
// Make newform 8001.2.a.x in Magma, downloaded from the LMFDB on 20 August 2025.
// To make the character of type GrpDrchElt, type "MakeCharacter_8001_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_8001_2_a_x();".
// 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_8001_a();"
function MakeCharacter_8001_a()
    N := 8001;
    order := 1;
    char_gens := [3557, 1144, 7750];
    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_8001_a_Hecke( : Kf := Kf)
    return MakeCharacter_8001_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_8001_2_a_x();".
// 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_8001_2_a_x( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_8001_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![-16, 0, 308, 0, -2300, 0, 8680, 0, -18281, 0, 22362, 0, -16187, 0, 7111, 0, -1912, 0, 307, 0, -27, 0, 1]>,<5,R![-64, 0, 3372, 0, -49728, 0, 194868, 0, -330463, 0, 285212, 0, -138490, 0, 40077, 0, -7048, 0, 737, 0, -42, 0, 1]>],Snew);
    return Vf;
end function;