
// Make newform 1470.2.d.g in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_1470_d();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_1470_2_d_g();".
// 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_1470_d();"
function MakeCharacter_1470_d()
    N := 1470;
    order := 2;
    char_gens := [491, 1177, 1081];
    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_1470_d_Hecke(Kf)
    return MakeCharacter_1470_d();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_1470_2_d_g();".
// 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_1470_2_d_g( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1470_d();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<11,R![4384, 0, 330880, 0, 266528, 0, 44976, 0, 3066, 0, 92, 0, 1]>,<13,R![429632, 0, -900544, 0, 486448, 0, -71072, 0, 4204, 0, -108, 0, 1]>,<23,R![-1264, -1024, 1192, -96, -62, 4, 1]>],Snew);
    return Vf;
end function;