
// Make newform 8035.2.a.e in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_8035_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_8035_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_8035_a();"
function MakeCharacter_8035_a()
    N := 8035;
    order := 1;
    char_gens := [4822, 4826];
    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_8035_a_Hecke(Kf)
    return MakeCharacter_8035_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_8035_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_8035_2_a_e( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_8035_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![145148388552576, -813334995914112, -44484093199779552, 239990850092435328, 5987583604348941904, -31419984512182338528, -470501239554114939098, 2428784289579501486023, 24248027511757313639240, -124670885081969408090980, -874619942483049790823342, 4539288205353337841897434, 23044267856073148918819850, -122484036993011548607370374, -457385722076748164188013361, 2529702554013665336832811637, 6997152386281218534139930236, -41018758463714343952071516363, -83882069186945921186116126447, 533099420898768497881341532685, 796172689692307895593420494544, -5649900104531968574372393531568, -5998043962707822891580933107358, 49547369878676569526356329277898, 35481666808607034831387581827549, -364058950712506421405913379170417, -158033064383774653863610012932096, 2265561697162353733582466966167700, 451632622645215693495629856086232, -12053244909766172159877520686884838, -1638386878136427182592157040970, 55273315415865612612672586449793567, -9525512576094101647565443676001047, -220056586129425781209820201716376726, 71481994709671686194099255576308346, 765430233995313908578829515180096765, -354214898074371039603507500169495717, -2339038038368394857473087769016741110, 1381507321209583852248371647203154222, 6310002651962681208452755329671419439, -4495199503807871145378040344175615200, -15090104361351973220192453703883888214, 12551758777901339763776621622898908761, 32103379009555481357339853914335641551, -30582668826531535267547112407301327694, -60930931457823991846407714746866128587, 65755617976575896806048649220519173593, 103387211410948318015355965509811833563, -125785717805213700682211011477510196781, -157027781445739881211470275008333803414, 215434116505920221061390554329493260261, 213514895157321061243282691744139006550, -332034724571600234553132795706902605192, -259547086074010646670309825276868844067, 462435477436076543712357307784530466442, 280998502250091769451517014507035533169, -584031066622867683667015572555643329631, -268826976202845468045790869229080295770, 670845953385125591911386239469627396934, 223652434411188863108161105273918536306, -702591802886712411505247458671628712716, -156188397504834920314388173152570024172, 672359601100630435387949802543323893807, 83037927713461371943610672732781341692, -588971889151488128777090058675941325557, -20137513526306292009493260602582116304, 472955592263189274310129523815280124781, -22665266598007033058029643341123835249, -348565758826227554357845381129795050934, 43502119257614603073556647445889568127, 235971749616856523908621849416685291582, -46776519301604309454732205107799729798, -146817659668614723605271365189581853628, 39629139489586594897908971136477898717, 83968494753453912044341286587097470570, -28689756222658579381932377572030771113, -44133626959722416492436438646593235177, 18338493138618329637091410923019387495, 21301438191765731700370251456647301043, -10522528264393875008252528133251040879, -9427788175300495069491402046928623078, 5472088903358659269151642128856780786, 3817098625230199436735123449289823631, -2594572881347817618270320513586116319, -1408370463987228661790030546153190283, 1126073132669063768625502773517275375, 470631501432562148325193828747980801, -448535411344885779042593574253935602, -140968539972126850980682414287938374, 164250609750523590506000699435763976, 37138713960551142362731004439803871, -55354920844435540671240403038178861, -8270364073286894434701019466116342, 17177784210686903755889804306855578, 1395551025977278855607349126631767, -4908568903128165994725562447380122, -95002476890820315415535791095811, 1291030830304683306975452436100422, -49202001456353553922475336806045, -312265724398929497458325549891555, 28976806486415150546826634572577, 69358573292463527502067579698568, -10146901477788280670531008120553, -14117852929641474710484455097288, 2828459245674868537700928439338, 2625874697418075896111719195383, -675008930865677501887381099355, -444485517407720883593129719824, 141941748326355428788593812990, 68077550964149433434647395742, -26661058948348180829685335570, -9353074299615513918365247423, 4503929128119115446705133682, 1136792690064639263001007561, -686516216388491496405652900, -119229496009428686715551168, 94506688437503701188697219, 10229319948328020793277359, -11741219445425442804077433, -609942956678201905489339, 1313642672266801191482075, 2456413186683742253222, -131893831955538966901402, 5842902997917860954538, 11823271874940162219272, -1048042168285183514333, -939541597488829291677, 125348541287005192412, 65521732222403140878, -11900679576017833023, -3951014121772393704, 941256162225526789, 201190662507428677, -63009173260701049, -8282474251567163, 3577933309522652, 248312544409955, -171305910956213, -3347966636643, 6824179967813, -156887061300, -221243236239, 13688564893, 5631719208, -569460574, -105646146, 15650249, 1271036, -289788, -5477, 3323, -79, -18, 1]>],Snew);
    return Vf;
end function;