
// Make newform 6014.2.a.k in Magma, downloaded from the LMFDB on 23 April 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6014_a();"
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6014_2_a_k();".
// 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_6014_a();"
function MakeCharacter_6014_a()
    N := 6014;
    order := 1;
    char_gens := [1553, 2915];
    v := [1, 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_6014_a_Hecke(Kf)
    return MakeCharacter_6014_a();
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6014_2_a_k();".
// 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_6014_2_a_k( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6014_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![36928, 806784, -2874428, -37671504, 113474396, 503433900, -1750770611, -1603541828, 8932995524, 142201009, -22166053682, 8469687820, 31037150516, -19614923127, -26183720498, 22391006582, 13568315892, -15628656346, -4082227034, 7235539521, 453119674, -2311578690, 158013460, 518116558, -86120718, -81258118, 20403811, 8678893, -2970936, -585075, 280752, 19243, -16855, 226, 586, -41, -9, 1]>],Snew);
    return Vf;
end function;