
// Make newform 525.3.l.e in Magma, downloaded from the LMFDB on 19 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_525_l();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_525_3_l_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_525_l();"
function MakeCharacter_525_l()
    N := 525;
    order := 4;
    char_gens := [176, 127, 451];
    v := [4, 3, 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_525_l_Hecke(Kf)
    return MakeCharacter_525_l();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_525_3_l_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_525_3_l_e( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_525_l();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,3,sign)));
    Vf := Kernel([<2,R![8151025, 22611600, 31363200, 7172680, 5439926, 16637328, 28377632, 2637128, 1555023, 4398976, 6580864, 412336, 233556, 480192, 395968, 66992, 13791, 12656, 8704, 2056, 278, 48, 32, 8, 1]>],Snew);
    return Vf;
end function;