
// Make newform 6028.2.a.c in Magma, downloaded from the LMFDB on 24 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6028_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6028_2_a_c();".
// 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_6028_a();"
function MakeCharacter_6028_a()
    N := 6028;
    order := 1;
    char_gens := [3015, 2741, 3565];
    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_6028_a_Hecke(Kf)
    return MakeCharacter_6028_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6028_2_a_c();".
// 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_6028_2_a_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6028_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![-1, 89, -901, -26844, -65204, 166751, 527343, -282470, -1464746, -91464, 1835877, 620231, -1182755, -625473, 403859, 303845, -62845, -81754, -1167, 12175, 1899, -879, -253, 14, 11, 1]>,<5,R![1809, -106275, 1059629, -3202348, -234256, 11747938, -6242434, -18276805, 12245974, 16556358, -10926138, -9747347, 5551783, 3870765, -1723177, -1038027, 334736, 185119, -40587, -21366, 2967, 1519, -119, -60, 2, 1]>],Snew);
    return Vf;
end function;