diff --git a/as_covers/as_cover_class.sage b/as_covers/as_cover_class.sage
index 6c0870c..9c01d64 100644
--- a/as_covers/as_cover_class.sage
+++ b/as_covers/as_cover_class.sage
@@ -449,7 +449,7 @@ class as_cover:
             i += 1
         return result_fcts
 
-    def lift_to_de_rham(self, fct, threshold = 30):
+    def lift_to_de_rham(self, fct, basis = 0, threshold = 30):
         '''Given function fct, find form eta regular on affine part such that eta - d(fct) is regular in infty. (Works for one place at infty now)'''
         from itertools import product
         x_series = self.x_series
@@ -469,17 +469,27 @@ class as_cover:
         #Tworzymy zbiór S form z^i x^j y^k dx/y o waluacji >= waluacja z^(p-1)*dx/y
         S = [(fct.diffn(), fct.diffn().expansion_at_infty())]
         pr = [list(GF(p)) for _ in range(n)]
-        holo = self.holomorphic_differentials_basis(threshold = threshold)
+        if basis == 0:
+            holo = self.holomorphic_differentials_basis(threshold = threshold)
+        else:
+            holo = basis
         for i in range(0, threshold*r):
             for j in range(0, m):
                 for k in product(*pr):
                     eta = as_form(self, x^i*prod(z[i1]^(k[i1]) for i1 in range(n))/y^j)
                     eta_exp = eta.expansion_at_infty()
                     S += [(eta, eta_exp)]
-        forms = holomorphic_combinations(S)
-        if len(forms) <= self.genus():
+        S = holomorphic_combinations(S)
+        ########
+        for i in range(delta):
+            for g in self.fiber(place = i):
+                if i!=0 or g != self.group.one:
+                    S = [(omega, omega.group_action(g).expansion_at_infty(place = i)) for omega in S]
+                    S = holomorphic_combinations(S)
+        ######
+        if len(S) <= self.genus():
             raise ValueError("Increase threshold!")
-        for omega in forms:
+        for omega in S:
             for a in F:
                 if (a*omega + fct.diffn()).is_regular_on_U0():
                     return a*omega + fct.diffn()
@@ -538,7 +548,7 @@ class as_cover:
         for omega in holo_basis:
             result += [as_cech(self, omega, as_function(self, 0))]
         for f in cohomology_basis:
-            omega = self.lift_to_de_rham(f, threshold = threshold)
+            omega = self.lift_to_de_rham(f, basis = holo_basis, threshold = threshold)
             result += [as_cech(self, omega, f)]
         return result