
// Make newform 7595.2.a.w in Magma, downloaded from the LMFDB on 13 June 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_7595_a();"
// To make the coeffs of the qexp of the newform in the Hecke field type "qexpCoeffs();"
// To make the newform (type ModFrm), type "MakeNewformModFrm_7595_2_a_w();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose lines below.
// The precision argument determines an initial guess on how many Fourier coefficients to use.
// This guess is increased enough to uniquely determine the newform.
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_7595_2_a_w();".
// 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 ConvertToHeckeField(input: pass_field := false, Kf := [])
    if not pass_field then
        poly := [2, -14, 4, 90, -2, -130, 0, 67, 0, -14, 0, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [88, -222, -890, 282, 1374, -134, -724, 28, 153, -2, -11], [-94, 222, 892, -282, -1374, 134, 724, -28, -153, 2, 11], [-112, 280, 1068, -380, -1634, 190, 858, -41, -181, 3, 13], [112, -290, -1068, 382, 1634, -190, -858, 41, 181, -3, -13], [-142, 362, 1378, -458, -2134, 212, 1124, -43, -237, 3, 17], [-156, 436, 1424, -630, -2154, 322, 1126, -69, -237, 5, 17], [-81, 217, 802, -280, -1244, 134, 657, -28, -139, 2, 10], [174, -440, -1720, 562, 2652, -268, -1392, 56, 293, -4, -21], [166, -426, -1573, 557, 2403, -268, -1259, 56, 265, -4, -19]];
    Rf_basisdens := [1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 1];
    Rf_basisnums := ChangeUniverse([[z : z in elt] : elt in Rf_num], Kf);
    Rfbasis := [Rf_basisnums[i]/Rf_basisdens[i] : i in [1..Degree(Kf)]];
    inp_vec := Vector(Rfbasis)*ChangeRing(Transpose(Matrix([[elt : elt in row] : row in input])),Kf);
    return Eltseq(inp_vec);
end function;


// To make the character of type GrpDrchElt, type "MakeCharacter_7595_a();"
function MakeCharacter_7595_a()
    N := 7595;
    order := 1;
    char_gens := [6077, 5736, 4901];
    v := [1, 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_7595_a_Hecke(Kf)
    return MakeCharacter_7595_a();
end function;


function ExtendMultiplicatively(weight, aps, character)
    prec := NextPrime(NthPrime(#aps)) - 1; // we will able to figure out a_0 ... a_prec
    primes := PrimesUpTo(prec);
    prime_powers := primes;
    assert #primes eq #aps;
    log_prec := Floor(Log(prec)/Log(2)); // prec < 2^(log_prec+1)
    F := Universe(aps);
    FXY<X, Y> := PolynomialRing(F, 2);
    // 1/(1 - a_p T + p^(weight - 1) * char(p) T^2) = 1 + a_p T + a_{p^2} T^2 + ...
    R<T> := PowerSeriesRing(FXY : Precision := log_prec + 1);
    recursion := Coefficients(1/(1 - X*T + Y*T^2));
    coeffs := [F!0: i in [1..prec]];
    coeffs[1] := 1; //a_1
    for i := 1 to #primes do
        p := primes[i];
        coeffs[p] := aps[i];
        b := p^(weight - 1) * F!character(p);
        r := 2;
        p_power := p * p;
        //deals with powers of p
