
// Make newform 930.2.y.b in Magma, downloaded from the LMFDB on 19 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_930_y();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_930_2_y_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_y();"
function MakeCharacter_930_y()
    N := 930;
    order := 10;
    char_gens := [311, 187, 871];
    v := [5, 5, 3];
    // 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_y_Hecke(Kf)
    return MakeCharacter_930_y();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_930_2_y_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_y_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_930_y();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<17,R![224461605092423348228709154816, -4929204718666195770447188459520, 21765804811565952515283631341568, 105329114050329385255182061076480, 201581198437426136044987420655616, 106464353681362473960186533273600, -116387729869844041626645529119488, -121238798724243020514066133484160, 66241973411953780941057640935184, 94479931832144135672509212316920, -52498047830213382344345139204088, -91327365113588423150227916476080, 19173487705785205834783970269933, 79002593432178055004022734776855, 28358640866180267075166140396283, -24321945401298844534764231808895, -21625663929530603506373615245705, -408211136014122092195108123790, 5964401072743271258729155536218, 2187739181372177864527170501405, -305144602286970010808235555460, -229570103473704411033586215990, 97013681036285245481417726827, 66746263499744822106523482780, -4452532290346118088180448547, -9558086415902489130512101665, -348686324772047694315714286, 1068158943856419732405580630, 97373572686305684842385033, -107056897695194150565702530, -14756002402973942464559489, 9468123827091132883643015, 1826119148216783216642615, -671538423548298958233585, -168542485172937001190198, 40019922946329745208795, 12452720991314490324360, -2102665753522635407755, -785333558655550695658, 98234809442794326725, 43592105258543793263, -3962166390169858640, -2110430564748612791, 141233531851417250, 89596630673938811, -4565647912413095, -3378311891369067, 131061703620005, 114188494838341, -3211377857390, -3402109331789, 72294681910, 88575513026, -1500593270, -2019251580, 22146010, 41209598, -380300, -656404, 4410, 8611, -45, -98, 0, 1]>],Snew);
    return Vf;
end function;