
// Make newform 6005.2.a.d in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6005_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6005_2_a_d();".
// 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_6005_a();"
function MakeCharacter_6005_a()
    N := 6005;
    order := 1;
    char_gens := [1202, 11];
    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_6005_a_Hecke(Kf)
    return MakeCharacter_6005_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6005_2_a_d();".
// 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_6005_2_a_d( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6005_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![-316, -103072, -1661024, 18230941, 321303925, -421040147, -17601132548, -6670840841, 504905613061, 426760970045, -9222729794686, -8111596150134, 117332234328936, 84852370777281, -1088996160803876, -537276642723364, 7573678645832388, 1931912570400083, -40227130875828395, -1620467186238466, 166001072241655420, -23314836373508873, -541371531967023231, 155865792068062425, 1418659499679190682, -577574574088575871, -3033373571559489220, 1528027785553471464, 5364989767167766583, -3125831446912774951, -7942313868900404115, 5144084765050423076, 9941268708301588122, -6976950957069769445, -10610743678771512693, 7928930487499783808, 9726166843618253640, -7641468199919531358, -7701522063793291760, 6302170586068110191, 5293297194978034940, -4478957338036344451, -3169920335429815759, 2757805391964059870, 1658910836523480251, -1477131807178988948, -760297796380671332, 690310812825672967, 305588453792063987, -282052362459836210, -107788533603604556, 100875920890747432, 33362922051738514, -31591515369411791, -9054367641313787, 8659062286241942, 2151056737634167, -2074463285400315, -446226742882675, 433395934585878, 80544555482120, -78696943041531, -12590256317791, 12363317293900, 1693737023122, -1670203443905, -194511161215, 192478947589, 18867749323, -18724335156, -1524297419, 1516242675, 100630874, -100284703, -5285953, 5275265, 212390, -212179, -6128, 6126, 113, -113, -1, 1]>],Snew);
    return Vf;
end function;