
// Make newform 6017.2.a.c in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6017_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6017_2_a_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_6017_a();"
function MakeCharacter_6017_a()
    N := 6017;
    order := 1;
    char_gens := [3830, 2190];
    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_6017_a_Hecke(Kf)
    return MakeCharacter_6017_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6017_2_a_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_6017_2_a_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6017_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![-180152, 7183420, 77753998, -6576678351, 92320557636, -125929971480, -7427852230601, 54397455491041, 94342673876700, -2379882052702071, 4523543241964063, 45274219542836007, -176645933344882874, -469221754558206062, 3066725058236107934, 2591789150012999490, -34368146655526341271, -1900248773085428867, 281203235608655176610, -97883635383819763381, -1789610252061573778092, 984183516505497529466, 9200524994177174436470, -5773086519465720891694, -39138969877042281244590, 24409030571134165039110, 139946675377335707171839, -79445318370496767731905, -425099027455952484200109, 204428422984404532119571, 1105379005009035039119362, -418409011010257262095862, -2475128635716532366441262, 670081948181958260217195, 4796082013904359677035660, -785078272292490729606718, -8076764963735885648045931, 490184995652920176941853, 11865902470613755164242860, 438786995796102487375523, -15259395557603979613088913, -1973031326192806538966021, 17227149214617618157633479, 3739536469527992104481914, -17115245032735188228673482, -5162902490455905523118087, 14992033557111536821802045, 5769870631715390814686548, -11592558774179985115604632, -5437006516959534160762521, 7916463922731246158344371, 4410355248074159487494255, -4771644388272761485312705, -3117502111459945588212495, 2533577048021693961835163, 1935365988372236496089288, -1180217519251406288367337, -1060791899271229952567725, 478709770485789990089089, 515180850558248920130948, -166704229143258976994596, -222211668138627212840646, 48437599197433235747950, 85238770477043446399057, -10951081689912943398155, -29092401087201259170731, 1476993950556344373710, 8831667460812402397521, 162580780366823846909, -2381774460359735607884, -194649860121475538020, 569383746524247158832, 80607186173311434564, -120252151187107057382, -24095015332829192271, 22326541314863240228, 5827181211869501230, -3618036415717328351, -1184664391559032143, 506276511621019835, 205632047618476525, -60140085319960400, -30650237165023400, 5884142115399887, 3923838893646655, -444317395496343, -429805771017478, 20997461784190, 39982214914917, 237866442417, -3121951697988, -170745668061, 201108247511, 20217713611, -10411828167, -1533560794, 415287149, 83766328, -11788478, -3321258, 193649, 91677, -44, -1586, -68, 13, 1]>,<3,R![9726334200, 437804399628, -54166617029295, -603832125456282, 44455613871742861, 175557248846583102, -6535181168403427524, -37213657386952125992, 229857779035176396137, 1646902018596652488539, -3804647339357728775851, -35904203947796119537108, 33997170424235844338673, 485931734423754797491375, -132234335372076270892837, -4549768193339541072646811, -595461822568737632488131, 31375530979080835543012846, 12720354698100708090156470, -165969964888737674056851870, -101784561480823992002737544, 692751641692961977915973930, 544311034268000902633167176, -2328802711863403521809441089, -2192005371900408331835519307, 6401269845027502738327045653, 6996311123792375819877135832, -14547295054154085313339104136, -18219412665725347025685392104, 27540318787909989864739372611, 39460327545659587488999411602, -43609490598602077893581313604, -72071032931658158203035086541, 57738789520240736847644503055, 112182931293133065833477966656, -63459443158209620547867247205, -150068361728866098869977454735, 56700333642094355120260996992, 173690069563007827184888337312, -38889094246667454256633729430, -174889265682450416661473402582, 16523721022119484081033740266, 153878906347986604479759745866, 2646694169754217451873096469, -118727484844579993815432894867, -13806351380350648886547849795, 80545048270085608623063772686, 16668127217832619380929098911, -48131955946092536891701230038, -14094773722968245114953886063, 25359008165811336583560812110, 9574969813032380367332196393, -11777962415104388358077300748, -5479171766310009940090313070, 4814908748593800760785763382, 2700835924247749973005747627, -1726555662895736787629073300, -1161034738599421481065810283, 539506452613552091151072807, 438499951623201186890753448, -145130485168052363754042102, -146168323710566679725519546, 32814742103258691477017976, 43119507774770206805144404, -5901636220498001152098305, -11272374627007071880775462, 704919761258259740118055, 2611980421190953741468014, 6274066240069501132149, -536005461775633052129653, -32654690734553756891807, 97221952724621119355911, 11232373780580049745590, -15536280495054469900983, -2620113319585195633705, 2176656676177338975970, 485358568419287118356, -265426462026188606852, -74913331615575633549, 27864297099301368348, 9818227882665355701, -2474293890040485938, -1100557793113365284, 180053181033782014, 105609049755178807, -10013714996109547, -8645970962007414, 335884429055229, 599494714387163, 5188680669427, -34799766457630, -1770023300362, 1662038599911, 150599703921, -63609052692, -8355237250, 1868675119, 334962617, -38839582, -9750278, 459102, 197423, 290, -2502, -95, 15, 1]>],Snew);
    return Vf;
end function;