        while p_power le prec do
            Append(~prime_powers, p_power);
            coeffs[p_power] := Evaluate(recursion[r + 1], [aps[i], b]);
            p_power *:= p;
            r +:= 1;
        end while;    
    end for;
    Sort(~prime_powers);
    for pp in prime_powers do
        for k := 1 to Floor(prec/pp) do
            if GCD(k, pp) eq 1 then
                coeffs[pp*k] := coeffs[pp]*coeffs[k];
            end if;
        end for;
    end for;
    return coeffs;
end function;


function qexpCoeffs()
    // To make the coeffs of the qexp of the newform in the Hecke field type "qexpCoeffs();"
    weight := 2;
    raw_aps := [[0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -1, -1, 0, 0, 0, 0, 0, 1, -1], [-1, 0, 0, 0, 1, -1, 1, 0, 0, 0, 1], [-2, 1, -1, -1, 0, 0, 1, 0, 0, 0, 0], [2, 1, 1, -1, 0, 0, -1, -1, 0, 0, 0], [0, 0, 0, 1, 0, 1, -1, 1, 0, -1, 0], [-1, 1, 0, 0, 0, 0, 0, 0, -2, 0, -1], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, -1, 1, -1, 1, 0, 1, -1, -1, 0], [1, -2, 2, 1, -1, 0, -2, -1, 1, 1, 0], [-4, 1, -1, 0, 0, 0, 0, 1, 0, 1, 1], [0, -1, 1, 0, 1, -1, 0, 2, 0, -1, 0], [-1, 1, -2, 0, 0, 1, 1, 2, -1, -1, -1], [0, -1, 0, -1, -1, -1, 0, -2, 0, 1, -1], [1, 2, 0, -2, 2, 3, 0, 2, -1, -1, -1], [1, 1, 0, -1, 0, -1, 1, 0, 0, -1, -1], [1, 5, 4, -1, 0, 1, 1, -2, 2, -1, 2], [0, 0, 0, 1, -4, 2, -1, 0, 0, -1, 0], [-2, -2, -1, -1, -1, -2, 1, -3, -1, 1, -1], [1, -2, -1, 2, -2, 0, -1, 0, -1, 0, 2], [0, 0, 1, -2, -1, -1, 0, 1, 1, -2, 0], [0, -2, -1, 4, -2, 0, -3, 1, -1, -1, -1], [0, -2, -4, 1, -1, 4, -3, 2, -1, 1, -4], [0, -1, 2, -2, 1, 1, 1, -1, 2, 2, -1], [-3, -2, -1, -1, 1, -1, 3, 1, 1, 0, 0], [-5, 1, -1, -3, 2, -2, 0, 2, 1, 0, 0], [-2, 2, 2, 0, 1, -2, 0, -1, 2, 0, 2], [-2, 6, 3, 0, 4, -2, 3, -2, 1, -1, 3], [-1, 2, 0, -3, 3, 0, 2, -1, 1, 1, 4], [-2, 3, 0, -2, 1, -2, 0, -6, 4, 3, 3], [3, 2, 3, 2, -2, 2, 0, 0, 2, -1, 3], [-4, -4, -1, 1, 0, 1, 0, 5, -1, -2, 0], [0, 0, -4, -2, -4, 4, -3, 3, -3, -3, -4], [3, -6, -2, -1, -4, -2, -2, 0, 1, -1, -2], [-1, -2, 1, 3, 0, 1, -3, 2, -3, 0, -2], [-5, 1, -2, -4, 2, 2, 1, 0, 1, 3, -4], [-3, 3, 2, -5, 5, 1, -1, -1, 3, -1, 3], [1, 2, -2, 2, -1, 4, 0, 2, -3, -1, 1], [-1, -1, 2, -3, 2, -1, 2, -1, 2, 2, -1], [5, -1, 3, 2, -2, 1, -3, -4, 4, -1, 2], [-6, 0, -2, -2, -2, -5, 0, -5, 2, 4, 4], [-5, -4, -2, 2, -6, -3, 0, -1, -2, 1, -1], [-6, -3, -3, 2, -4, -1, 2, 3, -3, 1, -1], [-4, 2, 3, -5, 2, -2, 0, 0, 0, 0, 2], [2, -4, -3, -1, -1, 1, 3, 2, 1, -1, 1], [-4, 2, -4, -3, -3, 1, -1, -3, -2, -1, 3], [0, 2, 0, -7, 1, -2, 0, -1, 3, 2, -3], [2, -2, 6, 6, 0, -1, -2, -1, 4, 2, 2], [-4, -1, 2, 6, -3, -4, -2, -2, 1, -1, 0], [-3, -5, -4, 5, -5, -1, 0, 2, -2, 2, -1], [-4, 3, -3, -2, 1, 7, 0, 4, -3, -1, -5], [-1, -1, -2, 1, -7, 1, -1, 3, -6, -1, -5], [4, -1, 5, 4, 4, -2, 2, 3, -2, -3, 3], [3, -2, -1, 3, 1, 0, 0, -3, -1, 3, 2], [-1, 2, -7, -6, -1, 2, 0, -3, 2, 3, 1], [-6, -1, -2, 4, 1, 0, 0, 6, -2, -1, 