added tests specifically for traces on the newsubspace

.gitignore

@@ -21,3 +21,5 @@ m4
 Makefile
 configure
 ltmain.sh
+*.sig
+Tests/*.sig

Tests/MagmaFormula.m

@@ -1,7 +1,11 @@
-import "magma_functions.m" : TraceFormulaGamma0AL;
+import "magma_functions.m" : TraceFormulaGamma0AL, TraceFormulaGamma0ALNew;
 
-procedure testPariVSMagma(N,k)
-    cmd := Sprintf("./src/traceALbatch_sta %o %o %o", N, N+1, k);
+procedure testPariVSMagma(N,k : New := false, OnlyPrimes := false, Prec := 1000)
+    if (New and (not OnlyPrimes)) then
+	printf("Error! Only supports newsubspace for prime Hecke operators!\n");
+	assert false;
+    end if;
+    cmd := Sprintf("./src/traceALbatch_sta %o %o %o %o %o %o", N, N+1, k, Prec, OnlyPrimes, New);
     System(cmd);
     fname := Sprintf("./data/traces_%o_%o.m", k, N);
     r := Read(fname);
@@ -11,8 +15,10 @@ procedure testPariVSMagma(N,k)
     fin := Index(r, "]") - 1;
     r := r[start..fin];
     traces_AL := [StringToInteger(x) : x in Split(r, ",")];
-    traces_magma := [TraceFormulaGamma0AL(n, N, k) : n in [1..1000]];
-    assert traces_magma eq traces_AL[2..1001];
+    trace_func := New select TraceFormulaGamma0ALNew else TraceFormulaGamma0AL;
+    val_list := OnlyPrimes select PrimesUpTo(Prec) else [0..Prec];
+    traces_magma := [trace_func(n, N, k) : n in val_list];
+    assert traces_magma eq traces_AL[1..#val_list];
     return;
 end procedure;
 
@@ -29,5 +35,15 @@ procedure testPariVSMagma(N,k)
     printf "(%o;%o),", N, k;
     testPariVSMagma(N,k);
 end for;
+
+printf "testing pari vs magma implementation on new subspaces... (N;k) = ";
+for i in [1..num_tests] do
+    N := Random(Ns);
+    max_weight := Floor(Sqrt(max_Nk2/N));
+    ks := [2..max_weight by 2];
+    k := Random(ks);
+    printf "(%o;%o),", N, k;
+    testPariVSMagma(N,k : New, OnlyPrimes);
+end for;
 printf "\n";
 

Tests/ModSym.m

@@ -1,8 +1,20 @@
 // SetDebugOnError(true);
 // SetVerbose("ModularSymbols", 3);
 
-procedure testPariVSMS(N,k,n)
-    cmd := Sprintf("./src/traceALbatch_sta %o %o %o", N, N+1, k);
+import "magma_functions.m" : get_trace;
+
+procedure testPariVSMS(N,k,n : New := false)
+    is_prime := IsPrime(n);
+    if (is_prime) then
+	n_idx := #PrimesUpTo(n);
+    else
+	if (New) then
+	    printf("Error! Only supports newsubspace for prime Hecke operators!\n");
+	    assert false;
+	end if;
+	n_idx := n + 1;
+    end if;
+    cmd := Sprintf("./src/traceALbatch_sta %o %o %o %o %o %o", N, N+1, k, n, is_prime, New);
     System(cmd);
     fname := Sprintf("./data/traces_%o_%o.m", k, N);
     r := Read(fname);
@@ -12,10 +24,10 @@ procedure testPariVSMS(N,k,n)
     fin := Index(r, "]") - 1;
     r := r[start..fin];
     traces_AL := [StringToInteger(x) : x in Split(r, ",")];
-    C := CuspidalSubspace(ModularSymbols(N,k,1));
-    al := AtkinLehner(C,N);
-    T := HeckeOperator(C,n);
-    assert traces_AL[n+1] eq Trace(al*T);
+    // C := CuspidalSubspace(ModularSymbols(N,k,1));
+    // al := AtkinLehner(C,N);
+    // T := HeckeOperator(C,n);
+    assert traces_AL[n_idx] eq get_trace(N,k,n : New := New); // Trace(al*T);
     return;
 end procedure;
 
@@ -29,8 +41,31 @@ procedure testPariVSMS(N,k,n)
     max_weight := Floor(Sqrt(max_Nk2/N));
     ks := [2..max_weight by 2];
     k := Random(ks);
-    n := Random([1..1000]);
+    n := Random([1..N]);
     printf "(%o;%o;%o),", N, k, n;
     testPariVSMS(N,k,n);
 end for;
+
+printf "testing trace on new subspace... (N;k;p) = ";
+for i in [1..num_tests] do
+    N := Random(Ns);
+    max_weight := Floor(Sqrt(max_Nk2/N));
+    ks := [2..max_weight by 2];
+    k := Random(ks);
+    p := Random(PrimesUpTo(N));
+    printf "(%o;%o;%o),", N, k, p;
+    testPariVSMS(N,k,p : New);
+end for;
+
+printf "testing trace on new subspace for bad primes... (N;k;p) = ";
+for i in [1..num_tests] do
+    N := Random(Ns);
+    max_weight := Floor(Sqrt(max_Nk2/N));
+    ks := [2..max_weight by 2];
+    k := Random(ks);
+    p := Random(PrimesDivisors(N));
+    printf "(%o;%o;%o),", N, k, p;
+    testPariVSMS(N,k,p : New);
+end for;
+
 printf "\n";

magma_functions.m

@@ -150,6 +150,7 @@ function alpha(n)
 // Theorem 4. 
 // (Also appears in Skoruppa-Zagier, but this way of stating the formula was easier to work with).
 function TraceFormulaGamma0AL(n, N, k)
+    if (n eq 0) return 0; // for compatibility with q-expansions
   S1 := 0;
 //  max_abst := Floor(SquareRoot(4*N*n));
   max_abst := Floor(SquareRoot(4*N*n)) div N;