check residual trace

Modularity.m

@@ -359,9 +359,20 @@ intrinsic ModPrimes(m :: Modularity, R2 :: FldNum,
                     proj :: Map, phi :: Map
           : debug := false, keep_going := false, PrimeBound := 500,
             no_order := false, only_order := false,
-            check_frob := false) -> []
+            check_frob := false,
+            check_residual := []) -> []
   { .. }
   fc := frobenius_classes(proj : no_order:=no_order, only_order:=only_order);
+  for p_ap in check_residual do
+    p, ap := Explode(p_ap);
+    pat1 := m`frobR1[p];
+    pat2 := FrobeniusStructure(R2, p);
+    cs := fc[<pat1,pat2>];
+    cc := [ c : c in cs | tr1(phi(c)) eq ap ];
+    if #cc eq 0 then
+      return -p;
+    end if;
+  end for;
   if &and [tr(phi(x)) eq 0 : x in fc[a], a in Keys(fc)] then
     // a cocycle with all traces equal to 0 is ok
     return 1;

run-353.m

-Attach("Modularity.m");
-Attach("GrpExt.m");
-Attach("Grp.m");
+AttachSpec("mod.spec");
 
 //load "ex.m";
 load "ex-353.m";
@@ -11,7 +9,8 @@ time for i := 1 to #all do
   R2:=NumberField(Polynomial(R1, [-all[i], 0, 1]));
   proj, phis := ModPhis(m, R2);
   dim := Integers() ! Log(2, #Domain(phis[1])/#G5);
-  ps := [ModPrimes(m, R2, proj, phi) : phi in phis];
+  ps := [ ModPrimes( m, R2, proj, phi
+        : check_residual:=[<5,1>] ) : phi in phis ];
   for p in ps do 
       Include(~PS, p);
   end for;