
// Make newform 984.2.f.b in Magma, downloaded from the LMFDB on 02 August 2026.
// To make the character of type GrpDrchElt, type "MakeCharacter_984_f();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_984_2_f_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_984_f();"
function MakeCharacter_984_f()
    N := 984;
    order := 2;
    char_gens := [247, 493, 329, 457];
    v := [2, 1, 2, 2];
    // 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_984_f_Hecke( : Kf := Kf)
    return MakeCharacter_984_f();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_984_2_f_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_984_2_f_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_984_f();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![12005146624, 0, 186402996224, 0, 1202825954304, 0, 4323823243776, 0, 9797379023424, 0, 14985646180480, 0, 16156018009600, 0, 12643121186560, 0, 7332998108176, 0, 3199456892576, 0, 1060978708288, 0, 269121373456, 0, 52357716024, 0, 7803829704, 0, 886077584, 0, 75765640, 0, 4782625, 0, 215576, 0, 6550, 0, 120, 0, 1]>],Snew);
    return Vf;
end function;