
// Make newform 6014.2.a.l in Magma, downloaded from the LMFDB on 25 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_l();".
// 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_l();".
// 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_l( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6014_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<3,R![-8280704, -159088896, -1008088336, -1618999968, 5988497556, 18219295016, -10543145843, -66329671593, -2686817826, 132262913209, 38348941159, -169442623666, -70418587880, 150791234653, 73124344101, -97498518114, -51096444174, 47073391050, 25670851998, -17252913439, -9582547021, 4842211062, 2703376062, -1043149252, -580493420, 171854088, 94797715, -21423972, -11671487, 1981809, 1063667, -131567, -69454, 5915, 3068, -161, -82, 2, 1]>],Snew);
    return Vf;
end function;