must be simple"
   639         extension_field = component.eigenvalue(1,name=names).parent()
   640         if extension_field != parent.base_ring(): # .degree() != 1 and rings.is_NumberField(extension_field):

ValueError: component must be simple

[davidloeffler]

Somehow, this sat idle for 3 years despite the fact that the fix is about 2 lines! It turns out that the code relies on the assumption that the trace of the type space down to the minimal level is simple, but if f is of CM type it can be the direct sum of two simple modules of opposite sign.

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New commits:

​1994692

Trac 13158: local components bug finding minimal twist

[chapoton]

This looks good to me. I have only made minor changes, and allow myself to set to positive review.

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New commits:

​9ce7fbc	Merge branch 'u/davidloeffler/local_components_bug_finding_minimal_twist' into 6.8.b6
​3577e02	trac #13518 review commit

[davidloeffler]

Thanks for the review! The patchbot seems a bit confused, but I'm sure it'll catch up shortly :-)