1], [-2, 0, 3, 1, 1, -2, -2, 1, 2, 2, 1], [-6, -4, -3, -1, -1, -7, 2, -2, 0, 2, -2], [1, 2, -2, -3, 2, 4, 2, 0, -2, -1, -2], [-5, -1, -5, -3, -3, -1, -2, 2, -3, -2, -4], [9, -2, 5, -2, 1, -5, 0, -4, 2, -3, 1], [-4, -5, -3, 0, -2, 7, -6, 4, -1, -1, -6], [2, 1, -3, 0, -1, 2, -2, -5, -1, 1, -1], [-6, -6, 4, 5, -5, -2, 0, -2, 4, 4, 5], [-7, 0, -5, -2, -4, 5, -1, 3, -1, -2, -4], [2, -5, 1, 6, -2, -4, 2, -3, -6, -1, -1], [5, 4, 2, 4, 0, -2, 1, 3, -4, -2, 2], [-8, 5, 4, 5, 3, -4, 2, -2, 0, 1, 3], [2, 2, 2, -1, 0, 1, 1, -2, -3, 1, 4], [-9, 1, -4, -3, 6, -2, 2, 4, 1, -2, 4], [-10, 5, 3, 0, 9, -5, 8, 0, -1, -1, 3], [-3, 3, 2, 1, 4, 3, 1, -6, 6, 3, 4], [-2, 1, 7, 0, 2, 1, -1, -4, 9, -4, 6], [-7, -2, -3, 1, -2, 2, 5, 1, 0, -2, 0], [6, 0, 4, -1, -3, -5, 1, -9, 2, 1, 5], [4, -1, 0, 7, 0, 4, -2, 2, 3, -3, 5], [3, 5, 0, 3, 1, 3, 4, -4, 2, 2, -1], [-1, 4, -3, -8, -1, -9, 6, -6, 2, 5, 5], [-6, 4, -2, -1, 2, 6, -5, 3, -4, 1, -6], [1, -3, 4, 2, 3, -7, 0, 0, -2, 0, 7], [0, -2, 2, 1, 0, 4, -5, -2, 6, 5, 0], [-8, 4, -8, -1, -1, -6, 3, 0, -3, 3, 2], [5, 6, 3, -1, 11, 0, 1, 0, -1, 0, -2], [3, 6, 6, 3, 4, 2, 4, 4, 2, -3, -1], [-1, -6, 5, 5, -4, 0, 2, 0, -1, 1, -2], [-6, 5, 1, 1, 7, -3, 4, 0, -4, -1, 6], [-3, 1, 6, 0, 7, 3, -2, 1, 0, -4, -4], [8, -1, 4, 10, 1, 1, 1, 1, 0, 0, -1], [-6, 1, -1, 0, 1, 6, 2, 5, 3, -1, -2], [-1, -5, -3, 3, -1, 4, 0, 2, 5, -2, 3], [-11, 5, -3, -3, 3, -4, 3, 1, 0, -3, 1], [-4, 7, -1, -6, 3, 6, 1, -3, 3, 4, -5], [5, -5, 0, 1, 3, 1, -1, 9, -3, -5, -1], [-2, 9, 0, 0, 5, -2, 2, 4, -6, -1, -1], [8, -2, 4, 3, 7, -4, 1, 4, 1, -7, 4], [-4, -7, -2, 9, -5, 0, -3, 2, -2, -4, 1], [-5, 5, 3, 4, 9, -1, 5, -5, 0, 1, 3], [-4, 0, -2, 4, 1, 2, -4, -5, 2, 2, 0], [-3, -7, -4, 3, -4, 0, 2, -5, -3, 2, -3], [-1, 0, 0, 3, -6, 0, -6, -4, 3, 7, -2], [8, -1, 2, 1, -4, 2, -2, 2, 4, -1, -2], [-5, -2, -1, -6, -1, 6, -1, 1, 7, 2, -2], [3, -2, -1, 4, -1, 1, -4, -8, 7, 3, 0], [-2, 11, 3, -8, 4, 7, -3, -4, 1, 0, -2], [-4, -11, 5, 5, -2, 4, -1, -1, -1, 0, 1], [-8, -8, -4, -3, 1, -4, 1, -4, 2, 5, 5], [-6, 2, 5, 0, 6, 5, -2, 0, -1, 4, -2], [10, 6, 7, 1, 9, 5, -2, -2, 4, -6, 6], [-10, -2, 0, -3, 5, -1, 2, -2, 5, 4, -5], [-6, 2, 2, -2, 3, -3, 2, -4, 6, 6, 6], [-8, -3, -1, 8, 4, -1, 6, -3, -3, 3, 1], [-3, -3, -3, -6, -2, 2, 0, -4, 2, 0, 5], [8, -4, 13, 0, 6, 4, -7, 1, 6, -3, 3], [11, -5, -1, -4, -1, -2, 0, 2, -3, -2, -7], [-3, 6, 0, -1, 9, -3, 5, -4, 2, 2, 3], [-12, -3, -3, 4, -10, -1, 0, -3, -3, -3, 3], [-10, 6, 2, -1, 3, -2, -1, 0, 0, 3, 7], [5, 0, 11, 9, 4, 1, -1, 0, 5, -2, 3], [-14, 3, -6, -7, 1, 1, 9, -3, 2, 4, 5], [-5, -8, -5, 4, 2, 1, 2, 6, -6, 3, 2], [-10, -11, -11, 2, -1, 4, 0, 3, -5, 1, -3], [-4, 3, -3, -7, 4, -6, 5, 5, -2, 2, -4], [0, 4, -2, -6, 3, 5, 2, 0, -3, 2, -7], [-1, 1, 3, -6, 2, 2, 1, -1, 2, 3, -4], [5, 5, -2, 6, -8, 1, -2, 3, -3, -6, -2], [-8, 6, 1, -4, 4, -2, 1, -1, 0, 1, 11], [-13, -6, 0, -1, 8, 0, 0, 0, -2, 7, 0], [-6, -9, -5, -8, -1, -2, -1, -5, 1, 4, 1], [7, -9, 1, 