
// Make newform 880.2.cm.a in Magma, downloaded from the LMFDB on 08 September 2025.
// To make the character of type GrpDrchElt, type "MakeCharacter_880_cm();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_880_2_cm_a();".
// 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_880_cm();"
function MakeCharacter_880_cm()
    N := 880;
    order := 20;
    char_gens := [111, 661, 177, 321];
    v := [20, 20, 5, 18];
    // 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_880_cm_Hecke( : Kf := Kf)
    return MakeCharacter_880_cm();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_880_2_cm_a();".
// 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_880_2_cm_a( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_880_cm();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![625, 1250, 1250, 3750, 5825, 50, -300, -5770, -21604, -9302, -7218, -11726, 33159, 32308, 10734, 33116, -4833, -27498, -198, 1836, 43959, 788, -592, -1156, -2328, 858, 16, 36, 29, -28, 8, -4, 1]>],Snew);
    return Vf;
end function;