
// Make newform 448.4.p.i in Magma, downloaded from the LMFDB on 27 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_448_p();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_448_4_p_i();".
// 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_448_p();"
function MakeCharacter_448_p()
    N := 448;
    order := 6;
    char_gens := [127, 197, 129];
    v := [3, 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_448_p_Hecke(Kf)
    return MakeCharacter_448_p();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_448_4_p_i();".
// 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_448_4_p_i( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_448_p();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,4,sign)));
    Vf := Kernel([<3,R![4676116197806541709109567689921, 0, 9394161400766762409131347842016, 0, 12686404844211936743585781455334, 0, 8886052974121192231073939387488, 0, 4356838756072247850806872344885, 0, 1284558218917654106446532410656, 0, 268384315640267182691984101010, 0, 40792489000176884633104315376, 0, 4756143179919866617599831642, 0, 431449248315000137169215264, 0, 31173615152506462376659038, 0, 1808464726268356068959616, 0, 85482265650796941761645, 0, 3316510092600763623008, 0, 106553225146940033694, 0, 2843568923387820624, 0, 63216983534888410, 0, 1167602862866208, 0, 17851857344466, 0, 223414613312, 0, 2257274037, 0, 17868192, 0, 106534, 0, 432, 0, 1]>],Snew);
    return Vf;
end function;