3, -7, -4, -6, -2, -1, 0, 3], [2, -6, 5, 2, 10, -3, 3, 2, 1, 3, -2], [-15, -5, -10, 0, -2, -1, 3, -4, -1, 1, 1], [14, -3, 9, -1, -1, -7, 0, -8, 6, 7, 2], [1, 2, -6, 8, -6, 6, -1, 7, -10, 2, -8], [-2, -1, -1, 12, -6, -3, 4, -2, -3, -1, -2], [-3, 5, -1, 2, -1, 10, 0, 8, -5, -10, -3], [-7, -6, 5, 4, -2, -3, -4, -4, 6, 1, 2], [-13, 3, 7, -12, 12, -2, 3, -1, 4, 3, 6], [15, -8, 9, 3, -4, 5, -11, -4, -1, 0, -3], [3, 12, 2, -1, 2, 4, -2, 0, 0, -3, 1], [-3, -5, 3, -1, -3, 2, -2, -2, 3, -6, 3], [-2, 2, -2, 7, -8, 1, 3, -3, -2, -1, -4], [0, -4, 5, -2, 5, -9, -2, -7, -1, 4, 6], [8, 12, 11, 5, 2, -3, 2, 3, 3, -2, 3], [6, 1, 0, -2, 1, -3, 1, 5, -5, 2, -9], [-4, 4, -7, 9, 1, -3, 8, 2, -5, 0, 2], [9, 1, -6, 4, -10, 9, -6, 7, -5, -2, -12], [7, 4, -3, 5, -1, -6, 3, 3, -2, -6, 5], [-6, -1, 5, -4, -5, -1, -2, -6, 3, 1, 3], [0, 0, 15, 12, 3, -3, 4, -5, -1, -6, 4], [2, -5, 3, -6, -2, -6, 0, -3, 2, -3, 9], [7, 1, 0, -6, 6, 0, 2, -10, 5, 6, 4], [-10, -8, -4, 8, -3, 1, 2, -2, -2, 0, -2], [-8, 12, 13, 2, 18, -2, 4, 4, 0, 0, 2], [0, 2, -1, 6, -2, -5, 3, 4, -7, -7, 0], [1, 7, -6, -5, 2, 7, -2, 1, 2, 4, -11], [4, 5, 4, -2, 5, -3, -1, -9, 0, -2, 1], [13, 8, -2, -10, 9, -1, 4, -5, 3, 1, 5], [1, 3, -1, -9, 7, -10, 10, 0, 3, -6, 9], [11, 6, 6, 0, 0, -3, 0, -11, 4, 7, 3], [1, -14, -6, -6, -5, -1, -1, -4, 11, 2, 4], [14, -11, -7, 5, -10, 0, 1, 3, -2, -2, 0], [-4, 8, 6, -12, 12, 2, 0, -4, 6, -4, 4], [1, 3, 3, 0, -5, 2, 0, 6, -5, -4, -11], [-9, 0, -1, 3, 4, 2, 4, 8, -3, -5, -2], [11, 11, -3, -5, 3, 1, 6, -2, 3, 6, -8], [14, -5, 6, 15, -6, 0, -12, -2, -1, -7, 3], [-8, -12, 5, 0, -7, -1, -5, -10, 7, 7, 3], [7, -7, 5, -6, -4, 6, -8, -6, 5, 0, -4], [3, -13, 0, -3, 5, -1, 2, 0, 8, -2, 5], [16, -6, -9, 1, -16, 6, -8, 4, -4, -6, -4], [-12, 9, 3, 2, 4, 5, 0, -3, 3, -7, -1], [-2, 2, -2, 1, 7, 4, 7, 8, -5, -11, 0], [4, -3, 0, 10, -10, -4, 2, 1, -12, 1, -7], [7, 7, 0, -8, 9, 1, 2, 8, -8, -8, -3], [5, -5, 2, -1, -2, 10, -1, -1, 9, -1, -2], [12, -2, -8, 2, 2, 10, 0, 4, -4, -2, -6], [1, 2, 7, -3, -4, -10, 4, -6, 1, 1, 12], [-8, -18, -6, 8, -1, -5, 0, -2, 0, 2, -2], [-7, 1, 6, -12, 9, 3, -2, -4, 1, 6, -6], [0, -3, 3, -2, 2, 2, -4, 10, -5, -7, -9], [-5, -11, -7, 2, -11, -5, -9, 8, -2, 3, -3], [3, -3, 8, 1, 5, 3, -1, -3, 8, -1, -5], [9, 4, 8, 0, 5, 1, -2, 5, 5, -1, -5], [-12, -5, 7, -2, 1, -4, -2, -9, 5, 5, 3], [-5, 1, 2, -5, 5, -3, 3, 7, 7, -1, 7], [-2, -6, 3, 2, 6, 2, -3, -5, 9, 7, 4], [3, -16, -14, -7, -9, 2, -2, -1, -3, 5, -10], [-6, 4, -1, -14, 3, -7, 3, -6, 5, 5, 1], [-8, 8, 0, 0, 9, 0, 6, 7, -8, -2, -4], [1, 4, 10, -2, 9, 8, -10, 8, 8, -3, 2], [7, -9, -1, 8, 2, 0, -2, 13, -10, -12, -4], [-12, -7, -9, 0, 3, -3, 0, 4, -5, 9, -5], [-14, 11, 3, -4, 0, -1, -4, -10, 5, 3, -2], [-1, -9, 11, 0, -6, -4, -7, -5, 4, 1, 0], [2, 8, 4, -14, 6, 12, 0, -2, 8, 2, -2], [-13, 12, 0, 1, 2, -4, 4, -2, 8, 1, 6], [-14, -10, -1, 11, -5, -3, -4, 8, -8, -6, 2], [5, -19, -3, -6, -3, 0, -3, 12, -7, -5, -11], [-11, -10, -1, -4, -2, -2, 