
// Make newform 290.2.l.a in Magma, downloaded from the LMFDB on 01 May 2026.
// To make the character of type GrpDrchElt, type "MakeCharacter_290_l();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_290_2_l_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_290_l();"
function MakeCharacter_290_l()
    N := 290;
    order := 14;
    char_gens := [117, 31];
    v := [7, 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_290_l_Hecke( : Kf := Kf)
    return MakeCharacter_290_l();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_290_2_l_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_290_2_l_a( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_290_l();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![4096, 269312, 5934336, 27371712, 256344336, 60911884, 1573273829, -2680583947, 19707720435, -27730984070, 71737755927, -135477631656, 86636962549, 115938244161, 20227450119, -569263090304, 1248289961066, -1476787285155, 1421922811375, -1117087555350, 827988707894, -537275004647, 369383223112, -173158070989, 118042863917, -37676721121, 27920868177, -7351699069, 5407060245, -1519976817, 983856182, -294586510, 172499757, -50749548, 27469796, -7649258, 3545983, -840935, 373390, -83703, 37784, -9864, 4296, -981, 346, -65, 24, -4, 1]>],Snew);
    return Vf;
end function;