
// Make newform 120.4.m.b in Magma, downloaded from the LMFDB on 17 March 2026.
// To make the character of type GrpDrchElt, type "MakeCharacter_120_m();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_120_4_m_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_120_m();"
function MakeCharacter_120_m()
    N := 120;
    order := 2;
    char_gens := [31, 61, 41, 97];
    v := [1, 1, 1, 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_120_m_Hecke( : Kf := Kf)
    return MakeCharacter_120_m();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_120_4_m_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_120_4_m_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_120_m();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,4,sign)));
    Vf := Kernel([<7,R![317032936243200000, 0, -57661282883403776, 0, 3651911524519424, 0, -91164670147584, 0, 707003826880, 0, -2379623680, 0, 3946344, 0, -3184, 0, 1]>],Snew);
    return Vf;
end function;