
// Make newform 6026.2.a.i in Magma, downloaded from the LMFDB on 24 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6026_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6026_2_a_i();".
// 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_6026_a();"
function MakeCharacter_6026_a()
    N := 6026;
    order := 1;
    char_gens := [787, 4325];
    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_6026_a_Hecke(Kf)
    return MakeCharacter_6026_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6026_2_a_i();".
// 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_6026_2_a_i( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6026_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![480, 8592, -75432, -20566, 572504, -31045, -1790863, 98986, 2984669, -7020, -2930821, -157487, 1787922, 182547, -698837, -98966, 177184, 30728, -28890, -5749, 2914, 640, -165, -39, 4, 1]>,<5,R![211472, 589040, -2114360, -5514395, 9206992, 19667280, -22090572, -33671119, 29724951, 30735161, -22546058, -16817018, 10201372, 5932777, -2885610, -1398236, 522683, 222057, -60535, -23410, 4330, 1566, -174, -60, 3, 1]>],Snew);
    return Vf;
end function;