2, -4, 4, 3, 1], [-12, -4, -7, -7, -3, 7, 0, 2, -3, 0, -4], [0, 12, -7, 8, 3, 11, 1, 7, -12, -5, -3], [-8, 9, -2, -3, 9, -5, 2, 0, 0, 1, 1], [19, 8, 3, 11, -6, -4, -5, 8, -11, -6, -6], [3, -10, -2, 1, -3, 8, 4, 15, -7, -1, -16], [14, -12, -9, 2, -12, -2, 3, -4, 7, 1, 5], [7, 13, 2, -7, 10, 3, 3, -6, -2, 9, -2], [10, -12, 6, -3, -3, -6, -7, 4, 1, -1, 8], [-4, 5, -3, -2, 11, -6, 7, 6, -7, -2, -2], [1, 0, 10, 18, 11, -3, -2, 1, 7, -5, 9], [2, -1, 1, 2, -7, 7, -8, 4, -1, 3, -11], [6, 15, 3, 10, -1, -3, 2, -6, 2, 1, 8], [-1, 13, 0, -10, 6, 3, -6, 5, 3, 0, 4], [4, 4, 0, -14, 10, -8, 6, 4, 0, -8, 14], [1, -7, -2, 11, -10, 2, -11, 7, -4, -3, -9], [3, -2, -4, -10, -2, 0, 3, -5, 6, 6, 2], [16, 6, 1, 14, 2, -2, 3, -8, 7, 5, 9], [14, 11, -1, -10, 4, 2, -6, 6, -3, -5, -7], [-7, -3, 5, 10, -4, 2, -9, -1, 5, 1, 7], [11, 8, -2, 0, -4, -4, 9, -9, 0, 6, 0], [12, -12, 0, 12, -3, -13, -2, -2, -7, -4, 1], [18, -3, 11, 24, 0, 4, 2, -2, -1, -5, 13], [-5, 1, 5, 7, -1, 3, 8, 8, -1, 0, -4], [-9, 3, -8, 4, 2, -2, 6, 4, -7, 2, 4], [-7, 7, 10, -17, 5, -3, 7, -9, 7, -1, 3], [0, -8, -8, -5, -17, -2, 0, 8, -9, -2, -12], [4, -24, -7, 5, -11, 6, -11, 2, -2, -5, -11], [30, -6, 0, -7, -10, 7, -9, 6, -1, 1, -8], [-25, 3, -14, -2, -6, -9, 5, -4, -1, 13, 1], [6, -7, -4, 0, 4, 11, -11, 12, 5, 2, -9], [-14, -10, -13, 12, -3, 6, -3, 4, -4, 3, 5], [-20, -4, -14, 4, -8, 2, 0, 0, -3, 8, -5], [21, -1, 13, 7, -7, -2, -1, -4, -3, 1, 7], [-8, -2, 6, 1, 6, 2, -6, -4, 4, 12, -4], [18, 2, 7, 2, 11, -9, 5, -13, 6, 7, -1], [-6, -7, -15, -4, -10, 3, -4, 9, -1, 9, -15], [-5, 6, -7, -5, -2, -2, 10, -6, 4, 1, 7], [-14, -5, -5, -12, 4, -5, -4, 1, 9, 5, 5], [11, -1, 6, 5, 8, -6, -1, -9, 6, 11, -5], [16, 8, 0, 12, -11, -2, -4, 3, -4, -4, 0], [-3, -23, 2, 8, -10, -11, -1, -8, -8, -1, -6], [-13, 0, -2, 7, 0, 0, 8, 8, -15, -3, 4], [-17, -12, -27, -3, -10, 8, -5, 10, -13, -6, -16], [0, 13, 9, 0, -3, -8, -2, -13, 5, 13, 0], [-1, 8, 0, 3, 3, -2, 5, -4, -7, 10, -9], [11, -8, -3, -2, 9, 6, -4, 1, -6, -3, -7], [-4, 16, 10, -22, 14, -18, 7, -7, 9, 3, 8], [1, 10, 3, -5, 8, -5, -3, -2, -5, 6, -2], [-4, -6, -2, 10, -11, -2, -2, 11, -12, -6, 6], [4, 0, -4, -12, 8, 10, 0, 6, 0, -6, -8], [8, -4, 8, -3, -6, -9, 5, -3, 2, -3, 0], [-12, -10, -7, 2, -7, 3, -3, 11, -4, -9, -11], [2, -11, 4, 8, -7, -7, -1, -3, 7, -8, 15], [7, 5, -1, 8, 2, -7, 11, -6, -4, 9, 4], [-22, 12, -3, 0, 3, -6, 5, 2, 0, 5, -1], [28, 17, 19, -4, 12, -6, 7, -8, 10, -10, 12], [0, -5, 17, 13, 2, -6, 5, 1, -1, 0, 9], [-3, 11, 1, -10, 18, -4, 17, -7, 8, 1, 9], [-5, 13, 0, 1, -2, 10, 3, 5, -8, -11, -3], [-6, -5, -2, -17, -16, -3, -8, -4, -3, 1, -6], [-10, 3, 2, -8, 6, -2, -2, -17, 0, 1, 3], [-6, -8, 3, 7, -11, -5, -6, -4, 4, 2, 0], [-19, 5, -4, -1, 0, -6, 15, 4, 1, 5, 6], [13, -8, 0, 14, -8, 2, -5, 7, -4, -6, -10], [12, -4, 15, -2, 4, 1, -9, 8, 3, -3, -2], [21, 2, 4, 3, -9, 4, 0, -1, -3, -7, -8], [31, 5, 8, 1, -9, 1, -13, -9, 8, -9, 3], [4, -1, 13, 