
// Make newform 201.4.e.a in Magma, downloaded from the LMFDB on 16 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_201_e();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_201_4_e_a();".
// 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_201_e();"
function MakeCharacter_201_e()
    N := 201;
    order := 3;
    char_gens := [68, 136];
    v := [3, 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_201_e_Hecke(Kf)
    return MakeCharacter_201_e();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_201_4_e_a();".
// 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_201_4_e_a( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_201_e();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,4,sign)));
    Vf := Kernel([<2,R![3280561357824, -9614714969088, 29840231661568, -37905337520896, 70811613259072, -64999946819872, 111542735415088, -70305249903656, 79563890472256, -33125008336786, 34186556342691, -11350052224861, 9694237689212, -2553047044387, 1925270623021, -426798474319, 277538043758, -49786043872, 29235807558, -4331565754, 2343373088, -278306416, 142164610, -13583227, 6636437, -485539, 230492, -12633, 5911, -210, 99, -2, 1]>],Snew);
    return Vf;
end function;