
// Make newform 105.4.s.b in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_105_s();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_105_4_s_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_105_s();"
function MakeCharacter_105_s()
    N := 105;
    order := 6;
    char_gens := [71, 22, 31];
    v := [3, 6, 5];
    // 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_105_s_Hecke(Kf)
    return MakeCharacter_105_s();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_105_4_s_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_105_4_s_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_105_s();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,4,sign)));
    Vf := Kernel([<2,R![16057958400, -18831605760, -602278336512, 714941199360, 22349212683840, 8414790503040, -31613771499072, -12846302748288, 32082272078368, 6143376998880, -16330597951524, -1983654307728, 5834154307284, 335728806336, -1274559616144, -38325600414, 200513506917, 2225812986, -22425704664, -51651252, 1902384306, -3155598, -120768972, 289980, 5885991, -9126, -211216, 162, 5598, 0, -96, 0, 1]>],Snew);
    return Vf;
end function;