load "mazur42p.mg"



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


Chi:= function(p)

G:=DirichletGroup(2^7*5^2,CyclotomicField(4));                       
eps:=(Elements(G)[26]); 

f:=order(eps(p)*KroneckerSymbol(p,5)*KroneckerSymbol(p,2));

if KroneckerSymbol(-5,p) eq 1 then
   f:=2*order(eps(p));
end if;
return f;
end function;

--------------------------------------------------------------------------------------------------------------------------------------------------------------

G:=DirichletGroup(2^7*5^2,CyclotomicField(4));                       
eps:=(Elements(G)[26]); 
M:=ModularSymbols(eps,2,1);
S:=NewSubspace(CuspidalSubspace(M));
new:=NewformDecomposition(S);
CM:=FormsWithCM(new);


> #new;
12
> #CM;
0

> for i in [1..#new] do
for> if i notin CM then
for|if> print(DiscardPlace(5,eps,Chi,new,i,1,30));
for|if> end if;
for> end for;
{@ 2 @}
{@ 2 @}
{@ 2 @}
{@ 2 @}
{@ 2, 7 @}
{@ 2, 7 @}
{@ 2, 7 @}
{@ 2, 7 @}
{@ 13 @}
{@ 13 @}
{@ 13 @}
{@ 13 @}


--------------------------------------------------------------------------------------------------------------------------------------------------------------

G:=DirichletGroup(2^8*5^2,CyclotomicField(4));                       
eps:=(Elements(G)[26]);   
M:=ModularSymbols(eps,2,1);
S:=NewSubspace(CuspidalSubspace(M));
new:=NewformDecomposition(S);
CM:=FormsWithCM(new);

> #new;
55

> #CM;
24


> for i in [1..#new] do
for> if i notin CM then
for|if> print(DiscardPlace(5,eps,Chi,new,i,1,20));
for|if> end if;
for> end for;
{@ 11, 2, 7 @}
{@ 11, 2, 7 @}
{@ 11, 2, 7 @}
{@ 11, 2, 7 @}
{@ 2, 7 @}
{@ 2, 7 @}
{@ 2, 7 @}
{@ 2, 7 @}
{@ 7 @}
{@ 7 @}
{@ 7 @}
{@ 7 @}
{@ 3 @}
{@ 3 @}
{@ 2, 3 @}
{@ 2, 3 @}
{@ 3, 7 @}
{@ 3, 7 @}
{@ @}
{@ @}
{@ 2, 3, 5, 7 @}
{@ 2 @}
{@ 2 @}
{@ 2 @}
{@ 2 @}
{@ 3 @}
{@ 3 @}
{@ 3 @}
{@ 3 @}
{@ 2, 5 @}
{@ 2, 5 @}


> for i in CM do                                 
for> print(MazurTrickMultiplicative(new,3,eps,[i]));
for> end for;
{@ 2 @}
{@ 2 @}
{@ 2 @}
{@ 2 @}
{@ 2 @}
{@ 2 @}
{@ 2 @}
{@ 2 @}
{@ 2, 3 @}
{@ 2, 3 @}
{@ 2, 3 @}
{@ 2, 3 @}
{@ 2, 5 @}
{@ 2, 5 @}
{@ 2 @}
{@ 2 @}
{@ 3, 139 @}
{@ 3, 139 @}
{@ 3, 139 @}
{@ 3, 139 @}
{@ 2, 29 @}
{@ 2, 29 @}
{@ 5, 101 @}
{@ 5, 101 @}

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


Chi:= function(p)

f:=1;

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

--------------------------------------------------------------------------------------------------------------------------------------------------------------
G:=DirichletGroup(2^8*3);
eps:=Elements(G)[6];
M:=ModularSymbols(eps,2,1);
S:=NewSubspace(CuspidalSubspace(M));
new:=NewformDecomposition(S);
CM:=FormsWithCM(new);


> #new;
10
> #CM;
6

> for i in [1..#new] do
for> if i notin CM then
for|if> print(DiscardPlace(6,eps,Chi,new,i,1,10));
for|if> end if;
for> end for;
{@ 2, 7 @}
{@ 2, 7 @}
{@ 2, 7 @}
{@ 2, 7 @}

