# q-expansion of newform 154.2.f.a, downloaded from the LMFDB on 01 May 2026.

# We generate the q-expansion using the Hecke eigenvalues a_p at the primes.
# Each a_p is given as a linear combination
# of the following basis for the coefficient ring.

def make_data():

    from sage.all import prod, floor, prime_powers, gcd, QQ, primes_first_n, next_prime, RR

    def discrete_log(elts, gens, mod):
        # algorithm 2.2, page 16 of https://arxiv.org/abs/0903.2785
        def table_gens(gens, mod):
            T = [1]
            n = len(gens)
            r = [None]*n
            s = [None]*n
            for i in range(n):
                beta = gens[i]
                r[i] = 1
                N = len(T)
                while beta not in T:
                    for Tj in T[:N]:
                        T.append((beta*Tj) % mod)
                    beta = (beta*gens[i]) % mod
                    r[i] += 1
                s[i] = T.index(beta)
            return T, r, s
        T, r, s = table_gens(gens, mod)
        n = len(gens)
        N = [ prod(r[:j]) for j in range(n) ]
        Z = lambda s: [ (floor(s/N[j]) % r[j]) for j in range(n)]
        return [Z(T.index(elt % mod)) for elt in elts]
    def extend_multiplicatively(an):
        for pp in prime_powers(len(an)-1):
            for k in range(1, (len(an) - 1)//pp + 1):
                if gcd(k, pp) == 1:
                    an[pp*k] = an[pp]*an[k]
    from sage.all import PolynomialRing, NumberField
    R = PolynomialRing(QQ, "x")
    f = R(poly_data)
    K = NumberField(f, "a")
    betas = [K.gens()[0]**i for i in range(len(poly_data))]
    convert_elt_to_field = lambda elt: sum(c*beta for c, beta in zip(elt, betas))
    # convert aps to K elements
    primes = primes_first_n(len(aps_data))
    good_primes = [p for p in primes if not p.divides(level)]
    aps = map(convert_elt_to_field, aps_data)
    if not hecke_ring_character_values:
        # trivial character
        char_values = dict(zip(good_primes, [1]*len(good_primes)))
    else:
        gens = [elt[0] for elt in hecke_ring_character_values]
        gens_values = [convert_elt_to_field(elt[1]) for elt in hecke_ring_character_values]
        char_values = dict([(
            p,prod(g**k for g, k in zip(gens_values, elt)))
            for p, elt in zip(good_primes, discrete_log(good_primes, gens, level))
            ])
    an_list_bound = next_prime(primes[-1])
    an = [0]*an_list_bound
    an[1] = 1
    
    from sage.all import PowerSeriesRing
    PS = PowerSeriesRing(K, "q")
    for p, ap in zip(primes, aps):
        if p.divides(level):
            euler_factor = [1, -ap]
        else:
            euler_factor = [1, -ap, p**(weight - 1) * char_values[p]]
        k = RR(an_list_bound).log(p).floor() + 1
        foo = (1/PS(euler_factor)).padded_list(k)
        for i in range(1, k):
            an[p**i] = foo[i]
    extend_multiplicatively(an)
    return PS(an)
level = 154
weight = 2
poly_data = [1, -1, 1, -1, 1]

