
// Make newform 156.3.l.c in Magma, downloaded from the LMFDB on 09 January 2026.
// To make the character of type GrpDrchElt, type "MakeCharacter_156_l();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_156_3_l_c();".
// 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_156_l();"
function MakeCharacter_156_l()
    N := 156;
    order := 4;
    char_gens := [79, 53, 145];
    v := [2, 2, 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_156_l_Hecke( : Kf := Kf)
    return MakeCharacter_156_l();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_156_3_l_c();".
// 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_156_3_l_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_156_l();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,3,sign)));
    Vf := Kernel([<5,R![6875062221305800657207296, 0, 0, 0, 942160568409654322580684800, 0, 0, 0, 362327559259273920287866880, 0, 0, 0, 24544597082835694804451328, 0, 0, 0, 635097874153701628869632, 0, 0, 0, 7649973272603568869696, 0, 0, 0, 46458501510483932656, 0, 0, 0, 146943603505826140, 0, 0, 0, 244444625842321, 0, 0, 0, 208188820460, 0, 0, 0, 85407078, 0, 0, 0, 15712, 0, 0, 0, 1]>,<7,R![3390902308382717825004100396376457216, 0, 0, 0, 475150032084897340875798872000954368, 0, 0, 0, 17337210431746876637919387954331648, 0, 0, 0, 231996376485041496349669977579520, 0, 0, 0, 1062477601467093525351640768000, 0, 0, 0, 1793951691196550380492967424, 0, 0, 0, 1401959298344125018675520, 0, 0, 0, 574088964070661162656, 0, 0, 0, 132923111574268017, 0, 0, 0, 17986204748884, 0, 0, 0, 1404716438, 0, 0, 0, 58452, 0, 0, 0, 1]>],Snew);
    return Vf;
end function;