
// Make newform 8035.2.a.c in Magma, downloaded from the LMFDB on 19 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_c();".
// 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_c();".
// 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_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_8035_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![-28908672, -2246069888, -50200167712, -100175622496, 9774004180624, 92080866915872, -567934943064986, -10428507048390815, 3648943342355929, 577096519198821830, 985809689525036738, -19651730691356700188, -53034595725964559980, 462972633666878391334, 1471538109191125726101, -8116521883604426931860, -26905570356572286663604, 110910296057416509522284, 354441141191572637134516, -1215294337453622491271856, -3530439559190726337700737, 10862784267661374235998718, 27427389333394814601149432, -80100723301039192799319173, -169848169580710602921348505, 491556986474570218917553667, 851631336610051950925766886, -2530423705106724203054686894, -3494968967737031676920338980, 11010359130956976965151630189, 11810145215390220869769517012, -40793322272319973839679095211, -32862929745704363179813691856, 129592652018638970962391472474, 74563378208645024467405696678, -355289061864347559502425234256, -133657952242484229369308509790, 845563334550199048396826688683, 171094829353798879919689037502, -1756109984220065452044277769939, -85227865678089304367175336180, 3197359773253356594491512117092, -287746791492030299568998174212, -5123472517281859339191815360693, 1114674710019241116093762681589, 7248741385755678072357866858801, -2451984129482293341663022862213, -9077113122442937772769937890672, 4141393724827140592092718592957, 10076418364904878911245542440860, -5805193486425198165322097023876, -9921266704070154007742797993856, 6980433400400232638823684606856, 8656715580027131671663203689448, -7328499315487598499130547135458, -6674200138432604877262423364289, 6790417589487833936120023068623, 4518458686408284237612992286023, -5592718550759242924813748435743, -2652885978468235466449835169686, 4114662017001638011821307333286, 1316081596319256439988856149045, -2713470926275163550318573130750, -517490486526753878746906010754, 1607714110648447734692202909040, 127490540083288668098820913488, -857031431153259399590097426448, 17099030239299465017792432975, 411270475092649232309191080377, -45843447828848959095127464709, -177603118021058129721464285465, 35376511642644716984535542977, 68922294019053430594286228933, -19791099284494737936469979707, -23969119334439270984050283936, 9113600810775847690256332567, 7434521737864419386616761082, -3608148095014605870449974919, -2040157243796513304857661395, 1252591852796798120446271752, 488366428200238888896936718, -385143937615329774807028169, -99224844907884587902346081, 105430179470440922307320479, 16052155868870488012632354, -25751357371243113110469026, -1651592570074036087883166, 5612762412805901439328419, -73102386079578621464982, -1089795564316297043888315, 91474259236778228909121, 187806890098039197143654, -28696615418267684221932, -28550115903458110019985, 6403506271817929478888, 3790981434899356883125, -1156585768652192390262, -432529875981173191904, 176150724811884902691, 41140327311334757407, -22975984528957074990, -3048005928876189000, 2578185311852099969, 139281126156195055, -248388950676446362, 2926402803224399, 20393962142767324, -1448839171134773, -1407604796983455, 182126922909863, 79791592189295, -15507801753211, -3560225250986, 1002402680752, 113643299461, -50286666544, -1793237354, 1934268229, -45448609, -54765569, 4103677, 1043516, -135985, -10468, 2414, -9, -19, 1]>],Snew);
    return Vf;
end function;