
// Make newform 1890.2.bk.b in Magma, downloaded from the LMFDB on 19 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_1890_bk();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_1890_2_bk_b();".
// 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_1890_bk();"
function MakeCharacter_1890_bk()
    N := 1890;
    order := 6;
    char_gens := [1541, 757, 1081];
    v := [5, 6, 5];
    // 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_1890_bk_Hecke(Kf)
    return MakeCharacter_1890_bk();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_1890_2_bk_b();".
// 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_1890_2_bk_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1890_bk();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<11,R![14197824, -101509920, 95688888, 1045514460, -662516447, -6238850064, 5284091106, 20187115416, -4841591358, -32480720730, 4427035076, 33978464478, 14097193170, -5797511820, -3383730237, 691093044, 518216412, -42262812, -46324254, 1859094, 3003606, -41034, -131338, 618, 4191, 0, -81, 0, 1]>],Snew);
    return Vf;
end function;