
// Make newform 289.10.a.f in Magma, downloaded from the LMFDB on 25 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_289_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_289_10_a_f();".
// 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_289_a();"
function MakeCharacter_289_a()
    N := 289;
    order := 1;
    char_gens := [3];
    v := [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_289_a_Hecke(Kf)
    return MakeCharacter_289_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_289_10_a_f();".
// 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_289_10_a_f( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_289_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,10,sign)));
    Vf := Kernel([<2,R![7801864302886912, -163370561667072, -199999161683968, 1073492625408, 1574980020224, -553645824, -4976376048, -201024, 6952624, 0, -4353, 0, 1]>,<3,R![107402923277166167536257955901629545204783513600, 0, -7793746970318963446774488950724872735933595648, 0, 14830316701491162945730762881388669093908480, 0, -9798637454514002132231233746227677327872, 0, 3041656055772959106121939762448512512, 0, -501451815139148401964262458702208, 0, 48056305266631153020871785024, 0, -2832961878053209915300512, 0, 105600489865287015376, 0, -2491134059265736, 0, 35998259964, 0, -290380, 0, 1]>],Snew);
    return Vf;
end function;