--------------------------------------------------------------------------------------------------------------------------------------------------------------
G:=DirichletGroup(2^9*3);
eps:=Elements(G)[6];
M:=ModularSymbols(eps,2,1);
S:=NewSubspace(CuspidalSubspace(M));
new:=NewformDecomposition(S);
CM:=FormsWithCM(new);

> #new;
13
> #CM;
3

> for i in [1..#new] do
for> if i notin CM then
for|if> print(DiscardPlace(6,eps,Chi,new,i,1,20));
for|if> end if; 
for> end for;
{@ 2, 7 @}
{@ 2, 7 @}
{@ 2, 7 @}
{@ 2, 7 @}
{@ 2, 5 @}
{@ 2, 5 @}
{@ 2, 5, 7 @}
{@ 2, 5, 7 @}
{@ 2 @}

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


Chi:= function(p)
f:=order(KroneckerSymbol(-1,p)*KroneckerSymbol(p,2)*KroneckerSymbol(p,7));
if KroneckerSymbol(-5,p) eq 1 then
   f:=2;
end if;
return f;
end function;

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

> #new;
2
> #CM;
0


> for i in [1..#new] do
for> if i notin CM then
for|if> print(DiscardPlace(7,eps,Chi,new,i,1,50));
for|if> end if;
for> end for;
{@ 2, 17, 7 @}
Cannot discard the form with parameter:  2
[]

--------------------------------------------------------------------------------------------------------------------------------------------------------------
G:=DirichletGroup(2^8*7^2);
eps:=Elements(G)[1];
M:=ModularSymbols(eps,2,1);
S:=NewSubspace(CuspidalSubspace(M));
new:=NewformDecomposition(S);
CM:=FormsWithCM(new);

> #new;
98
> #CM;
30

> CM;
[ 1, 2, 3, 4, 9, 10, 11, 15, 17, 18, 24, 25, 26, 28, 36, 37, 39, 40, 41, 42, 43, 44, 45, 49, 50, 56, 58, 65, 78, 92 ]


> for i in [1..#new] do
for> if i notin CM then
for|if> print(DiscardPlace(7,eps,Chi,new,i,1,20));
for|if> end if;
for> end for;
{@ 2, 7 @}
{@ 2, 7 @}
{@ 2, 7 @}
{@ 2, 7 @}
{@ 2, 7 @}
{@ 2, 7 @}
{@ 2, 7 @}
{@ 2, 7 @}
{@ 2, 7 @}
{@ 2, 7 @}
{@ 2, 7 @}
{@ 2, 7 @}
{@ 5, 7 @}
{@ 11, 2, 7, 17 @}
{@ 5, 7 @}
{@ 23, 2 @}
{@ 2, 31 @}
{@ 23, 2 @}
{@ 2, 31 @}
{@ 11, 2, 7 @}
{@ 11, 2, 7 @}
{@ 5, 7 @}
{@ 2, 17, 7 @}
{@ 2, 17, 7 @}
{@ 11, 2, 7, 17 @}
{@ 2, 31 @}
{@ 5, 7 @}
{@ 23, 2 @}
{@ 23, 2 @}
{@ 2, 31 @}
{@ 11, 2, 7 @}
{@ 11, 2, 7 @}
{@ 11, 2, 3 @}
{@ 11, 2, 3 @}
{@ 7 @}
{@ 17, 7 @}
{@ 2, 3 @}
{@ 2 @}
{@ 2 @}
{@ 2 @}
{@ 7 @}
{@ 17, 7 @}
{@ 11, 2, 3 @}
{@ 11, 2, 3 @}
{@ 7 @}
{@ 17, 7 @}
{@ 2, 7 @}
{@ 2, 7 @}
{@ 2, 3 @}
{@ 2 @}
{@ 7 @}
{@ 17, 7 @}
{@ 7 @}
{@ 3 @}
{@ 7 @}
{@ 3 @}
{@ 7 @}
{@ 3 @}
{@ 7 @}
{@ 3 @}
{@ 5, 7 @}
{@ 11, 2 @}
{@ 5, 7 @}
{@ 7 @}
{@ 11, 2 @}
{@ 7 @}
{@ 2 @}
{@ 2 @}