
// Make newform 552.2.j.c in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_552_j();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_552_2_j_c();".
// 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_552_j();"
function MakeCharacter_552_j()
    N := 552;
    order := 2;
    char_gens := [415, 277, 185, 97];
    v := [1, 1, 1, 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_552_j_Hecke(Kf)
    return MakeCharacter_552_j();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_552_2_j_c();".
// 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_552_2_j_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_552_j();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![-24576, 81920, 1161728, -2604544, -1057792, 5175360, -695168, -4343136, 1357216, 1998768, -770480, -566000, 226032, 105136, -38152, -13112, 3716, 1064, -192, -50, 4, 1]>],Snew);
    return Vf;
end function;