Trac #32349: Remove base ring attribute for the class ModularFormsRing

After the implementation of the parent/element framework for the class
{{{ModularFormsRing}}} in #31559, the {{{__base_ring}}} attribute was
not removed in the code. This ticket aims to remove this attribute and
associated method so that the class use the inherited parent base ring
method instead.

This ticket is part of #31560.

URL: https://trac.sagemath.org/32349
Reported by: gh-DavidAyotte
Ticket author(s): David Ayotte
Reviewer(s): Vincent Delecroix

src/sage/modular/modform/element.py

@@ -418,19 +418,6 @@ def _latex_(self):
         """
         return self.q_expansion()._latex_()
 
-    def base_ring(self):
-        """
-        Return the base_ring of self.
-
-        EXAMPLES::
-
-            sage: (ModularForms(117, 2).13).base_ring()
-            Rational Field
-            sage: (ModularForms(119, 2, base_ring=GF(7)).12).base_ring()
-            Finite Field of size 7
-        """
-        return self.parent().base_ring()
-
     def character(self, compute=True):
         """
         Return the character of self. If ``compute=False``, then this will

src/sage/modular/modform/ring.py

@@ -236,7 +236,6 @@ def __init__(self, group, base_ring=QQ):
             raise ValueError("Base ring (=%s) should be QQ, ZZ or a finite prime field" % base_ring)
 
         self.__group = group
-        self.__base_ring = base_ring
         self.__cached_maxweight = ZZ(-1)
         self.__cached_gens = []
         self.__cached_cusp_maxweight = ZZ(-1)
@@ -267,19 +266,6 @@ def group(self):
         """
         return self.__group
 
-    def base_ring(self):
-        r"""
-        Return the coefficient ring of this modular forms ring.
-
-        EXAMPLES::
-
-            sage: ModularFormsRing(Gamma1(13)).base_ring()
-            Rational Field
-            sage: ModularFormsRing(Gamma1(13), base_ring = ZZ).base_ring()
-            Integer Ring
-        """
-        return self.__base_ring
-
     def gen(self, i):
         r"""
         Return the `i`-th generator of ``self``.