
// Make newform 3024.2.df.e in Magma, downloaded from the LMFDB on 03 September 2025.
// To make the character of type GrpDrchElt, type "MakeCharacter_3024_df();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_3024_2_df_e();".
// 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_df();"
function MakeCharacter_3024_df()
    N := 3024;
    order := 6;
    char_gens := [1135, 757, 785, 2593];
    v := [6, 6, 5, 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_3024_df_Hecke( : Kf := Kf)
    return MakeCharacter_3024_df();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_3024_2_df_e();".
// 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_df_e( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_3024_df();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![-6476, 220260, -2383875, 11529738, -25983819, 19294080, 23713832, -47326098, 6433746, 33359910, -15323967, -11791020, 8008817, 2387970, -2188401, -287724, 357756, 20280, -36005, -768, 2175, 12, -72, 0, 1]>],Snew);
    return Vf;
end function;