
// Make newform 483.2.q.d in Magma, downloaded from the LMFDB on 19 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_483_q();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_483_2_q_d();".
// 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_483_q();"
function MakeCharacter_483_q()
    N := 483;
    order := 11;
    char_gens := [323, 346, 442];
    v := [11, 11, 6];
    // 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_483_q_Hecke(Kf)
    return MakeCharacter_483_q();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_483_2_q_d();".
// 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_483_2_q_d( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_483_q();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![59049, 3050865, 66718809, 822987783, 6655533804, 38355862851, 167568971697, 558898220619, 1466017178184, 2945523677313, 4621962120610, 5601139276251, 6278999116426, 6313749895316, 5045740985831, 2173036978081, 2318480801167, 215694456076, 626157593652, 951741265125, 1361714713112, 2013042470250, 2374384728046, 2298682788068, 2459607670697, 1555405315787, 1423892950739, 572899459439, 500823775361, 66510834698, 109475340284, -27147586455, 27657508867, -8349761612, 12325241776, -1681386329, 3359225035, -849236365, 609889212, -199106827, 166013146, -22043228, 28770294, -4641299, 3924007, -316920, 873066, -165743, 98081, -17735, 23510, -3384, 3030, -143, 729, -20, 50, -14, 8, 1, 1]>],Snew);
    return Vf;
end function;