
// Make newform 6003.2.a.t in Magma, downloaded from the LMFDB on 20 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6003_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6003_2_a_t();".
// 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_6003_a();"
function MakeCharacter_6003_a()
    N := 6003;
    order := 1;
    char_gens := [668, 3133, 4555];
    v := [1, 1, 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_6003_a_Hecke(Kf)
    return MakeCharacter_6003_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6003_2_a_t();".
// 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_6003_2_a_t( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6003_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![-8, 72, 160, -2210, -367, 17913, 1897, -47584, -7005, 62065, 11841, -46018, -10527, 20569, 5350, -5619, -1603, 914, 279, -81, -26, 3, 1]>,<5,R![-11776, 12544, 174456, -200000, -803402, 766338, 1754456, -1148070, -2026985, 797776, 1302361, -287664, -487751, 57170, 110310, -6288, -15211, 356, 1244, -8, -55, 0, 1]>],Snew);
    return Vf;
end function;