
// Make newform 891.2.n.h in Magma, downloaded from the LMFDB on 28 December 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_891_n();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_891_2_n_h();".
// 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_891_n();"
function MakeCharacter_891_n()
    N := 891;
    order := 15;
    char_gens := [650, 244];
    v := [10, 3];
    // 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_891_n_Hecke(Kf)
    return MakeCharacter_891_n();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_891_2_n_h();".
// 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_891_2_n_h( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_891_n();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![625, 0, 3125, 0, -42750, 0, 435625, 0, 5774700, 0, -7088350, 0, 4852840, 0, -3074520, 0, 1341341, 0, -95164, 0, -34480, 0, 10994, 0, -1116, 0, 39, 0, 30, 0, -9, 0, 1]>],Snew);
    return Vf;
end function;