==============================================================================================================================================================
🔸️d=5:


Chi:= function(p)
Eps1:=Generators(DirichletGroup(15,CyclotomicField(4)));
Eps1:=Eps1[1]*Eps1[2];
Eps2:=Generators(DirichletGroup(20,CyclotomicField(4)));
Eps2:=Eps2[1]*Eps2[2];
if KroneckerSymbol(-5,p) eq -1 then
   f:=order(Eps1(p));
else
	f:=order(Eps2(p))*2;
end if;
return f;
end function;

--------------------------------------------------------------------------------------------------------------------------------------------------------------
G:=DirichletGroup(2^4*3^2*5^2,CyclotomicField(4));                           
eps:=(Elements(G)[50]);
M:=ModularSymbols(eps,2,1);
S:=NewSubspace(CuspidalSubspace(M));
new:=NewformDecomposition(S);
CM:=FormsWithCM(new);

[ 1, 2, 3, 4, 7, 9, 10 ]


for i in [1..#new] do         
if i notin CM then
print(DiscardPlace(5,eps,Chi,new,i,13,50));
end if;
end for;      

{@ 2, 5 @}
{@ 2, 5 @}
Cannot discard the form with parameter:  8
[]
Cannot discard the form with parameter:  11
[]
Cannot discard the form with parameter:  12
[]
Cannot discard the form with parameter:  13
[]
{@ 2, 5 @}
{@ 2, 5 @}

--------------------------------------------------------------------------------------------------------------------------------------------------------------
eps:=Extend(eps,2^4*3^3*5^2);
M:=ModularSymbols(eps,2,1);
S:=NewSubspace(CuspidalSubspace(M));
new:=NewformDecomposition(S);
CM:=FormsWithCM(new);

[ 1, 2, 3, 4, 5, 6 ]

for i in [1..#new] do         
if i notin CM then
print(DiscardPlace(5,eps,Chi,new,i,13,50));
end if;
end for;      

Cannot discard the form with parameter:  7
[]
Cannot discard the form with parameter:  8
[]
Cannot discard the form with parameter:  9
[]
Cannot discard the form with parameter:  10
[]
{@ 2, 5 @}
{@ 2, 5 @}
{@ 2, 5 @}
{@ 2, 3, 5 @}
{@ 2, 5 @}
{@ 2, 3, 5 @}
{@ 2, 3, 5 @}
{@ 2, 3, 5 @}
{@ 2, 3, 7 @}
{@ 2, 5 @}
{@ 2, 5 @}
{@ 2, 3 @}
{@ 2, 3 @}
{@ 2, 5 @}


==============================================================================================================================================================
🔸️d=6:


Chi:= function(p)
if KroneckerSymbol(-6,p) eq -1 then
	f:=order(KroneckerSymbol(-1,p)*KroneckerSymbol(p,2)*KroneckerSymbol(p,3));
else
   f:=2*order(KroneckerSymbol(-1,p)*KroneckerSymbol(p,3));
end if;
return f;
end function;

--------------------------------------------------------------------------------------------------------------------------------------------------------------
G:=DirichletGroup(2^8*3^5);
eps:=Generators(G)[1]*Generators(G)[3];
M:=ModularSymbols(eps,2,1);
S:=NewSubspace(CuspidalSubspace(M));
new:=NewformDecomposition(S);
CM:=FormsWithCM(new);


> #new;
58
> #CM;
8

> CM;
[ 1, 2, 3, 4, 5, 6, 41, 42 ]


> for i in [1..51] do
for> if i notin CM then
for|if> print(DiscardPlace(6,eps,Chi,new,i,1,13));
for|if> end if;
for> end for;
{@ 2, 3 @}
{@ 2, 3 @}
{@ 11, 2, 3 @}
{@ 11, 2, 3 @}
{@ 2 @}
{@ 2 @}
{@ 2, 3, 5 @}
{@ 2, 7 @}
{@ 2, 3 @}
{@ 2, 3 @}
{@ 2, 5 @}
{@ 2, 5 @}
{@ 11, 2, 3 @}
{@ 2, 3 @}
{@ 11, 2, 3 @}
{@ 2, 3 @}
{@ 11, 2, 5 @}
{@ 11, 2, 5 @}
{@ 11, 2, 5 @}
{@ 11, 2, 5 @}
{@ 3 @}
{@ 3 @}
{@ 2 @}
{@ 2 @}
{@ 2, 13 @}
{@ 2, 13 @}
{@ 2 @}
{@ 2 @}
{@ 2, 13 @}
{@ 2, 13 @}
{@ 2, 3 @}
{@ 2 @}
{@ 2, 3, 5 @}
{@ 2, 3, 5 @}
{@ 2 @}
{@ 2, 5 @}
{@ 2 @}
{@ 2, 7 @}
{@ 37 @}
{@ 37 @}
{@ 37 @}
{@ 37 @}
{@ @} 

