# q-expansion of newform 154.2.f.d, downloaded from the LMFDB on 02 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, 2, -1, 2], [-1, 2, -1, 0], [0, 0, 0, 1], [-3, 2, -4, 2], [3, -3, 3, -3], [4, -3, 4, 0], [0, -4, 1, -4], [-3, 0, -4, 4], [0, 0, 0, -3], [-1, -5, 5, 1], [-7, 7, 0, 1], [0, 4, -8, 4], [1, 0, 3, -3], [0, -3, 6, -3], [-7, 5, -5, 7], [-9, 9, 0, 9], [3, 5, 3, 0], [13, 0, 0, 0], [-2, -1, -2, 0], [9, -9, 0, -6], [11, -9, 9, -11], [-1, 4, -1, 0], [3, 0, 3, -3], [6, -2, 2, -6], [-13, 9, -9, 13], [-1, 1, 0, 10], [0, 1, 16, 1], [-10, 0, 3, -3], [0, 2, -12, 2], [-13, 1, -13, 0], [-4, 0, 10, -10], [-16, 12, -16, 0], [4, -4, 0, 14], [3, -6, 3, 0], [0, -8, 0, -8], [0, 6, -11, 6], [6, 9, -9, -6], [-12, 11, -11, 12], [0, -2, 7, -2], [0, -13, -2, -13], [6, 12, 6, 0], [-7, 7, 0, -10], [-6, 11, -6, 0], [5, 0, -7, 7], [4, 0, 6, -6], [-9, -5, 5, 9], [0, -15, 3, -15], [7, -7, 0, -9], [-16, 9, -9, 16], [24, -16, 16, -24], [0, -7, -8, -7], [0, 0, 11, -11], [22, -14, 14, -22], [8, -8, 0, 7], [21, 0, -3, 3], [5, -2, 5, 0], [-11, 11, 0, 8], [12, -18, 18, -12], [-3, 9, -3, 0], [0, -14, -7, -14], [13, -13, 0, -22], [-13, 0, -6, 6], [0, 4, 27, 4], [3, 3, 3, 0], [-19, 3, -3, 19], [22, 0, -6, 6], [-15, 15, 0, 13], [14, 5, 14, 0], [0, 0, -20, 0], [-11, 0, 5, -5], [9, -9, 0, -6], [18, -18, 0, -11], [15, 0, -10, 10], [10, -9, 10, 0], [-17, 18, -18, 17], [11, -11, 0, 17], [11, 0, -6, 6], [12, -3, 12, 0], [-27, 25, -25, 27], [18, 0, 15, -15], [0, 10, 23, 10], [-13, 9, -9, 13], [6, -6, 0, 15], [-8, 0, -2, 2], [0, 23, -15, 23], [1, 10, -10, -1], [-12, 4, -12, 0], [-21, 0, 3, -3], [6, 0, 1, -1], [-14, 7, -14, 0], [16, -22, 16, 0], [0, 6, -11, 6], [9, -9, 0, -6], [10, -10, 0, 21], [0, 26, -19, 26], [0, -2, -2, -2], [-15, 15, 0, 0], [-12, 15, -12, 0], [-6, 12, -12, 6], [0, 0, 13, 0], [6, -6, 0, -27], [2, -16, 16, -2], [0, -21, -6, -21], [-21, 0, -8, 8], [1, 8, 1, 0], [-2, 2, 0, 3], [-10, 0, 14, -14], [-4, -7, -4, 0], [0, 0, 0, -3], [40, -39, 39, -40], [0, 21, -12, 21], [-15, 0, 4, -4], [0, -29, 5, -29], [27, -27, 0, -14], [0, -4, -19, -4], [12, -25, 12, 0], [-9, 23, -23, 9], [12, -12, 0, 24], [-13, 0, 5, -5], [-11, 0, -17, 17], [29, -17, 17, -29], [8, 20, 8, 0], [9, 0, 21, -21], [-12, -5, 5, 12], [0, 16, -38, 16], [-13, 21, -13, 0], [19, -19, 0, -26], [35, 0, 0, 0], [-5, 5, 0, 17], [18, -6, 6, -18], [-12, 15, -12, 0], [0, 34, -4, 34], [-10, -23, 23, 10], [2, 6, -6, -2], [-6, 0, -29, 29], [0, -32, 18, -32], [1, -1, 1, 0], [-4, 48, -4, 0], [-2, 1, -2, 0], [0, -3, -18, -3], [10, -10, 0, 12], [-33, 19, -19, 33], [12, -18, 18, -12], [-12, 12, 0, 21], [0, -13, 9, -13], [-6, 11, -6, 0], [-5, 0, -4, 4], [-41, 0, -8, 8], [-11, -28, -11, 0], [0, -32, 5, -32], [-31, 0, -22, 22], [0, -12, 12, -12], [-13, 13, 0, 38], [-23, -9, -23, 0], [6, 9, -9, -6], [-6, -11, -6, 0], [-2, -34, -2, 0], [-13, 31, -31, 13], [-7, 30, -7, 0], [34, 0, 41, -41], [17, -17, 0, 6], [1, 0, 3, -3], [0, 19, -16, 19], [6, 20, -20, -6], [-10, 10, 0, 2], [-12, 0, 24, -24], [-33, 33, 0, 41]]