
// Make newform 1260.2.cu.e in Magma, downloaded from the LMFDB on 03 May 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_1260_cu();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_1260_2_cu_e();".
// 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_1260_cu();"
function MakeCharacter_1260_cu()
    N := 1260;
    order := 6;
    char_gens := [631, 281, 757, 1081];
    v := [6, 1, 6, 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_1260_cu_Hecke(Kf)
    return MakeCharacter_1260_cu();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_1260_2_cu_e();".
// 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_1260_2_cu_e( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1260_cu();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<11,R![66918059712, -19307629152, -294061664736, 85380334200, 1003812366312, 468170065062, -1020424104461, -721781791725, 758329986540, 803283239673, -135817926036, -348868191207, -5294340556, 105891521571, 18115349046, -18333153729, -4431157653, 2308901625, 683736051, -190442421, -61404816, 11658348, 3950394, -487287, -164803, 14727, 4971, -270, -87, 3, 1]>,<13,R![117031476966732, 295785842788098, -98746473602727, -879376407482664, 629173884908919, 641831981782170, -404947314594170, -295719173692707, 156192253997829, 105886190168838, -26912616247077, -22307952208491, 3018500557254, 3368580747567, -122072787921, -344628109791, -6192160773, 26290286847, 1594577231, -1462536525, -128583282, 62117361, 6860229, -1932966, -242523, 44547, 6222, -666, -99, 6, 1]>],Snew);
    return Vf;
end function;