24, 3, -8, 2, 15, -5, -13, 9], [14, 10, 5, 8, -3, 1, -7, 11, -6, -5, -5], [-6, 0, -6, -1, -4, 11, 1, 13, -8, -1, -12], [-17, 16, 6, 3, 7, -2, 6, 4, -9, -5, 3], [-14, -7, -16, 6, -3, 2, 4, 6, -8, -5, -3], [-3, 16, 10, 14, 1, 3, 3, -7, 6, -2, 15], [-8, 8, 10, 7, 17, 5, -1, 7, -6, 3, -1], [9, 2, -19, 7, -8, 3, 7, 2, -13, 4, -12], [-13, -3, -6, 12, -10, 20, 2, 18, -5, -4, -12], [-12, -14, -5, 10, -10, -14, -3, 7, -3, 5, -6], [22, -4, -4, 24, -11, 2, -4, 3, -4, 6, -2], [0, 5, 11, 0, -7, -1, 2, -4, -4, -7, 4], [6, 4, 15, 17, 4, 0, 0, 12, -2, -2, -2], [-23, 1, -1, 6, -2, -2, -1, -3, -3, -3, -1], [1, -12, -12, 6, -16, 0, -1, 1, -8, -2, -12], [-21, -10, -5, 2, 5, -5, 0, 0, 7, 5, 4], [13, 11, 1, -12, 2, -2, 4, -4, 2, 2, 3], [-6, 8, 1, 11, -7, 11, -7, 2, -12, -7, -4], [2, -4, -19, 5, -3, 5, -1, 8, -2, -1, -8], [-17, -8, -1, 10, -1, 13, -2, 2, 0, -1, -1], [10, 6, 1, -2, 7, 5, 0, -1, 13, 2, 10], [-12, -2, -6, 10, -10, -7, 2, -5, -3, -2, 4], [17, -7, 12, 5, -3, -9, -5, 1, -3, -5, 3], [5, 15, 8, 3, 8, 4, 8, -1, 3, 6, 5], [-1, -10, 6, 6, 6, -6, 1, -1, -2, 8, 6], [7, -1, 0, -10, 0, 5, -9, -12, 13, 7, -7], [-11, -5, -14, 5, -3, -3, 2, 8, -6, 0, -3], [-3, 8, -1, -8, 6, -8, 0, -6, 6, 3, -1], [5, 9, -1, -23, 15, -13, 2, -12, 3, 0, 4], [19, -2, 9, 18, 9, 0, 8, -1, 2, -1, 5], [-30, 10, -6, 8, 10, -4, 3, 16, 0, -3, 0], [-12, 21, 2, 4, -3, -3, 7, -3, -8, -2, -9], [-2, -2, 13, 18, -5, -10, -6, -1, -4, 4, -4], [7, 23, 19, -11, 9, 2, -1, -11, 4, 1, 1], [-17, 5, -2, -13, -4, 2, -1, 7, 12, 1, 3], [4, -3, -7, -5, -4, -4, 2, 8, -7, -3, 7], [12, 20, 12, -16, 19, -8, 10, -13, 14, 4, 10], [-9, -4, -9, -1, 3, 6, -5, 13, 2, 2, -5], [-2, 16, 4, -6, 16, 2, 12, -8, 10, 4, 10], [12, 1, 6, -2, -1, -8, 0, 6, -4, -7, 11], [-4, 2, 6, 14, 10, 0, 2, 6, 2, -10, 4], [-13, -2, 5, 6, -10, -3, 1, -4, 12, -4, 10], [-17, 4, -15, -5, -12, 6, -5, 11, -8, -4, -2], [0, -2, -12, -12, -17, 4, -2, -3, 4, 6, -9], [3, -3, -2, 24, -7, -7, 2, -1, -4, 6, -2], [-3, 14, -9, -9, 1, 24, -3, 16, -9, -4, -16], [-14, 21, 9, -5, 2, 5, -2, -7, 14, -7, 6], [1, 5, -8, -14, -8, 7, 0, 1, -5, -4, -4], [-6, 9, 0, -3, 12, 4, 1, 9, -5, -8, -8], [16, -15, -1, 8, -5, -1, -6, 2, 10, 1, 2], [0, 8, -5, -8, 8, -12, 3, -9, 11, 1, 0], [-15, -1, -4, 2, -1, -7, 8, 2, 7, 6, 2], [6, 8, -1, 4, -5, 0, 0, -3, -16, -8, -2], [7, 4, 16, 10, 8, -10, 11, -9, 4, 14, 10], [-7, -3, -14, -23, 3, 1, 11, 7, -10, 9, -9], [10, -1, 9, -8, 0, 11, -20, 1, 3, -5, -9], [8, 17, -15, 11, -5, -3, 0, 2, -12, -3, 8], [-12, 2, -6, 7, 5, 2, -3, 12, -8, 1, -1], [16, -10, 18, 24, 4, -8, 2, -8, 6, 10, 2], [20, 14, 15, -2, 10, -8, 13, 2, 5, -1, 13], [8, 2, 2, 2, -3, -16, 9, 1, -3, 1, 9], [-22, -28, -3, 14, -11, 8, -1, 8, 6, 3, -9], [14, -5, 3, -2, 8, -15, 10, -9, 1, 5, 9], [16, 3, 16, 4, 16, -5, 5, -18, 19, 6, 15], [-8, -2, -18, 6, 0, -2, 5, 10, -8, 1, 0], [-26, 6, -11, 2, -5, -20, 9, -16, 4, 9, 17], [-5, 5, 5, -3, -17, -17, 6, -8, -5, 6, -2], [1, -22, -1, 5, -16, -2, -11, 