
// Make newform 6017.2.a.e in Magma, downloaded from the LMFDB on 08 May 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_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_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_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_6017_2_a_e( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6017_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![3654928, -14166822446, -850666435415, 8385609950962, 294613934873435, -2143702364263821, -32495402139200046, 193365951908389937, 1878650570610983801, -8729270205998935568, -67176999354004785872, 231771667594423237924, 1599426635487690185676, -3988957935748556830316, -26564906381323085815410, 48050474368104447391163, 321130867929945772431563, -431769403118790887751925, -2937392006587090851933721, 3050211652821685198424271, 21009443876146672334461843, -17679915780031511081958150, -120655987793908395157907290, 86896890875826107923165948, 568168941006821977116570465, -370366997541476041352462340, -2230436428951372844916123955, 1385623618934758186333369029, 7395706413273010894099628348, -4569824345883690425019647797, -20930882258666629907146171378, 13285585781496598442385404838, 50987167156155495000738116010, -34006274013350659839137112726, -107632528857707234679335622203, 76587312369002167954409769755, 197973862649400606398385679976, -151842294047428254093775008275, -318668499529032517405357246345, 265422625688603163098807276366, 450379166250627084080105720118, -409990368202544603995951446718, -560173853059499559190938845743, 561109915611013578327115252415, 613872358135178424581334901593, -682282037443051196839179530872, -592564132320471233227824815611, 739098916070604754323725971584, 502715302368588433565782318181, -715109315919548135269158266105, -372812993131974030290551952978, 619410162316569682833283246331, 238998925294589315018325106640, -481283720239396432767419230038, -129374549707812877812090825703, 336034797777725630688093099166, 55878495553037484124642807505, -211116250190854594915765288766, -15847004098341378315955423749, 119466438479687834084168134734, -903441639639149573399640542, -60927271276192977541205182657, 5114665341839950337084923539, 28007381044043747091998159722, -4376901356552258669362092951, -11599641484464341302968627453, 2630106942270243009364717521, 4323656116487399766124527437, -1287387870329117657920372328, -1447543506211195625728835914, 538912418678817382774833140, 433898789495223697817419159, -197190673177645633188535215, -115854627177502966017399027, 63787772754254786874710185, 27331239136406797799553157, -18355909283222688073932112, -5618318673219100563325680, 4714546467603336744837802, 980459495863370750854234, -1082271098605100259647389, -136938143914656733197380, 222046699261880246177389, 12597250567259504784726, -40663260935576560434470, 204349816542957709004, 6629931186922644620954, -408254181126576085985, -958645915080942928395, 110677771384299981254, 122230185504043685586, -20695410684022717409, -13630873012870144378, 3088432855142683363, 1313595559170644951, -384299317340976299, -107338420492980075, 40502193467064317, 7191730116333312, -3629039583865843, -367209393267384, 275535236110321, 11131426104566, -17567732264438, 186371693646, 926338926255, -51802291129, -39439036252, 3915466768, 1304212569, -190173158, -31225948, 6463884, 458276, -150680, -1533, 2187, -73, -15, 1]>,<3,R![-14226059242, 80622570500077, 2236548293304130, -33226062855575959, -1009323121475392300, 6764685760966209374, 162039909581850162318, -913183890197906743089, -11191120560854736300345, 66979247035951535703604, 387459516747081221832274, -2748750081850877865833530, -6964508875691173514651021, 67868155526610408599281656, 52474800952193718184606583, -1075371662817176505915661584, 313575614434047083348586131, 11521600937033704582040452174, -11908968531097903022343913368, -86845944256634598342652383244, 143653011520226501409689391650, 472534696360139137666017439141, -1087514986157678957787236975377, -1868486464475615442440177098848, 5919233402964622344437221286000, 5206140361678543634054488988680, -24607384786699487590976252734628, -8665950092826633567843317419038, 80953003783908175040424825285016, -1562643536205262035989186616847, -215782607530678612204496713692769, 66175714597248129578528178687656, 473830785150962194585208692012434, -260354634644054633252857036953020, -867228652612306359223565435380736, 671083495601360410582473777970766, 1333115080040657599201231964859971, -1335404709444388621386689939132003, -1727308637621690513616630044510391, 2172707559336379473816014318823947, 1883293701161840771007815833001110, -2974547090821358194219530021614856, -1710237254156394585604029871249343, 3486575028801093052051624563286211, 1256906745963342733636431554839922, -3539995407699184755632178464835045, -687172787429561059738190787177505, 3139596945387123123252520742642173, 185584198941977423291544149045034, -2447515094326384133986500609389275, 134437674778379233591455317347522, 1684996847343802312572540790097069, -261259765579215269257556783794197, -1028025936471509018675352682145528, 253386782052470016481380161800707, 557163233421231815708395009029825, -185826667991362886431704024339196, -268609901380898003578408058798550, 112881207516883791427112263181743, 115216698852671468737805265601806, -58885977571852187587498087027504, -43918511514801042359846050628556, 26867659658234587184666837833283, 14830696725081531523987062158527, -10836518541697310574529900287966, -4409413151775885809870119547418, 3889409949075280037392581543389, 1140955348652406804038033952641, -1247636523281571584827410343991, -251095920273151901277133095486, 358682119866044560698497995584, 44578454579712279926688742230, -92569231606692827276602709997, -5385061042394563987994817462, 21462622327306243306597260678, -2362698484051217972943196, -4470249013471694967584463961, 236388517578865950250333530, 835688302632515948935208907, -85283124032562608115690015, -139985665687709161702753678, 20910790009656613264318477, 20954676689511753806724974, -4121539226744569799345700, -2792009414740569710243425, 687327129049917957512704, 329233668546974034704308, -99061720546865152267059, -34070920329744719444097, 12458371617368244779953, 3054241188648624435840, -1372439167142261755016, -232020253263724809612, 132475586059748446277, 14306742792535944597, -11178798352228797689, -640355821250755071, 820864203073716575, 11330082656802770, -52084224808514846, 1287446435474742, 2827223485455545, -170087590754863, -129464763372519, 12221339839989, 4901840597468, -636455007461, -148846018901, 25392599366, 3442416173, -778598683, -54422555, 17901786, 400181, -292149, 4093, 3027, -130, -15, 1]>],Snew);
    return Vf;
end function;