
// Make newform 3024.2.cc.d in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_3024_cc();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_3024_2_cc_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_3024_cc();"
function MakeCharacter_3024_cc()
    N := 3024;
    order := 6;
    char_gens := [1135, 757, 785, 2593];
    v := [6, 6, 5, 3];
    // 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_3024_cc_Hecke(Kf)
    return MakeCharacter_3024_cc();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_3024_2_cc_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_3024_2_cc_d( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_3024_cc();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![16, 0, 53856, 0, 177993612, 0, 10951738504, 0, 493057962489, 0, 10249478613054, 0, 156264354114236, 0, 372991724020632, 0, 596164407077046, 0, 488854659933268, 0, 272106041302614, 0, 110071636201932, 0, 34440299378437, 0, 8543807905098, 0, 1718546285013, 0, 282606885476, 0, 38300303967, 0, 4274287194, 0, 392587973, 0, 29379510, 0, 1771392, 0, 83564, 0, 2973, 0, 72, 0, 1]>],Snew);
    return Vf;
end function;