
// Make newform 8048.2.a.t in Magma, downloaded from the LMFDB on 25 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_t();".
// 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_t();".
// 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_t( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_8048_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![-3, -174, -1053, 24613, 72941, -122224, -198841, 242586, 202685, -245992, -91271, 138242, 12689, -43853, 3792, 7568, -1646, -607, 219, 8, -10, 1]>,<5,R![82944, 41472, -864000, -565248, 2852544, 1866176, -4182576, -2496704, 3086156, 1640802, -1254476, -600907, 298761, 130866, -42634, -17275, 3571, 1349, -161, -57, 3, 1]>,<7,R![-64245, -67680, 1210434, -387271, -6765650, 8808502, 7522849, -22153317, 12186683, 5026591, -7227954, 1137696, 1294593, -511746, -65584, 63322, -4680, -3045, 571, 31, -15, 1]>,<13,R![-620548203, 922654287, 3293647129, -2645615958, -6996291202, 886251149, 5759437133, 1215972425, -1830253539, -766310241, 181182565, 135914396, 1436755, -10403708, -1204538, 368507, 73110, -4684, -1788, -36, 16, 1]>],Snew);
    return Vf;
end function;