Trac #34698: Fix conversion bug in modular forms rings

We currently have the following behavior:
{{{
sage: M = ModularFormsRing(Gamma0(2))
sage: E4 = ModularForms(1, 4).0
sage: F = M(E4)
sage: F[4].parent()
Modular Forms space of dimension 1 for Modular Group SL(2,Z) of weight 4
over Rational Field
}}}
The parent of `F[4]` is wrong as the group should be `Gamma0(2)`.

URL: https://trac.sagemath.org/34698
Reported by: gh-DavidAyotte
Ticket author(s): David Ayotte
Reviewer(s): Vincent Delecroix

Author: Release Manager

src/sage/modular/modform/element.py

@@ -3234,6 +3234,14 @@ def __init__(self, parent, forms_datum):
             Traceback (most recent call last):
             ...
             ValueError: the group and/or the base ring of at least one modular form (q - 6*q^2 + 9*q^3 + 4*q^4 + 6*q^5 + O(q^6)) is not consistant with the base space
+            sage: M = ModularFormsRing(Gamma0(2))
+            sage: E4 = ModularForms(1, 4).0
+            sage: M(E4)[4].parent()
+            Modular Forms space of dimension 2 for Congruence Subgroup Gamma0(2) of weight 4 over Rational Field
+            sage: M = ModularFormsRing(Gamma1(3), base_ring=GF(7))
+            sage: E6 = ModularForms(1, 6, base_ring=GF(7)).0
+            sage: M(E6)[6].parent()
+            Modular Forms space of dimension 3 for Congruence Subgroup Gamma1(3) of weight 6 over Finite Field of size 7
         """
         forms_dictionary = {}
         if isinstance(forms_datum, dict):
@@ -3245,7 +3253,8 @@ def __init__(self, parent, forms_datum):
                     elif is_ModularFormElement(f):
                         if f.weight() == k:
                             if parent.group().is_subgroup(f.group()) and parent.base_ring().has_coerce_map_from(f.base_ring()):
-                                forms_dictionary[k] = f
+                                M = parent.modular_forms_of_weight(f.weight()).change_ring(parent.base_ring())
+                                forms_dictionary[k] = M(f)
                             else:
                                 raise ValueError('the group and/or the base ring of at least one modular form (%s) is not consistant with the base space' % (f))
                         else:
@@ -3261,7 +3270,8 @@ def __init__(self, parent, forms_datum):
                     if (chi is not None) and (not chi.is_trivial()):
                         raise NotImplementedError("graded modular forms for non-trivial characters is not yet implemented")
                     if parent.group().is_subgroup(f.group()) and parent.base_ring().has_coerce_map_from(f.base_ring()):
-                        forms_dictionary[f.weight()] = forms_dictionary.get(f.weight(), 0) + f
+                        M = parent.modular_forms_of_weight(f.weight()).change_ring(parent.base_ring())
+                        forms_dictionary[f.weight()] = M(forms_dictionary.get(f.weight(), 0) + f)
                     else:
                         raise ValueError('the group and/or the base ring of at least one modular form (%s) is not consistant with the base space' % (f))
                 else:

src/sage/modular/modform/ring.py

@@ -397,7 +397,7 @@ def _generators_variables_dictionnary(self, poly_parent, gens):
         nb_gens = self.ngens()
         if nb_var != nb_gens:
             raise ValueError('the number of variables (%s) must be equal to the number of generators of the modular forms ring (%s)'%(nb_var, self.ngens()))
-        return {poly_parent.gen(i) : self(gens[i]) for i in range(0, nb_var)}
+        return {poly_parent.gen(i): self(gens[i]) for i in range(0, nb_var)}
 
     def from_polynomial(self, polynomial, gens=None):
         r"""
@@ -518,7 +518,7 @@ def _element_constructor_(self, forms_datum):
             forms_dictionary = forms_datum._forms_dictionary
         elif is_ModularFormElement(forms_datum):
             if self.group().is_subgroup(forms_datum.group()) and self.base_ring().has_coerce_map_from(forms_datum.base_ring()):
-                forms_dictionary = {forms_datum.weight():forms_datum}
+                forms_dictionary = {forms_datum.weight(): forms_datum}
             else:
                 raise ValueError('the group (%s) and/or the base ring (%s) of the given modular form is not consistant with the base space: %s'%(forms_datum.group(), forms_datum.base_ring(), self))
         elif forms_datum in self.base_ring():