5, -10, 2, -6], [-6, 9, 8, 13, 16, -6, 2, 4, -4, -5, 4], [-23, 2, -11, -20, -7, 1, -8, -12, 4, -3, -1], [-7, -23, -2, 10, 4, 1, -7, 18, 0, -7, 0], [-29, -10, -1, 4, 14, -9, 3, -1, -1, 14, 6], [-13, -7, -24, 4, -10, 5, -5, 12, -19, -3, -13], [30, -15, 1, 15, -13, 1, -10, -4, -6, -7, 8], [-4, -4, -6, -12, 2, -22, 13, -13, 1, 21, 0], [-4, 22, 8, -16, 10, -4, 8, -4, 6, -8, 8], [3, -13, 13, 24, -7, -20, -3, -6, -7, -1, -1], [11, -4, -18, -3, -1, -8, -2, -3, -5, 7, 2], [-13, 9, -8, -2, 11, 25, -4, 11, -6, -4, -12], [3, -8, 1, 18, -16, -2, -6, 8, -20, 3, -11], [4, -14, -16, 24, -22, 2, -4, 10, -23, -4, -6], [-8, 31, -1, 14, 7, -9, 12, -4, -1, -1, 13], [-18, 11, 1, 3, -5, 5, 8, 7, -3, -1, -10], [4, 6, -3, 4, 0, 11, 5, 10, -1, -9, -4], [-11, 7, 7, -19, 3, -20, 9, -16, 1, 3, 5], [-29, 17, 6, -9, 4, 2, -5, -11, 7, 3, 2], [1, -13, -22, -13, -10, 10, -5, 0, 1, -5, -8], [27, 21, 8, 6, 9, -5, 14, 0, -7, -8, -2], [-8, -7, 7, 10, 1, -3, -2, -8, 3, -5, 9], [-8, 6, -9, -4, 3, -2, -8, -1, 4, 0, -6], [4, 9, 3, -4, 5, 10, -10, -1, 5, -7, 5], [0, 16, -6, -32, -8, 7, -4, 1, -4, -8, -10], [3, -2, 4, 12, 8, -5, 6, 6, 3, -5, 3], [7, 11, -6, -14, -3, 9, 2, -13, -6, 8, 2], [21, 9, 2, -15, 11, 4, -3, 2, -5, -11, -11], [5, -1, 14, 10, 6, -10, 8, -8, 3, 10, 4], [1, 1, -4, -13, 4, -2, -4, -9, -5, 12, -7], [-11, 13, 1, 12, 2, 14, -7, -3, -4, -1, -3], [-2, 9, -13, -14, -2, 8, -4, 5, -2, 7, -9], [12, -8, 7, 0, -5, -5, -9, -5, -5, 3, -1], [-12, -22, -15, 10, -8, -1, 1, 10, 1, 7, -2], [13, -26, -5, 19, -2, -7, -9, 2, 5, 0, 5], [20, 13, 13, -14, 9, -3, -16, -4, 5, 5, -1], [-36, -10, -19, -4, 8, 3, 9, 12, -3, 5, -2], [0, 19, -3, -24, -5, 10, 0, -3, 5, 5, -10], [-31, 9, -12, -15, -4, 4, -8, 1, 3, -4, -13], [9, 9, -12, -4, -13, -15, 6, 0, 5, -2, 6], [-4, -16, 11, 13, -10, -18, 4, -6, 0, 6, -2], [21, -1, 27, -8, 12, 2, -3, -15, 14, -11, 7], [14, 16, 13, 10, -3, 5, 3, 9, 8, -3, 7], [-1, 8, 16, -5, -7, -6, -4, -12, 1, 5, 3], [9, -16, -17, 7, -7, 14, -8, 5, -7, -5, -24], [-1, 4, 25, -11, 12, 4, -4, -4, 9, -7, 4], [-10, -3, 6, -1, 14, -9, 6, 10, -5, 1, -10], [-7, -15, -6, -10, -6, -1, -9, -6, 11, -9, 1], [-13, 1, 4, 0, 2, 15, -10, -7, 17, 12, 10], [11, 16, 14, -16, 21, 1, 3, -1, 11, 4, 1], [-11, -1, -8, 22, 7, 1, 0, -2, -6, 2, 11], [26, -11, -9, 8, -10, -11, 0, -6, -5, 13, 0], [-17, 27, 2, -6, -1, -3, 12, -5, -2, 2, 2], [-5, -23, -15, 10, -23, -3, 0, 0, -4, 4, -7], [9, 8, 1, 11, 0, -6, 7, 11, -6, -2, 4], [-20, 13, -2, 4, -1, 1, -3, 12, 1, -2, 1], [-3, -3, -7, -13, 14, 4, 0, 14, -3, 4, -12], [-16, -2, -12, -4, 8, 14, -2, 2, -2, 10, -12], [-1, 17, -8, 14, -3, 15, 0, 12, -12, -8, 1], [-18, 0, 8, -6, 2, -19, 16, -1, -4, 4, 6], [-10, 12, 0, -4, 6, -10, 12, 4, -6, 2, 12], [22, 8, -1, 1, 0, -1, -6, -11, 7, 6, 7], [2, -27, 2, 5, -2, -14, -5, 5, 1, -6, 2], [13, -7, 0, 6, -2, 6, -8, 2, 1, 0, -6], [-18, -32, -5, 6, -2, 9, -6, 14, -5, -14, -2], [6, 5, -7, -16, -7, -4, 2, -3, -11, -9, -3], [20, -13, 5, 