
// Make newform 201.3.h.b in Magma, downloaded from the LMFDB on 18 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_201_h();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_201_3_h_b();".
// 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_h();"
function MakeCharacter_201_h()
    N := 201;
    order := 6;
    char_gens := [68, 136];
    v := [6, 5];
    // 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_h_Hecke(Kf)
    return MakeCharacter_201_h();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_201_3_h_b();".
// 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_3_h_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_201_h();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,3,sign)));
    Vf := Kernel([<2,R![7001316, 7834806, -28689255, -35375067, 105177328, 63101289, -113120469, -56022093, 90847476, 19109964, -34708986, -4432512, 9296878, 508494, -1587316, -41421, 198747, 1779, -16998, -51, 1063, 0, -41, 0, 1]>],Snew);
    return Vf;
end function;