diff --git a/src/sage/algebras/cellular_basis.py b/src/sage/algebras/cellular_basis.py
index 873bd899b3e..8aad8efcd71 100644
--- a/src/sage/algebras/cellular_basis.py
+++ b/src/sage/algebras/cellular_basis.py
@@ -135,21 +135,21 @@ class CellularBasis(CombinatorialFreeModule):
         sage: len(S.basis())
         6
         sage: a,b,c,d,e,f = C.basis()
-        sage: a
+        sage: f
         C([3], [[1, 2, 3]], [[1, 2, 3]])
         sage: c
         C([2, 1], [[1, 3], [2]], [[1, 2], [3]])
         sage: d
         C([2, 1], [[1, 2], [3]], [[1, 3], [2]])
-        sage: a * a
+        sage: f * f
         C([3], [[1, 2, 3]], [[1, 2, 3]])
-        sage: a * c
+        sage: f * c
         0
         sage: d * c
         C([2, 1], [[1, 2], [3]], [[1, 2], [3]])
         sage: c * d
         C([2, 1], [[1, 3], [2]], [[1, 3], [2]])
-        sage: S(a)
+        sage: S(f)
         1/6*[1, 2, 3] + 1/6*[1, 3, 2] + 1/6*[2, 1, 3] + 1/6*[2, 3, 1]
          + 1/6*[3, 1, 2] + 1/6*[3, 2, 1]
         sage: S(d)
diff --git a/src/sage/categories/finite_dimensional_algebras_with_basis.py b/src/sage/categories/finite_dimensional_algebras_with_basis.py
index b8ed6332ead..2ba4069a8d5 100644
--- a/src/sage/categories/finite_dimensional_algebras_with_basis.py
+++ b/src/sage/categories/finite_dimensional_algebras_with_basis.py
@@ -1437,7 +1437,15 @@ def simple_module_parameterization(self):
 
                     sage: S = SymmetricGroupAlgebra(QQ, 4)                              # needs sage.groups sage.modules
                     sage: S.simple_module_parameterization()                            # needs sage.groups sage.modules
-                    ([4], [3, 1], [2, 2], [2, 1, 1], [1, 1, 1, 1])
+                    ([1, 1, 1, 1], [2, 1, 1], [2, 2], [3, 1], [4])
+
+                    sage: S = SymmetricGroupAlgebra(GF(3), 4)                           # needs sage.groups sage.modules
+                    sage: S.simple_module_parameterization()                            # needs sage.groups sage.modules
+                    ([2, 1, 1], [2, 2], [3, 1], [4])
+
+                    sage: S = SymmetricGroupAlgebra(GF(4), 4)                           # needs sage.groups sage.modules
+                    sage: S.simple_module_parameterization()                            # needs sage.groups sage.modules
+                    ([3, 1], [4])
                 """
                 return tuple([mu for mu in self.cell_poset()
                               if self.cell_module(mu).nonzero_bilinear_form()])
diff --git a/src/sage/combinat/symmetric_group_algebra.py b/src/sage/combinat/symmetric_group_algebra.py
index 70704a0e9f7..1d87c0bf31d 100644
--- a/src/sage/combinat/symmetric_group_algebra.py
+++ b/src/sage/combinat/symmetric_group_algebra.py
@@ -739,14 +739,15 @@ def _from_cellular_index(self, x):
             from sage.combinat.rsk import RSK_inverse
             from sage.sets.recursively_enumerated_set import RecursivelyEnumeratedSet
             G = self.basis().keys()
-            one = self.base_ring().one()
+            R = self.base_ring()
+            one = R.one()
             # check if the KL polynomials can be computed using ``coxeter3``
             try:
                 from sage.libs.coxeter3.coxeter_group import CoxeterGroup as Coxeter3Group
             except ImportError:
                 # Falback to using the KL polynomial
                 from sage.combinat.kazhdan_lusztig import KazhdanLusztigPolynomial
-                q = PolynomialRing(self.base_ring(), 'q').gen()
+                q = PolynomialRing(QQ, 'q').gen()
                 KLG = SymmetricGroup(self.n)
                 self._cellular_KL = KazhdanLusztigPolynomial(KLG, q)
                 polyfunc = self._cellular_KL.P
@@ -758,7 +759,7 @@ def _from_cellular_index(self, x):
             def func(S, T, mult=None):
                 w = KLG.from_reduced_word(RSK_inverse(T, S, output="permutation").reduced_word())
                 bruhat = RecursivelyEnumeratedSet([w], lambda u: u.bruhat_lower_covers(), structure='graded')
-                return self.element_class(self, {G.from_reduced_word(v.reduced_word()): c(q=one)
+                return self.element_class(self, {G.from_reduced_word(v.reduced_word()): R(c(q=one))
                                                  for v in bruhat if (c := polyfunc(v, w))})
 
         else:
diff --git a/src/sage/modules/with_basis/cell_module.py b/src/sage/modules/with_basis/cell_module.py
index 66d72f648f8..25e6509dde7 100644
--- a/src/sage/modules/with_basis/cell_module.py
+++ b/src/sage/modules/with_basis/cell_module.py
@@ -334,9 +334,9 @@ def _acted_upon_(self, scalar, self_on_left=False):
                 sage: elt = W.an_element(); elt
                 2*W[[1, 2], [3]] + 2*W[[1, 3], [2]]
                 sage: sc = C.an_element(); sc
-                3*C([2, 1], [[1, 3], [2]], [[1, 2], [3]])
+                2*C([1, 1, 1], [[1], [2], [3]], [[1], [2], [3]])
+                 + 3*C([2, 1], [[1, 3], [2]], [[1, 2], [3]])
                  + 2*C([2, 1], [[1, 3], [2]], [[1, 3], [2]])
-                 + 2*C([3], [[1, 2, 3]], [[1, 2, 3]])
                 sage: sc * elt
                 10*W[[1, 3], [2]]
 
@@ -448,9 +448,9 @@ def _acted_upon_(self, scalar, self_on_left=False):
                 sage: elt = L.an_element(); elt
                 2*L[[1, 2], [3]] + 2*L[[1, 3], [2]]
                 sage: sc = C.an_element(); sc
-                3*C([2, 1], [[1, 3], [2]], [[1, 2], [3]])
+                2*C([1, 1, 1], [[1], [2], [3]], [[1], [2], [3]])
+                 + 3*C([2, 1], [[1, 3], [2]], [[1, 2], [3]])
                  + 2*C([2, 1], [[1, 3], [2]], [[1, 3], [2]])
-                 + 2*C([3], [[1, 2, 3]], [[1, 2, 3]])
                 sage: sc * elt
                 10*L[[1, 3], [2]]