
// Make newform 336.2.s.c in Magma, downloaded from the LMFDB on 19 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_336_s();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_336_2_s_c();".
// 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_336_s();"
function MakeCharacter_336_s()
    N := 336;
    order := 4;
    char_gens := [127, 85, 113, 241];
    v := [2, 1, 2, 4];
    // 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_336_s_Hecke(Kf)
    return MakeCharacter_336_s();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_336_2_s_c();".
// 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_336_2_s_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_336_s();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![4096, 0, 0, 0, 97953792, 0, 0, 0, 76121088256, 0, 0, 0, 120968371712, 0, 0, 0, 60484955136, 0, 0, 0, 10173002880, 0, 0, 0, 699116768, 0, 0, 0, 19415584, 0, 0, 0, 201200, 0, 0, 0, 784, 0, 0, 0, 1]>],Snew);
    return Vf;
end function;