
// Make newform 930.2.bj.b in Magma, downloaded from the LMFDB on 16 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_930_bj();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_930_2_bj_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_930_bj();"
function MakeCharacter_930_bj()
    N := 930;
    order := 20;
    char_gens := [311, 187, 871];
    v := [20, 5, 6];
    // 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_930_bj_Hecke(Kf)
    return MakeCharacter_930_bj();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_930_2_bj_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_930_2_bj_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_930_bj();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<7,R![344148528744680629897567854960054866176, 2616250016028775292361291548982562430464, 19222451478713770485674674275451230678528, 85789321114937811320801262418740250196736, 314369699864352633269543076251235539124160, 878316138717180656735750392116461882450560, 2034998366034595353791784190377901834158848, 3460643188813572525441067622548062102933888, 5986509429830092668476320003790205646644624, 5500636763018317285170640985710258707544384, 10240512225560636330244630745182798580795712, 4835405795403993544971910455228319805421648, 14147949342888446322809023053070816621058492, -13218070588816644610597151302915047980204808, 85955030451862420537071069681157432232270200, -171347600950856139326191506225819758500190020, 401509191267335834095276390732666307012641321, -640874603362946982168119323353291917968111304, 1008853482809159030159545017216801990313172524, -1264475572952428777513636901580588380541961880, 1413788995953109877649583343183205906705845478, -1262031201286319212319246775296533772157616892, 885058275365776396235834530974786791942871086, -327881698531043688061341348008383729145109844, -138038607928831129281898684860215469326545647, 472310600043978375075260199677668760792781388, -522708448175637753280431597904318109607837152, 392658959878735845344380871896485986198835368, -163375654313300765588816367478736915234080325, -34329265117937665397559152986580295791067468, 140321115837403727116817630046630340688151656, -141293760628767613706513088413804332516295504, 82954395661449132664397209270157314308942554, -11979542217285238560577205968664847581181812, -28873824873148526378751314958386011834463180, 35127693939137938568113253456347298702137668, -20520206535771754627839213013012365492530933, 3656752034457635702185681259435957737856920, 5278483298370401862283764042422682221221176, -6348722537656104310739905547761542873799448, 3724085649570543536889459091743737303652311, -793565028351362802772884669176306645844196, -797204609570204207400597860592439383556896, 1043888892262495604545762963532378033605388, -599991482192520602182656842274753784111107, 103530888770682618939752330906945273919544, 137601517044409619541441838478575305039246, -149820918120557300372895082489334843621604, 70875899014705146956894184315386148124459, -3181852058887457492473807201404503147112, -20920178229035975775349469767100823818656, 16229690664981813821873056244313220358844, -5139568071901277874087928656547959413492, -1191495162822596687072075715769063229336, 2193046912840219360574411659952468070944, -1106693198506958038305412525810841439956, 153202509334221785930826405867648793301, 172587720533897479075758838089630734272, -138572183376555055608179337792916659700, 43646499794052154511550895471221169260, 3605703291547737326093193758238523336, -10781574300731861373113408756678140936, 5234515814769186227014404565423876578, -890892531717156906549848018053148912, -400793805822858885299883956499933659, 361587892289216309414323891748062136, -132857971034645495004287219224557788, 17199731623334073041377614205323288, 11282757262740567293608384653501879, -10086431782124748558006781972413432, 4029669202784119193413032650031688, -431789244235314438205011597265104, -488299803658711200701677870995526, 332510761196642482881683725981848, -80290687866636994262555591620132, -14858752631610480472032850784408, 17072789672482614572091252479605, -5077839178667553388574980405912, 16353813861577069803295318336, 536690176791997949151342062264, -194131461743718549108101482431, 30040826484995398130517270320, 2840003824010375664414372440, -4705794484793035237723480116, 2137966940761823093305710123, -547711529639733520308760368, -19066794201364098642970710, 91252382950391889608112908, -32175573468089248268701423, 1954224004660013729713580, 2008233603213732639280936, -921879365285701377829096, 169136529447864225537852, 19284453138997154245756, -20147580484703836454488, 5792587167710654716792, -331809051077718839757, -333090086983111300424, 110277998832776165380, -15759288532419552560, -1040590324216858908, 1496046067511002280, -376248364661645818, 39126505183015044, 7321834028047975, -5112767721240388, 902969070274612, -70248223113672, -14789737146271, 13725905798936, -2310602585592, 102498439348, 49506777602, -38265251568, 4947591508, 254676752, -118646475, 58780240, -5811848, -269932, 108383, -127580, 4044, 3256, 475, 84, -42, -4, 1]>],Snew);
    return Vf;
end function;