Add coefficient_field() method to ModularSymbols/ModularForms

[jonhanke]

Define a newform (up to conjugation)

time nf = ModularSymbols(100,2,1).cuspidal_subspace().new_subspace().decomposition()[0]

nf.coefficient_field() -- should return the field of definition of the newform. (This appears to be accomplished with nf.eigenvalue(1).parent(). It would be nice to know that this really does give the field of definition.)

nf.degree() -- should return the degree of the coefficient field.

Component: modular forms

Issue created by migration from https://trac.sagemath.org/ticket/4483

[aghitza]

comment:1

There is something like this in Sage: look at the class Newform in modular/modform/element.py. It has a method hecke_eigenvalue_field() which returns the field of definition of the newform. There is no degree() method, although that's of course easy to get at this point as nf.hecke_eigenvalue_field().degree().

It remains to add such a method to modular symbols (nf.eigenvalue(1).parent() is indeed correct), and maybe make coefficient_field() an alias for hecke_eigenvalue_field().

[aghitza]

Description changed:

--- 
+++ 
@@ -1,6 +1,8 @@
+Define a newform (up to conjugation)
 
-## Define a newform (up to conjugation)
-`time nf = ModularSymbols(100,2,1).cuspidal_subspace().new_subspace().decomposition()[0]`
+```
+time nf = ModularSymbols(100,2,1).cuspidal_subspace().new_subspace().decomposition()[0]
+```
 
 `nf.coefficient_field()` -- should return the field of definition of the newform.  (This appears to be accomplished with `nf.eigenvalue(1).parent()`.  It would be nice to know that this really does give the field of definition.)