0, -12, 6, -12, -6, 13, 5, -9], [-15, -5, -20, -21, -1, -13, 5, -11, 11, 9, 1], [-24, -5, 4, -2, 6, 0, 12, -5, 4, -3, 3], [12, 23, 0, -14, -6, 5, -1, 2, 3, -4, -1], [-8, -4, -8, -24, -11, 14, -14, -5, 10, 2, -10], [7, -3, 2, 24, 6, 4, -2, 10, -4, -2, 9], [-25, 8, 7, -6, 4, -18, 9, -6, 1, 2, 14], [13, -1, 2, 6, 2, 7, -10, -7, 3, 0, 2], [5, 14, -10, 3, -13, -4, -6, -2, -7, 7, 3], [-34, 1, -13, 2, 0, 1, -4, -1, -3, 3, 5], [-2, -15, -5, 22, -16, 16, -8, 1, -2, -1, -13], [-15, -16, 1, -1, -20, -8, -12, -12, 7, 5, 10], [2, 5, -1, -6, 11, 11, 2, 4, -1, -7, 11], [2, 18, 14, 6, -2, -10, 4, -4, -4, -4, 8], [12, -3, -10, 15, -12, 12, -3, 17, -11, 2, -12], [2, -2, -22, -38, 2, 16, 2, 2, -4, 8, -14], [-11, -12, 14, 12, -7, -19, -3, -5, 2, 0, -1], [-2, -16, 9, -5, 3, -1, -6, 10, 6, -12, 6], [22, 0, 5, 2, 10, 2, 3, 1, -1, -5, -6], [-5, -7, -1, -32, 13, 3, -5, -2, -2, 7, -3], [-27, -13, -1, 11, -3, -8, -2, -12, 11, -2, 27], [30, -13, 14, 1, 3, 17, -10, 6, 10, -3, -13], [16, 19, 3, 9, -8, -4, -1, 9, -3, -6, -9], [-38, 11, 5, -12, 6, -31, 2, -14, -3, 17, 0], [31, -9, -10, -3, -8, 8, -17, 1, 2, 7, -9], [15, -7, 8, -18, 2, 6, -2, 4, 1, 0, -6], [-14, -1, -1, 8, 5, 17, -4, 16, 1, -11, -7], [-5, 14, -7, -16, -5, -2, 6, -7, -12, 5, -3]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_7595_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_7595_2_a_w();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose lines below.
// The precision argument determines an initial guess on how many Fourier coefficients to use.
// This guess is increased enough to uniquely determine the newform.
function MakeNewformModFrm_7595_2_a_w(:prec:=11)
    chi := MakeCharacter_7595_a();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 2));
    S := BaseChange(S, Kf);
    maxprec := NextPrime(2999) - 1;
    while true do
        trunc_vec := Vector(Kf, [0] cat [f_vec[i]: i in [1..prec]]);
        B := Basis(S, prec + 1);
        S_basismat := Matrix([AbsEltseq(g): g in B]);
        if Rank(S_basismat) eq Min(NumberOfRows(S_basismat), NumberOfColumns(S_basismat)) then
            S_basismat := ChangeRing(S_basismat,Kf);
            f_lincom := Solution(S_basismat,trunc_vec);
            f := &+[f_lincom[i]*Basis(S)[i] : i in [1..#Basis(S)]];
            return f;
        end if;
        error if prec eq maxprec, "Unable to distinguish newform within newspace";
        prec := Min(Ceiling(1.25 * prec), maxprec);
    end while;
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_7595_2_a_w();".
// 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_7595_2_a_w( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_7595_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<2,R![-2, -14, -4, 90, 2, -130, 0, 67, 0, -14, 0, 1]>,<3,R![-2, -12, 6, 86, -25, -133, 25, 73, -9, -15, 1, 1]>,<11,R![2458, 6412, 730, -11098, -10039, -325, 2575, 627, -161, -49, 3, 1]>],Snew);
    return Vf;
end function;