
// Make newform 288.2.w.b in Magma, downloaded from the LMFDB on 16 September 2025.
// To make the character of type GrpDrchElt, type "MakeCharacter_288_w();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_288_2_w_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_288_w();"
function MakeCharacter_288_w()
    N := 288;
    order := 8;
    char_gens := [127, 37, 65];
    v := [4, 3, 4];
    // 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_288_w_Hecke( : Kf := Kf)
    return MakeCharacter_288_w();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_288_2_w_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_288_2_w_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_288_w();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![4096, -196608, 3506176, -24920064, 54394880, -140255232, 2096988160, 2732515328, 4815478784, 1798410240, 588259328, -803289088, -209092608, 315368448, 17272832, -47824896, 83787904, 13038592, -6281728, 380672, 155648, -181376, 188416, -87168, 48512, -6080, 896, -224, 0, 16, 0, 0, 1]>],Snew);
    return Vf;
end function;