/* Discarding new[i] for i=52,...,58. */

/* Magma */

> ApCand(6,5);
{ -3, 0, 3 }

> ApCand(6,11);
{ -6, -3, 0, 3, 6 }

/* new[52] */

f:=PowerSeries(new[52],12);
Write("Form52Coef5.txt",Coefficient(f,5));
Write("Form52Coef11.txt",Coefficient(f,11));
Write("Form52Pol.txt",Parent(Coefficient(f,5)));

/* new[53] */

f:=PowerSeries(new[53],12);
Write("Form53Coef5.txt",Coefficient(f,5));
Write("Form53Coef11.txt",Coefficient(f,11));
Write("Form53Pol.txt",Parent(Coefficient(f,5)));

/* new[54] */

f:=PowerSeries(new[54],12);
Write("Form54Coef5.txt",Coefficient(f,5));
Write("Form54Coef11.txt",Coefficient(f,11));
Write("Form54Pol.txt",Parent(Coefficient(f,5)));

/* new[55] */

f:=PowerSeries(new[55],12);
Write("Form55Coef5.txt",Coefficient(f,5));
Write("Form55Coef11.txt",Coefficient(f,11));
Write("Form55Pol.txt",Parent(Coefficient(f,5)));

/* new[56] */

f:=PowerSeries(new[56],12);
Write("Form56Coef5.txt",Coefficient(f,5));
Write("Form56Coef11.txt",Coefficient(f,11));
Write("Form56Pol.txt",Parent(Coefficient(f,5)));

/* new[57] */

f:=PowerSeries(new[57],12);
Write("Form57Coef5.txt",Coefficient(f,5));
Write("Form57Coef11.txt",Coefficient(f,11));
Write("Form57Pol.txt",Parent(Coefficient(f,5)));

/* new[58] */

f:=PowerSeries(new[58],12);
Write("Form58Coef5.txt",Coefficient(f,5));
Write("Form58Coef11.txt",Coefficient(f,11));
Write("Form58Pol.txt",Parent(Coefficient(f,5)));

/* PARI/GP */

/* new[52] */

P=read("Form52Pol.txt");
coef5=read("Form52Coef5.txt");
coef11=read("Form52Coef11.txt");
P=subst(P,x,a);

n5=norm(coef5*Mod(1,P))*norm(coef5^2*Mod(1,P)+9)*norm(coef5^2*Mod(1,P)+36);
n11=norm(coef11*Mod(1,P))*norm(coef11^2*Mod(1,P)-9)*norm(coef11^2*Mod(1,P)-36)*norm(144-coef11^2*Mod(1,P));

factor(gcd(n5,n11))

%11 = 
[ 2 84]

[13  8]


/* new[53] */

P=read("Form53Pol.txt");
coef5=read("Form53Coef5.txt");
coef11=read("Form53Coef11.txt");
P=subst(P,x,a);

n5=norm(coef5*Mod(1,P))*norm(coef5^2*Mod(1,P)+9)*norm(coef5^2*Mod(1,P)+36);
n11=norm(coef11*Mod(1,P))*norm(coef11^2*Mod(1,P)-9)*norm(coef11^2*Mod(1,P)-36)*norm(144-coef11^2*Mod(1,P));

factor(gcd(n5,n11))

%18 = 
[ 2 36]

[11  4]

[13  8]


/* new[54] */

P=read("Form54Pol.txt");
coef5=read("Form54Coef5.txt");
coef11=read("Form54Coef11.txt");
P=subst(P,x,a);

n5=norm(coef5*Mod(1,P))*norm(coef5^2*Mod(1,P)+9)*norm(coef5^2*Mod(1,P)+36);
n11=norm(coef11*Mod(1,P))*norm(coef11^2*Mod(1,P)-9)*norm(coef11^2*Mod(1,P)-36)*norm(144-coef11^2*Mod(1,P));

factor(gcd(n5,n11))

%25 = 
[2 132]


/* new[55] */

P=read("Form55Pol.txt");
coef5=read("Form55Coef5.txt");
coef11=read("Form55Coef11.txt");
P=subst(P,x,a);

n5=norm(coef5*Mod(1,P))*norm(coef5^2*Mod(1,P)+9)*norm(coef5^2*Mod(1,P)+36);
n11=norm(coef11*Mod(1,P))*norm(coef11^2*Mod(1,P)-9)*norm(coef11^2*Mod(1,P)-36)*norm(144-coef11^2*Mod(1,P));

factor(gcd(n5,n11))

