# q-expansion of newform 9680.2.a.bc, downloaded from the LMFDB on 30 April 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 = 9680
weight = 2
poly_data = [0, 1]

# The basis for the coefficient ring is just the power basis
# in the root of the defining polynomial above.
hecke_ring_character_values = None
aps_data = [[0], [3], [-1], [-5], [0], [-4], [1], [5], [-4], [5], [1], [3], [2], [-8], [-6], [11], [0], [-5], [4], [15], [6], [-8], [-8], [1], [10], [18], [6], [-2], [-2], [-8], [0], [-7], [12], [12], [7], [20], [11], [23], [15], [18], [2], [-8], [12], [-23], [18], [-5], [-7], [-26], [-18], [-8], [9], [22], [2], [8], [-12], [-19], [4], [24], [-14], [18], [28], [-14], [2], [1], [-10], [-31], [12], [31], [-18], [6], [4], [18], [-20], [-2], [16], [34], [-8], [22], [-1], [26], [-18], [-30], [28], [-22], [34], [32], [18], [-17], [23], [32], [11], [-6], [32], [-19], [-38], [-4], [-30], [-22], [-26], [-19], [-42], [0], [26], [14], [-25], [-32], [5], [-34], [-15], [22], [-3], [24], [30], [-2], [19], [35], [-13], [-12], [-3], [-33], [-18], [-15], [-10], [29], [18], [15], [-10], [-11], [-20], [-32], [-16], [-25], [-3], [-26], [22], [-22], [7], [14], [-42], [48], [-17], [-6], [26], [22], [12], [-52], [40], [-11], [-36], [-42], [-22], [-10], [13], [16], [-9], [-37], [-32], [-21], [38], [-3], [-7], [-25], [41], [-38], [38], [36], [-40], [48], [16], [-29], [53], [32], [-18], [1], [8], [-29], [44], [-54], [-11], [-37], [20], [21], [61], [-51], [0], [32], [52], [-20], [20], [6], [28], [-24], [50], [12], [42], [42], [-32], [30], [-30], [1], [61], [-10], [-23], [-18], [26], [-9], [-8], [-52], [-44], [50], [-1], [-44], [26], [57], [18], [-1], [-11], [0], [28], [-43], [-22], [-22], [-35], [-48], [12], [-25], [22], [-57], [32], [12], [50], [39], [10], [16], [36], [-7], [-5], [-64], [38], [29], [53], [28], [38], [38], [66], [2], [-10], [54], [5], [-3], [12], [54], [-22], [31], [-18], [-27], [-14], [46], [30], [43], [52], [-64], [-41], [14], [76], [-42], [30], [33], [6], [-36], [40], [-47], [66], [-4], [37], [-14], [0], [-2], [52], [-69], [67], [24], [-72], [-5], [20], [-15], [-22], [84], [63], [-6], [54], [44], [-71], [-57], [-2], [-14], [-32], [-87], [68], [-54], [39], [-78], [-14], [12], [50], [-16], [4], [-44], [-3], [-16], [-40], [36], [-12], [55], [-1], [82], [-66], [2], [-44], [-72], [63], [2], [-78], [-22], [-81], [87], [-10], [52], [59], [88], [53], [50], [-70], [-78], [25], [-69], [-2], [-79], [13], [-33], [74], [-48], [-51], [23], [39], [67], [10], [25], [28], [-23], [77], [-48], [80], [-43], [19], [-37], [-31], [-25], [54], [-96], [50], [-50], [0], [59], [39], [16], [50], [-21], [58], [-4], [70], [64], [-41], [-30], [22], [-46], [-62], [97], [-78], [11], [6], [-78], [-12], [-9], [-12], [-28], [-40], [5], [18], [-84], [-43], [-3], [56], [68], [24], [-2], [52], [-69], [94], [-21], [-99], [-24], [-8], [-98], [-10], [-12], [-59], [72], [25], [-54], [-38], [32], [20], [28], [94], [-82], [-104], [-76], [-30], [-29], [-56], [10], [92], [-51], [12], [-67], [-19], [78], [22], [24], [-31], [97], [34], [-48], [69], [90], [-30], [24], [-68], [34], [81], [55], [-21], [0], [100], [-3], [40], [-63], [-103]]