
// Make newform 882.2.l.c in Magma, downloaded from the LMFDB on 17 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_882_l();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_882_2_l_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_882_l();"
function MakeCharacter_882_l()
    N := 882;
    order := 6;
    char_gens := [785, 199];
    v := [1, 1];
    // 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_882_l_Hecke(Kf)
    return MakeCharacter_882_l();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_882_2_l_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_882_2_l_c( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_882_l();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![5801854959616, 0, 52059454439424, 0, 317870407139328, 0, 915445847130112, 0, 1763628260331264, 0, 2407302859539456, 0, 2499086632353728, 0, 2022730086777216, 0, 1310957208385665, 0, 687937261293688, 0, 295842709935840, 0, 104704605218928, 0, 30674385473278, 0, 7444259677464, 0, 1500214956096, 0, 250619750360, 0, 34716454275, 0, 3969185640, 0, 373119872, 0, 28497576, 0, 1745790, 0, 83216, 0, 2976, 0, 72, 0, 1]>],Snew);
    return Vf;
end function;