
// Make newform 1050.3.e.e in Magma, downloaded from the LMFDB on 19 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_1050_e();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_1050_3_e_e();".
// 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_1050_e();"
function MakeCharacter_1050_e()
    N := 1050;
    order := 2;
    char_gens := [701, 127, 451];
    v := [1, 2, 2];
    // 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_1050_e_Hecke(Kf)
    return MakeCharacter_1050_e();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_1050_3_e_e();".
// 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_1050_3_e_e( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_1050_e();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,3,sign)));
    Vf := Kernel([<11,R![2289048336, 0, 817879680, 0, 95989320, 0, 4209048, 0, 76657, 0, 526, 0, 1]>,<13,R![989983296, 0, -30447344608, 0, 2156635604, 0, -48657988, 0, 379213, 0, -1082, 0, 1]>],Snew);
    return Vf;
end function;