The traceback (from SMC) mostly speaks for itself.
sage: N = Newforms(83,2, names="a")
sage: f = N[1]
sage: K = f.hecke_eigenvalue_field()
sage: print K
Number Field in a1 with defining polynomial x^6 - x^5 - 9*x^4 + 7*x^3 + 20*x^2
- 12*x - 8
sage: l = f.coefficients(20)
sage: print l[-1].parent()
Number Field in alpha with defining polynomial x^6 - x^5 - 9*x^4 + 7*x^3 +
20*x^2 - 12*x - 8
sage: K(l[-1])
Error in lines 2-2
Traceback (most recent call last):
File
"/projects/sage/sage-6.10/local/lib/python2.7/site-packages/smc_sagews/sage_server.py",
line 905, in execute
exec compile(block+'\n', '', 'single') in namespace, locals
File "", line 1, in <module>
File "sage/structure/parent.pyx", line 1111, in
sage.structure.parent.Parent.__call__
(/projects/sage/sage-6.10/src/build/cythonized/sage/structure/parent.c:9821)
return mor._call_(x)
File "sage/structure/coerce_maps.pyx", line 109, in
sage.structure.coerce_maps.DefaultConvertMap_unique._call_
(/projects/sage/sage-6.10/src/build/cythonized/sage/structure/coerce_maps.c:4542)
raise
File "sage/structure/coerce_maps.pyx", line 104, in
sage.structure.coerce_maps.DefaultConvertMap_unique._call_
(/projects/sage/sage-6.10/src/build/cythonized/sage/structure/coerce_maps.c:4435)
return C._element_constructor(x)
File
"/projects/sage/sage-6.10/local/lib/python2.7/site-packages/sage/rings/number_field/number_field.py",
line 1489, in _element_constructor_
return self._coerce_from_other_number_field(x)
File
"/projects/sage/sage-6.10/local/lib/python2.7/site-packages/sage/rings/number_field/number_field.py",
line 6595, in _coerce_from_other_number_field
raise TypeError("No compatible natural embeddings found for %s and
%s"%(KF,LF))
TypeError: No compatible natural embeddings found for Number Field in a1 with
defining polynomial x^6 - x^5 - 9*x^4 + 7*x^3 + 20*x^2 - 12*x - 8 and Number
Field in alpha with defining polynomial x^6 - x^5 - 9*x^4 + 7*x^3 + 20*x^2 -
12*x - 8
So why are the coefficients being created in a different copy of the same
number field than the one returned by hecke_eigenvalue_field?
Kiran
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