
// Make newform 3467.2.a.b in Magma, downloaded from the LMFDB on 11 February 2025.
// To make the character of type GrpDrchElt, type "MakeCharacter_3467_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_3467_2_a_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_3467_a();"
function MakeCharacter_3467_a()
    N := 3467;
    order := 1;
    char_gens := [2];
    v := [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_3467_a_Hecke(Kf)
    return MakeCharacter_3467_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_3467_2_a_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_3467_2_a_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_3467_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![41591, -1153203, -30739739, 745666005, 8394030048, -195489192333, -1059469012545, 26983759433269, 60298442947204, -2155463401668448, -691128137524015, 105517006529290988, -91230534349029219, -3334948874173789363, 5415576674956895996, 71774659553423392212, -153658076448651874718, -1105499918473675492345, 2781086316131110906536, 12740997594198651670582, -35643518149051146469137, -114233996667641540218746, 343291826811327242929923, 823546070408332604873629, -2585987008868511141283448, -4906595428472938636136991, 15683417249439522024694982, 24696756162917174420076677, -78266174361221659474781776, -106816187121870325574881627, 326845959603767755184514016, 401927109102642658744006531, -1157481807769453799574720469, -1327001135151927743794676644, 3513219785169487345602351748, 3865903803779278797414105006, -9218555111171352914727740717, -9974764023674524547782310700, 21059783033684706499327857872, 22855038526019267611024110570, -42130796239258480840473020826, -46605761692634207083296810102, 74159218673571662844788379440, 84755213155128439528817337632, -115296014340322495002438993127, -137739031184067582464933895100, 158794539983179992665509335929, 200457986192391736006399743573, -194149937190607879896336699613, -261808272825001474021323085788, 210962839003679797741821490073, 307496877596832195291955677827, -203709143327264496861048987873, -325434829463540303159926085437, 174506589247643780703020401726, 310934604939042635203429542995, -132065062741323313519553221213, -268660945299805766725161403120, 87548391984099421691680054266, 210252674522769698559754359982, -49978693444944705335456599504, -149233115427221091604702970634, 23661228502936674328420669909, 96176327453021841249093240506, -8358255601326929123866267262, -56330609122466476614403913615, 1207885740150411538313034638, 30004255064607619879502884385, 1170908151252407091213133582, -14539833637516477135458656169, -1389827764291333901823339738, 6411023416232673598284315453, 957039140529361804192442233, -2571598176926111519677660240, -517223434333089153239260175, 937879626191037150394027478, 236544890855423716293155822, -310696072505470991841047307, -94370718830921232984273023, 93351269126953272809700516, 33342281235536858771370059, -25384197902977353892268317, -10519210049928625105361816, 6227885299169534786916976, 2977452828749880419137452, -1372692869821244358007471, -758043923286340730123051, 270107004116559507975984, 173787709188121110992488, -46998878182899142966868, -35878672268238935375616, 7119515448866582700171, 6664565944730412329277, -912258328930424731708, -1111964248411958474209, 92643992230402376509, 166225094593984959258, -5963346188437996395, -22187096969546153026, -153323422942849277, 2632454199051476473, 121833733011302221, -276046411811293523, -23016291216200856, 25395386901473617, 3031697008068444, -2030005402541727, -316057440532419, 139193049131279, 27043752516280, -8041046398409, -1917227505704, 380991946973, 112213185734, -14152984575, -5352244050, 375343705, 203311537, -5164726, -5926711, -66912, 124649, 5240, -1685, -115, 11, 1]>],Snew);
    return Vf;
end function;