# q-expansion of newform 9702.2.a.cu, 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, ZZ
    R = PolynomialRing(QQ, "x")
    f = R(poly_data)
    K = NumberField(f, "a")
    betas = [K([c/ZZ(den) for c in num]) for num, den in basis_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 = 9702
weight = 2
poly_data = [-1, -1, 1]

# The entries in the following list give a basis for the
# coefficient ring in terms of a root of the defining polynomial above.
# Each line consists of the coefficients of the numerator, and a denominator.
basis_data  = [[[1, 0], 1], [[-1, 2], 1]]

hecke_ring_character_values = None
aps_data = [[-1, 0], [0, 0], [1, 1], [0, 0], [-1, 0], [1, -1], [-2, -2], [5, -1], [-4, 0], [0, 2], [-2, 0], [-2, -4], [2, 2], [-6, 2], [-2, 0], [-4, 2], [5, 1], [3, 1], [-2, -6], [-2, 2], [-4, 4], [0, 0], [-1, 5], [10, 0], [-8, 2], [-3, -5], [6, -4], [2, 2], [-10, 0], [-4, -2], [-12, 0], [7, 1], [2, -8], [15, -3], [0, -10], [12, 0], [-3, -7], [-6, 6], [-2, -6], [-1, 1], [0, -4], [-7, 1], [-2, -2], [-6, 4], [-18, 0], [-10, 4], [-18, -2], [-4, -2], [-17, 1], [-15, 1], [6, -4], [-20, 0], [-2, 6], [27, -1], [-2, -4], [-4, -4], [-25, -1], [8, 4], [8, 2], [-2, 12], [1, 7], [-11, 7], [-3, -13], [-8, 6], [-24, -2], [22, -4], [-8, 4], [18, 0], [2, 2], [-15, 3], [-26, -4], [0, 12], [-8, -6], [-6, 0], [10, -2], [-6, 8], [-20, 6], [17, -3], [8, 10], [10, 6], [15, -1], [12, -2], [-32, -4], [-24, 2], [0, 4], [16, -4], [-10, 4], [18, -4], [27, 1], [-26, 2], [-7, 9], [-10, -10], [8, -4], [8, -4], [-10, 10], [4, 0], [-5, -13], [12, 10], [21, 3], [-18, 4], [8, 4], [2, 12], [29, -1], [10, -12], [-28, -8], [-18, 4], [-17, -5], [24, 0], [10, -10], [8, -12], [32, 0], [24, -2], [-8, 6], [15, 15], [-18, 6], [-32, -2], [21, 1], [-2, 12], [-24, 10], [-30, -6], [-17, -9], [14, 8], [3, 13], [-24, 4], [3, 7], [-2, -20], [0, -2], [-10, -12], [-18, 0], [-29, 9], [20, 0], [-4, 8], [-8, 4], [8, 14], [2, 6], [30, -6], [9, -3], [17, -5], [-17, 11], [30, 4], [-7, -1], [-12, -6], [-6, 18], [-8, 4], [-5, 3], [-10, -12], [1, 15], [-42, 2], [5, 9], [-14, -6], [18, 4], [2, -12], [24, 12], [-22, 10], [-2, 10], [28, 0], [-40, -8], [0, -18], [12, 4], [-23, -5], [-8, 4], [-14, 4], [28, -8], [17, -15], [2, -12], [14, 0], [22, 10], [-13, 5], [-30, -4], [19, 3], [-10, -18], [-27, 9], [28, 4], [-26, -8], [-10, 4], [-30, 12], [32, 4], [18, 12], [-44, 8], [-5, -19], [-12, -20], [17, -13], [-16, -18], [-12, -8], [36, -4], [15, -17], [18, 8], [31, 15], [30, 0], [2, -10], [-14, 8], [-14, -6], [-18, -6], [-13, 23], [12, 24], [34, 0], [-18, -4], [-26, 4], [-52, 4], [24, -4], [0, 6], [-2, 10], [-13, -25], [-20, -12], [-15, -7], [-7, 1], [-50, 4], [16, 4], [10, 0], [13, 5], [-2, 4], [-3, -15], [24, 0], [13, -7], [0, 12], [28, 2], [-12, -4], [2, -2], [2, 14], [36, 14], [-48, -10], [0, -12], [-10, 12], [-36, -4], [-37, -3], [10, -4], [-6, 20], [0, 8], [12, 24], [-22, 2], [-6, 8], [-5, -19], [12, 20], [-2, 0], [51, 3], [8, 4], [0, 2], [-44, 10], [10, 6], [-48, 10], [-14, -18], [33, -13], [56, 6], [0, 10], [-16, 4], [30, 10], [-28, 2], [57, 5], [-20, -16], [36, 12], [18, 16], [-8, 0], [2, -18], [10, -4], [9, -13], [10, 