
// Make newform 560.2.ci.e in Magma, downloaded from the LMFDB on 19 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_560_ci();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_560_2_ci_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_560_ci();"
function MakeCharacter_560_ci()
    N := 560;
    order := 12;
    char_gens := [351, 421, 337, 241];
    v := [12, 12, 3, 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_560_ci_Hecke(Kf)
    return MakeCharacter_560_ci();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_560_2_ci_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_560_2_ci_e( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_560_ci();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![16, -96, 288, -576, -254356, -992880, 10546056, 282620724, 3316308805, 14953045788, 38873693664, 57400499340, -59760950417, -178197690192, 355688393040, -436015842120, 300366469871, -44975130792, -65244262752, 91700497224, -59760709994, 7335287088, 7957675224, -12111625044, 8744524425, -1130059980, -450345600, 795912084, -595284143, 61843488, 17943696, -35199336, 29303893, -2687784, -396288, 940104, -837746, 59808, 5832, -16524, 17131, -996, 0, 108, -153, 0, 0, 0, 1]>],Snew);
    return Vf;
end function;