
// Make newform 105.3.k.d in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_105_k();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_105_3_k_d();".
// 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_k();"
function MakeCharacter_105_k()
    N := 105;
    order := 4;
    char_gens := [71, 22, 31];
    v := [2, 1, 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_105_k_Hecke(Kf)
    return MakeCharacter_105_k();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_105_3_k_d();".
// 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_3_k_d( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_105_k();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,3,sign)));
    Vf := Kernel([<2,R![33062500, 0, 0, 0, 2187309, 0, 0, 0, 47127, 0, 0, 0, 383, 0, 0, 0, 1]>,<11,R![25047000, 0, 2343020, 0, 63614, 0, 497, 0, 1]>,<13,R![253806379264, 0, 0, 0, 17091165504, 0, 0, 0, 288088400, 0, 0, 0, 66241, 0, 0, 0, 1]>],Snew);
    return Vf;
end function;