%32 = 
[3 40]


/* new[56] */

P=read("Form56Pol.txt");
coef5=read("Form56Coef5.txt");
coef11=read("Form56Coef11.txt");
P=subst(P,x,a);

n5=norm(coef5*Mod(1,P))*norm(coef5^2*Mod(1,P)+9)*norm(coef5^2*Mod(1,P)+36);
n11=norm(coef11*Mod(1,P))*norm(coef11^2*Mod(1,P)-9)*norm(coef11^2*Mod(1,P)-36)*norm(144-coef11^2*Mod(1,P));

factor(gcd(n5,n11))

%47 = 
[3 40]

/* new[57] */

P=read("Form57Pol.txt");
coef5=read("Form57Coef5.txt");
coef11=read("Form57Coef11.txt");
P=subst(P,x,a);

n5=norm(coef5*Mod(1,P))*norm(coef5^2*Mod(1,P)+9)*norm(coef5^2*Mod(1,P)+36);
n11=norm(coef11*Mod(1,P))*norm(coef11^2*Mod(1,P)-9)*norm(coef11^2*Mod(1,P)-36)*norm(144-coef11^2*Mod(1,P));

factor(gcd(n5,n11))

%65 = 
[ 3 60]

[37  8]


/* new[58] */

P=read("Form58Pol.txt");
coef5=read("Form58Coef5.txt");
coef11=read("Form58Coef11.txt");
P=subst(P,x,a);

n5=norm(coef5*Mod(1,P))*norm(coef5^2*Mod(1,P)+9)*norm(coef5^2*Mod(1,P)+36);
n11=norm(coef11*Mod(1,P))*norm(coef11^2*Mod(1,P)-9)*norm(coef11^2*Mod(1,P)-36)*norm(144-coef11^2*Mod(1,P));

gcd(n5,n11)
%10 = 1

==============================================================================================================================================================
🔸️d=7:

Chi:= function(p)
if KroneckerSymbol(-7,p) eq -1 then
   f:=1;
else
	f:=2*order(KroneckerSymbol(p,3)*KroneckerSymbol(p,7));
end if;
return f;
end function;

--------------------------------------------------------------------------------------------------------------------------------------------------------------
G:=DirichletGroup(2*3*7^2);
eps:=Generators(G)[1]*Generators(G)[2];
M:=ModularSymbols(eps,2,1);
S:=NewSubspace(CuspidalSubspace(M));
new:=NewformDecomposition(S);

for i in [1..#new] do         
print(DiscardPlace(7,eps,Chi,new,i,13,23));
end for;      

Cannot discard the form with parameter:  1
[]
{@ 2, 7 @}

--------------------------------------------------------------------------------------------------------------------------------------------------------------
G:=DirichletGroup(2^2*3*7^2);
eps:=Generators(G)[2]*Generators(G)[3];
M:=ModularSymbols(eps,2,1);
S:=NewSubspace(CuspidalSubspace(M));
new:=NewformDecomposition(S);


CM:=FormsWithCM(new);
> [1]

for i in [2..#new] do
for> print(DiscardPlace(7,eps,Chi,new,i,2,20));
for> end for;
{@ 2, 3 @}
{@ 2, 3 @}
{@ 2, 7 @}

--------------------------------------------------------------------------------------------------------------------------------------------------------------
G:=DirichletGroup(2^2*3^3*7^2);
eps:=Generators(G)[2]*Generators(G)[3];
M:=ModularSymbols(eps,2,1);
S:=NewSubspace(CuspidalSubspace(M));
new:=NewformDecomposition(S);

FormsWithCM(new);
[ 1, 2, 3 ]

for i in [4..#new] do
for> DiscardPlace(7,eps,Chi,new,i,2,20);             
for> end for;
{@ 5, 2, 3 @}
{@ 3, 7 @}
{@ 2, 7 @}
{@ 2, 7 @}

--------------------------------------------------------------------------------------------------------------------------------------------------------------
G:=DirichletGroup(2*3^3*7^2);
eps:=Generators(G)[1]*Generators(G)[2];
M:=ModularSymbols(eps,2,1);
S:=NewSubspace(CuspidalSubspace(M));
new:=NewformDecomposition(S);

for i in [1..#new] do
for> DiscardPlace(7,eps,Chi,new,i,2,13);
for> end for;
Cannot discard the form with parameter:  1
[]
Cannot discard the form with parameter:  2
[]
Cannot discard the form with parameter:  3
[]
{@ 2, 3 @}
{@ 2, 7 @}
{@ 2, 7 @}