
// Make newform 930.2.bn.b in Magma, downloaded from the LMFDB on 24 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_930_bn();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_930_2_bn_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_bn();"
function MakeCharacter_930_bn()
    N := 930;
    order := 30;
    char_gens := [311, 187, 871];
    v := [30, 15, 4];
    // 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_bn_Hecke(Kf)
    return MakeCharacter_930_bn();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_930_2_bn_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_bn_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_930_bn();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<7,R![119961435612561189036937084665856, 0, -528422635356308149563989494929031168, 0, 459412875067103332066564178126493974528, 0, 346883075165209816086068716309029232574464, 0, 85283633257419129379303939278061718618439680, 0, 10060597882108891837604123611763588628512186368, 0, 608418859437014903865106487152634168094444647168, 0, 17775009157795517435588619952648289792554255247728, 0, 265577789655015525610750036507914600169592232602753, 0, 1951875033855687954236593738056606178543366758534360, 0, 6782113919947036108200199672819814227222725109801130, 0, 4751245915356379200249383154549322614803621461667064, 0, -33322389844561748374885768120815202417564662803792647, 0, -73875447774459333526649463344172401810916688380803998, 0, 105419605947965865216710989182608751717859908050283840, 0, 114533432303950068604275009957635411498130569057736, 0, 88922174366409060995703900731056491952750774774404518, 0, 12617741624492840893279428868625236006697860129301850, 0, 13592455403366539951958540878037400772173200100711967, 0, -28721880573993286166743779376918885685680807153652630, 0, -3054266226437143142305397211174020063158610614827904, 0, 255855917694526243039686043102297429558853350252548, 0, 1742137744102053890988739656260566460548509818467225, 0, 219181631053236225520565454192400683995799148646772, 0, 63320651709906103053523910232490084448170356684825, 0, -25456295414471812879453657151523052940905633173174, 0, -7619941424773539120315899970421427020079889011462, 0, -2736217909024668409499593104943474997277140049930, 0, 11083891713248203025777180866666912669250724422, 0, 83540692226712524434966785236657148361459928420, 0, 31506764140600814165291714160358043022312375467, 0, 6567647656488974218505123125663798482209032400, 0, 824208421812946902704616395688188146517164903, 0, 3632616539805876674446006213533881203942066, 0, -14192986329623960271808366717600106550058860, 0, -4081602438969773403564008143056380515345386, 0, -525418765717072054676099197098997261707809, 0, -30400692020721323568192938062014700810722, 0, 4599723686434956653895898497004420466255, 0, 1314832786595419281795244612346371718860, 0, 192258180162631888072678208257637898946, 0, 13576322350790270209545973801649901472, 0, -337194177982129852092201120315632537, 0, -245512112976494446452282466712444086, 0, -32301991357537916413034678904852600, 0, -2446130157403489278090679482555472, 0, 18459797433598250127533141618833, 0, 27207961589117378051200041344658, 0, 3598953894745092225471833720683, 0, 213637356115176868166292085830, 0, -1095332312880673879446784320, 0, -1894827488212562419827290336, 0, -214700306180372038112479067, 0, -11244158616467596703584698, 0, 210663155414966028431910, 0, 79792000912179938227282, 0, 7005087005411739965730, 0, 282553085672181938408, 0, -5065895617903058844, 0, -1680126457385506910, 0, -112495170620037495, 0, -2800382440955352, 0, 141275403892931, 0, 18180667097914, 0, 882801412180, 0, 9459188784, 0, -1530919115, 0, -99109344, 0, -1977413, 0, 53720, 0, 4183, 0, 102, 0, 1]>],Snew);
    return Vf;
end function;