
// Make newform 735.2.j.e in Magma, downloaded from the LMFDB on 20 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_735_j();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_735_2_j_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_735_j();"
function MakeCharacter_735_j()
    N := 735;
    order := 4;
    char_gens := [491, 442, 346];
    v := [2, 1, 4];
    // 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_735_j_Hecke(Kf)
    return MakeCharacter_735_j();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_735_2_j_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_735_2_j_e( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_735_j();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![100, 0, 0, 0, 11180, 0, 0, 0, 20736, 0, 0, 0, 9508, 0, 0, 0, 1477, 0, 0, 0, 70, 0, 0, 0, 1]>,<13,R![30976, -49280, 39200, -15848, 6361, -4826, 3682, -1504, 334, -26, 8, -4, 1]>,<17,R![310204441600, 0, 0, 0, 173525086080, 0, 0, 0, 12787676836, 0, 0, 0, 288386740, 0, 0, 0, 2187636, 0, 0, 0, 3624, 0, 0, 0, 1]>],Snew);
    return Vf;
end function;