# The basis for the coefficient ring is just the power basis
# in the root of the defining polynomial above.
hecke_ring_character_values = [[45, [1, 0, 0, 0]], [57, [0, 0, 0, -1]]]
aps_data = [[-1, 1, -1, 1], [0, 0, -1, 0], [-1, 2, -1, 0], [0, 0, 0, -1], [1, -2, -2, 0], [3, 1, -1, -3], [4, -5, 4, 0], [0, 6, -3, 6], [-5, 0, 2, -2], [-4, 4, 0, 7], [3, -3, 3, -3], [3, -3, 0, 3], [0, 4, 0, 4], [-9, 0, -1, 1], [0, 1, 0, 1], [3, -9, 9, -3], [-7, 7, 0, 1], [3, 9, 3, 0], [1, 0, 6, -6], [0, 3, 0, 0], [3, -3, 0, 2], [9, -1, 1, -9], [-7, 2, -7, 0], [5, 0, 5, -5], [-10, 6, -6, 10], [3, -3, 3, -3], [-3, 3, 0, 0], [0, 5, -2, 5], [-6, 0, -7, 7], [0, -10, 4, -10], [3, 3, 3, 0], [-8, 0, -10, 10], [8, -12, 8, 0], [-8, 8, 0, 14], [5, -10, 5, 0], [0, 0, -8, 0], [0, 14, 1, 14], [4, -3, 3, -4], [18, -21, 21, -18], [0, -10, -1, -10], [0, 15, 0, 15], [-6, -4, -6, 0], [1, -1, 0, 0], [-18, 15, -18, 0], [-1, 0, 7, -7], [8, 0, 6, -6], [-13, 1, -1, 13], [0, -1, 7, -1], [1, -1, 0, -21], [4, 9, -9, -4], [-24, 24, -24, 24], [0, -1, -2, -1], [0, 0, 1, -1], [6, -10, 10, -6], [8, -8, 0, -27], [21, 0, -1, 1], [-11, -2, -11, 0], [-1, 1, 0, 6], [-4, -18, 18, 4], [13, -11, 13, 0], [0, 12, -7, 12], [-7, 7, 0, 2], [-3, 0, -12, 12], [0, 10, -3, 10], [-15, 21, -15, 0], [7, 13, -13, -7], [-10, 0, 6, -6], [-11, 11, 0, 5], [-8, -9, -8, 0], [0, -24, 12, -24], [-21, 0, -5, 5], [5, -5, 0, -20], [0, 0, 0, -3], [-3, 0, -14, 14], [8, 21, 8, 0], [5, 8, -8, -5], [17, -17, 0, -1], [15, 0, -6, 6], [-4, -15, -4, 0], [3, 3, -3, -3], [-16, 0, -17, 17], [0, -10, -23, -10], [9, 13, -13, -9], [6, -6, 0, -7], [-12, 0, 6, -6], [0, -3, -27, -3], [13, -2, 2, -13], [12, -4, 12, 0], [27, 0, 15, -15], [12, 0, 21, -21], [-8, 31, -8, 0], [-36, 18, -36, 0], [0, -12, 9, -12], [-1, 1, 0, 16], [12, -12, 0, -11], [0, 8, 15, 8], [0, 34, -22, 34], [-13, 13, 0, -8], [18, -13, 18, 0], [-6, -12, 12, 6], [0, -2, -21, -2], [-6, 6, 0, 15], [6, 4, -4, -6], [0, -9, -18, -9], [-21, 0, -6, 6], [7, -24, 7, 0], [-28, 28, 0, 21], [-2, 0, -2, 2], [2, -31, 2, 0], [-24, 24, 0, 15], [-22, 9, -9, 22], [0, -17, 0, -17], [1, 0, -4, 4], [0, -21, 3, -21], [-5, 5, 0, 8], [0, -4, 29, -4], [18, -33, 18, 0], [7, -27, 27, -7], [-36, 36, 0, 24], [-3, 0, 9, -9], [-3, 0, 15, -15], [1, -21, 21, -1], [8, 28, 8, 0], [23, 0, 13, -13], [26, -35, 35, -26], [0, 16, -6, 16], [-11, 23, -11, 0], [-19, 19, 0, 12], [-1, 0, -18, 18], [-13, 13, 0, 45], [22, 2, -2, -22], [-10, 31, -10, 0], [0, -6, 0, -6], [26, 7, -7, -26], [14, -22, 22, -14], [18, 0, 1, -1], [0, -8, -2, -8], [-3, 21, -3, 0], [4, -40, 4, 0], [-14, 17, -14, 0], [0, 3, -52, 3], [-6, 6, 0, 36], [-11, -13, 13, 11], [8, -6, 6, -8], [0, 0, 0, 25], [0, 21, -3, 21], [-6, -41, -6, 0], [-15, 0, 4, -4], [33, 0, 6, -6], [23, -38, 23, 0], [0, 36, -25, 36], [35, 0, -14, 14], [0, -28, 28, -28], [13, -13, 0, -12], [-1, 15, -1, 0], [8, -33, 33, -8], [0, 5, 0, 0], [-2, -34, -2, 0], [-51, 45, -45, 51], [5, -2, 5, 0], [-4, 0, 31, -31], [37, -37, 0, -30], [-3, 0, -7, 7], [0, 1, -26, 1], [-38, 28, -28, 38], [10, -10, 0, 26], [-28, 0, 0, 0], [-21, 21, 0, 25]]