
// Make newform 8048.2.a.w in Magma, downloaded from the LMFDB on 19 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_8048_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_8048_2_a_w();".
// 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_8048_a();"
function MakeCharacter_8048_a()
    N := 8048;
    order := 1;
    char_gens := [1007, 6037, 2017];
    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_8048_a_Hecke(Kf)
    return MakeCharacter_8048_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_8048_2_a_w();".
// 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_8048_2_a_w( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_8048_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![-6975, 96075, -352393, -201656, 3283135, -3552545, -8616843, 16057667, 9102362, -30297247, -1517343, 32502445, -6135414, -21987083, 7259134, 9778677, -4242683, -2880795, 1532820, 547243, -361198, -60915, 55568, 2583, -5370, 203, 295, -29, -7, 1]>,<5,R![16384, -679936, -4202496, 5040128, 44774400, -9321984, -193010432, -15729280, 433183552, 86852064, -559528688, -142573640, 438757456, 121533088, -216194521, -60921514, 68579183, 19083015, -14229831, -3870424, 1941171, 515671, -171998, -44755, 9505, 2432, -297, -75, 4, 1]>,<7,R![64747, 14611448, -25586220, -1241989768, -5384748307, -5723248017, 9406901591, 19142053658, -4087711971, -21275240495, -692942392, 13091596848, 1023712539, -5175904367, -263036371, 1385181085, -7271766, -252702977, 17386870, 30762437, -4047703, -2376115, 465151, 104502, -29380, -1832, 969, -24, -13, 1]>,<13,R![-3458323023, -34875208174, 11645601274, 276677070242, 52725641564, -772645999885, -285748580416, 1004301005795, 410409685893, -735213449827, -274506482565, 340367669628, 99409122718, -105467473685, -19904790711, 22157390972, 1894019408, -3103512781, 13372937, 278908353, -21693273, -15108228, 2131755, 439767, -94601, -4659, 2000, -47, -16, 1]>],Snew);
    return Vf;
end function;