
// Make newform 6010.2.a.j in Magma, downloaded from the LMFDB on 23 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6010_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6010_2_a_j();".
// 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_6010_a();"
function MakeCharacter_6010_a()
    N := 6010;
    order := 1;
    char_gens := [3607, 2411];
    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_6010_a_Hecke(Kf)
    return MakeCharacter_6010_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6010_2_a_j();".
// 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_6010_2_a_j( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6010_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![-657664, 1732160, 22149312, -14181520, -233442640, -38699716, 1042601108, 462050385, -2465797698, -1276673808, 3531238536, 1748334422, -3340940267, -1419053708, 2201296380, 736220099, -1040380819, -250755340, 357699643, 55097339, -89736586, -6993978, 16324818, 227073, -2119079, 82065, 190460, -15516, -11223, 1302, 389, -56, -6, 1]>],Snew);
    return Vf;
end function;