
// Make newform 4023.2.a.e in Magma, downloaded from the LMFDB on 17 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_4023_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_4023_2_a_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_4023_a();"
function MakeCharacter_4023_a()
    N := 4023;
    order := 1;
    char_gens := [299, 3727];
    v := [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_4023_a_Hecke(Kf)
    return MakeCharacter_4023_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_4023_2_a_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_4023_2_a_e( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_4023_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![-72, -1315, 1914, 23057, -21482, -135992, 84303, 397153, -128221, -655068, 45894, 636153, 73945, -373639, -95149, 133613, 49584, -28232, -14090, 3119, 2275, -87, -196, -14, 7, 1]>],Snew);
    return Vf;
end function;