
// Make newform 6034.2.a.m in Magma, downloaded from the LMFDB on 23 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6034_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6034_2_a_m();".
// 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_6034_a();"
function MakeCharacter_6034_a()
    N := 6034;
    order := 1;
    char_gens := [1725, 869];
    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_6034_a_Hecke(Kf)
    return MakeCharacter_6034_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6034_2_a_m();".
// 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_6034_2_a_m( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6034_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![-4, -502, -515, 8474, 756, -35624, -3629, 69210, 16140, -71161, -26535, 39484, 19951, -11444, -7657, 1479, 1546, -5, -155, -16, 6, 1]>,<5,R![-1721, -5563, 38040, 80243, -282544, -321315, 713317, 597766, -786300, -607364, 407587, 353928, -86999, -113339, -1753, 17851, 3184, -1077, -350, 5, 11, 1]>,<11,R![-206981567, -274820533, 457651853, 766321083, -272216648, -830299414, -94152681, 424597614, 174164718, -90267992, -73546061, -2134972, 11786108, 3485592, -312972, -353290, -60918, 3617, 2886, 462, 34, 1]>],Snew);
    return Vf;
end function;