
// Make newform 6033.2.a.e in Magma, downloaded from the LMFDB on 02 May 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6033_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6033_2_a_e();".
// 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_6033_a();"
function MakeCharacter_6033_a()
    N := 6033;
    order := 1;
    char_gens := [2012, 2014];
    v := [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_6033_a_Hecke(Kf)
    return MakeCharacter_6033_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6033_2_a_e();".
// 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_6033_2_a_e( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6033_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![-3597258368, 46968525952, 1264505173504, -9265221117840, -125391057938464, 723415475841976, 5430405522885138, -27868090331249016, -131827259471976284, 629609587985745873, 2036585750168868954, -9316475538374593015, -21579865668655415183, 97195340180532204324, 164623366357557367973, -752228824410777888947, -933261370087488066855, 4478828983592327715158, 4004485974483114906067, -21074998179569288452087, -13053419347689260372717, 79993809630674863465741, 31652479705748441641274, -248879189427302556004667, -52127415334804592097402, 642868676818059784739616, 32915822323052193523024, -1393054861921954754923357, 119902426190282523821488, 2554001542511385835258812, -530917676330988451762680, -3989420253347666456617264, 1271829812703806399442453, 5339357092203014092084074, -2258228242696619808637486, -6150149891535445147650634, 3224434384567767039527034, 6116482369735310403148766, -3835960788532600070311236, -5262169432331091977713886, 3877073717435584052142901, 3917459091842951630347532, -3370458842461710852234150, -2518799036217936205339576, 2541486042049029691912919, 1391281207237549292359647, -1672328085065185690765206, -652643257447934195873648, 964497893355609530735909, 253670827072262517862790, -489106600543681787913321, -76892554306121721371343, 218557481933280122813553, 14639050258283379343736, -86165546586336507706440, 1033934227149396183658, 29982956406431203889132, -2491634812122974871602, -9203600612036601603017, 1373050111597639425577, 2488292201278040155829, -529902160652699878116, -590833377892828164188, 163871861691770207705, 122647045865944743922, -42450368407893893790, -22099122068186775852, 9387782315190234709, 3417326220679821454, -1787571661002723184, -444851251653573648, 293985879852232997, 46968219152610622, -41740439448106879, -3671391865503584, 5099542926231439, 142490456454554, -532883611583432, 12823626407571, 47192563025393, -3350437010233, -3495109742735, 403951038372, 212276766193, -34195051468, -10259156821, 2184174960, 374699872, -106124057, -9271878, 3835105, 104494, -97687, 1783, 1570, -85, -12, 1]>],Snew);
    return Vf;
end function;