
// Make newform 950.2.l.j in Magma, downloaded from the LMFDB on 24 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_950_l();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_950_2_l_j();".
// 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_950_l();"
function MakeCharacter_950_l()
    N := 950;
    order := 9;
    char_gens := [77, 401];
    v := [9, 7];
    // 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_950_l_Hecke(Kf)
    return MakeCharacter_950_l();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_950_2_l_j();".
// 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_950_2_l_j( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_950_l();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![361, 7011, 30519, -94541, 189279, -249030, 213039, -186606, 407952, -566631, 465867, -305019, 229042, -30366, -792, 4734, 423, -9, 630, -81, 9, -13, 0, 0, 1]>],Snew);
    return Vf;
end function;