
// Make newform 6034.2.a.q in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6034_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6034_2_a_q();".
// 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_6034_a();"
function MakeCharacter_6034_a()
    N := 6034;
    order := 1;
    char_gens := [1725, 869];
    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_6034_a_Hecke(Kf)
    return MakeCharacter_6034_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6034_2_a_q();".
// 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_6034_2_a_q( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6034_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![4000, 120800, 1196240, 3364872, -9827408, -44806804, 25462546, 193447870, -11765005, -410534586, -49852756, 501675844, 98023896, -386130240, -85568716, 198056327, 44091430, -70193714, -14662921, 17555277, 3268182, -3122689, -493453, 392793, 49840, -34149, -3226, 1952, 121, -66, -2, 1]>,<5,R![1373520896, -29285341952, 40674673488, 139056378352, -208995590008, -231641622016, 406285341165, 174571865905, -426285209175, -43364755564, 273724561635, -26889287711, -113548677525, 27795526376, 30885081755, -11691524177, -5371202754, 2935343306, 530887946, -475677065, -12430999, 50348824, -3824986, -3379357, 533303, 130693, -32817, -2041, 1021, -26, -13, 1]>,<11,R![-154646665216, -9444875264, 3304042648064, -4017086851648, -10670835150584, 18357337659892, 9770908530865, -30777132332867, 4283958465634, 23062703369204, -12064721052220, -6993391574220, 7253885299754, -93482921219, -1854102288073, 519644066754, 195514326200, -119608463344, 1519943487, 11666486690, -2196657593, -448633022, 193661210, -5442929, -6896038, 984675, 71556, -27400, 1402, 205, -28, 1]>],Snew);
    return Vf;
end function;