
// Make newform 184.2.i.b in Magma, downloaded from the LMFDB on 14 April 2026.
// To make the character of type GrpDrchElt, type "MakeCharacter_184_i();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_184_2_i_b();".
// 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_184_i();"
function MakeCharacter_184_i()
    N := 184;
    order := 11;
    char_gens := [47, 93, 97];
    v := [11, 11, 5];
    // 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_184_i_Hecke( : Kf := Kf)
    return MakeCharacter_184_i();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_184_2_i_b();".
// 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_184_2_i_b( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_184_i();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![175561, -483107, 7598293, -8348514, 17085578, -43579794, 45690577, -40479703, 48107131, -30857315, 19631836, -16271151, 12041169, -4170647, 2472814, -1411230, 732569, -117465, 96337, -56644, 32930, -4232, 698, 247, 379, -99, -21, 17, -4, -2, 1]>],Snew);
    return Vf;
end function;