
// Make newform 441.4.p.d in Magma, downloaded from the LMFDB on 10 May 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_441_p();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_441_4_p_d();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose line below.
// The default sign is -1.  You can change this with the optional parameter "sign".
// To make the character of type GrpDrchElt, type "MakeCharacter_441_p();"
function MakeCharacter_441_p()
    N := 441;
    order := 6;
    char_gens := [344, 199];
    v := [3, 1];
    // chi(gens[i]) = zeta^v[i]
    assert UnitGenerators(DirichletGroup(N)) eq char_gens;
    F := CyclotomicField(order);
    chi := DirichletCharacterFromValuesOnUnitGenerators(DirichletGroup(N,F),[F|F.1^e:e in v]);
    return MinimalBaseRingCharacter(chi);
end function;

function MakeCharacter_441_p_Hecke(Kf)
    return MakeCharacter_441_p();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_441_4_p_d();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose line below.
// The default sign is -1.  You can change this with the optional parameter "sign".
function MakeNewformModSym_441_4_p_d( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_441_p();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,4,sign)));
    Vf := Kernel([<2,R![5473632256, 0, -16825737216, 0, 42514440960, 0, -24897057888, 0, 10112445249, 0, -2004524136, 0, 276807698, 0, -26083200, 0, 1836003, 0, -90912, 0, 3282, 0, -72, 0, 1]>],Snew);
    return Vf;
end function;