
// Make newform 9065.2.a.bc in Magma, downloaded from the LMFDB on 06 November 2025.
// To make the character of type GrpDrchElt, type "MakeCharacter_9065_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_9065_2_a_bc();".
// 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_9065_a();"
function MakeCharacter_9065_a()
    N := 9065;
    order := 1;
    char_gens := [3627, 5736, 7106];
    v := [1, 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_9065_a_Hecke( : Kf := Kf)
    return MakeCharacter_9065_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_9065_2_a_bc();".
// 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_9065_2_a_bc( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_9065_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![-322, 4580, 25454, -87444, -384896, 789912, 2629814, -4201352, -9991676, 13759080, 23600172, -28777776, -37257324, 39939192, 41200624, -38008184, -32845968, 25436812, 19191441, -12180138, -8284193, 4210688, 2644571, -1050878, -620447, 187272, 105319, -23208, -12555, 1898, 995, -92, -47, 2, 1]>,<3,R![12175, -307170, 2201023, -2216208, -21461394, 47186144, 72936744, -247480536, -85642395, 644310410, -83807567, -979049260, 385648731, 931377990, -543774543, -571664960, 438719284, 225101104, -229247316, -52497516, 81275570, 4356472, -19841700, 1351052, 3306053, -540422, -361585, 91480, 23427, -8702, -621, 452, -15, -10, 1]>,<11,R![-1048867859392, 738766795392, 24813580393128, -21590136563264, -144428375573759, 124313329963282, 341144775311511, -253377530882792, -432816938124811, 246042385165566, 337974938616947, -126927658288568, -172937256719891, 34065250003886, 59217240256891, -2887160724032, -13572380800383, -958839816590, 2050080508703, 355943542272, -195483297085, -55635679826, 10324150281, 4978105592, -118887897, -263534062, -19872379, 7578008, 1264383, -73870, -30811, -1392, 243, 30, 1]>],Snew);
    return Vf;
end function;