10], [-18, -20], [7, -11], [-7, 1], [22, -2], [44, 8], [-8, 20], [-25, 5], [-29, 13], [8, -22], [25, 21], [-20, 18], [22, -16], [24, 12], [-44, -10], [-7, -19], [-2, 18], [26, -8], [60, 8], [-28, -12], [56, 2], [-28, 16], [-50, -4], [-18, -16], [-33, 5], [4, 4], [62, -6], [18, 18], [3, -27], [37, 7], [28, -16], [-6, 20], [72, 6], [50, 0], [20, -24], [-32, 22], [-27, 5], [66, 4], [27, 25], [4, 22], [-5, -15], [-32, 14], [-1, -9], [45, -1], [-53, -7], [-14, 6], [62, -4], [0, 8], [-34, 10], [22, 10], [-2, 16], [12, 8], [-5, 27], [-60, -4], [4, -2], [4, -4], [20, -18], [-2, 4], [4, 0], [-48, -8], [-20, -4], [15, 11], [28, -4], [46, -20], [-30, -16], [3, -35], [38, 12], [57, -5], [34, -14], [-54, 0], [48, -10], [-10, 10], [-29, -21], [32, -20], [6, 28], [-18, -28], [2, 12], [30, -6], [9, 27], [12, -32], [-27, -19], [10, 16], [-36, -8], [18, -28], [-18, -10], [-66, -8], [-8, -18], [55, 1], [2, -22], [-44, 14], [20, -16], [13, -19], [-42, -6], [-28, 28], [13, 1], [-77, 1], [18, -4], [58, 0], [6, 6], [20, 6], [-36, 0], [70, 0], [67, -3], [-18, 0], [56, 8], [-32, 26], [-8, 4], [12, -20], [-60, 0], [-33, -17], [-16, -14], [43, 21], [4, 0], [-18, 0], [38, 10], [5, 5], [-44, -12], [-30, 12], [-32, 0], [-52, 6], [5, -11], [-32, 4], [16, 4], [90, 2], [22, 22], [-13, 15], [-24, 14], [48, -16], [22, 8], [55, 13], [-36, -30], [-18, 6], [27, 3], [-6, -22], [18, -20], [0, 42], [-51, 9], [50, 6], [57, -11], [8, -16], [14, 16], [-30, 2], [0, 18], [22, -6], [38, 12], [-25, 21], [-34, 16], [28, -20], [8, 2], [-45, 5], [38, -6], [18, 20], [18, 16], [41, -23], [-45, -13], [-4, -20], [-28, -2], [56, 12], [92, 0], [-22, -12], [47, -13], [20, -12], [22, 16], [-92, -2], [-36, 12], [-40, 2], [47, 21], [22, -30], [-35, 27], [-64, 14], [-7, 21], [-34, -22], [-10, -36], [-7, -7], [-10, -10], [-12, 10], [-42, -2], [20, -16], [84, -6], [27, -29], [32, -10], [30, -28], [-28, 18], [-42, 18], [-10, 2], [39, -13], [80, 6], [20, 18], [20, -12], [48, 16], [42, -24], [41, 19], [38, -14], [40, -6], [-57, 5], [-22, -22], [-28, 22], [-14, -14], [10, 18], [8, -14], [-22, 0], [60, -22], [-3, 11], [51, 17], [52, 14], [0, -12], [32, 20], [10, -14], [2, -12], [7, 21], [54, 16], [-20, 8], [-41, 3], [-10, -8], [-27, -15], [4, -8], [42, -18], [0, 18], [-18, -40], [8, -4], [21, 7], [30, 8], [-12, 22], [68, -12], [-104, -2], [-24, 14], [-40, -12], [12, 2], [-3, 39], [-14, -28], [-18, 6], [-70, 8], [-33, -5], [-5, -21], [52, 0], [-73, -7], [48, -20], [-10, -32], [19, -7], [-20, 24], [33, 15], [17, 1], [-58, -12], [-30, -26], [-28, 0], [-42, -20], [36, -12], [26, 28], [-32, -28], [54, -8], [-52, -10], [-34, -10], [8, -22], [-32, 14], [-9, 33], [35, -15], [-48, 24], [-24, -8], [-38, -32], [22, -18], [-22, -20], [7, 27], [-25, -27], [20, -8], [72, 6], [-76, 18], [0, -20], [-42, 4], [2, 46], [-10, -26], [-35, -21], [16, 26], [-17, -27], [-4, -16], [17, 1], [24, -16], [46, -8], [8, 12], [58, 22], [51, 7], [-16, -36], [37, -11], [72, 10], [30, -12], [-82, 6], [32, -20], [22, 28], [40, -34], [9, 19], [70, -4], [22, 26], [4, 32], [-37, -5], [-38, -38], [15, 17], [-22, -20], [21, -1], [-72, -14], [-14, 36], [-80, 12], [-7, -5], [-32, -20]]