
// Make newform 33.8.e.a in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_33_e();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_33_8_e_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_33_e();"
function MakeCharacter_33_e()
    N := 33;
    order := 5;
    char_gens := [23, 13];
    v := [5, 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_33_e_Hecke(Kf)
    return MakeCharacter_33_e();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_33_8_e_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_33_8_e_a( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_33_e();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,8,sign)));
    Vf := Kernel([<2,R![74869965115833756999378534400, 56752958678298055049687859200, 27571515762117164751687516160, 7475085117526352138950410240, 1540809738324818667335909376, 102152753282923405109755904, 30699613129576828353740800, -92818137928059844280320, 781574790556839177900032, 10191885946048529793024, 7675186969274741022720, 402633713373875745792, 90388394794494254336, 805420971411167488, 751685582598174208, 23139496901245888, 4554658107971664, 188547905635968, 26873462699128, 922138087708, 94011380549, 2089735763, 234979339, 6855516, 574889, 16944, 1036, 22, 1]>],Snew);
    return Vf;
end function;