# q-expansion of newform 5904.2.a.w, downloaded from the LMFDB on 13 July 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 = 5904
weight = 2
poly_data = [-2, 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, 0], [0, 0], [-2, 1], [2, -1], [1, -1], [2, -3], [-1, -1], [4, -1], [0, 1], [-1, -5], [3, 0], [-1, 6], [1, 0], [5, 0], [9, -1], [-4, 2], [0, 6], [1, 4], [-2, 6], [3, -5], [1, 8], [2, -4], [-6, -5], [6, -4], [12, 3], [-1, -1], [5, 8], [-6, -4], [-2, -7], [6, 9], [2, 8], [-12, -1], [-11, -5], [2, 4], [-6, 8], [16, 0], [18, 0], [1, -6], [2, 4], [2, -5], [5, 7], [4, 8], [16, -2], [2, 1], [-18, 3], [12, -3], [16, -6], [-16, -4], [11, 7], [4, 3], [18, 0], [4, -10], [1, -6], [6, -2], [15, 7], [1, -1], [0, -6], [1, 14], [1, 20], [1, 13], [-19, -2], [-11, -1], [-11, -8], [24, -2], [-2, 19], [5, -5], [-12, 3], [3, -12], [-9, -7], [-5, -10], [18, -12], [12, -3], [1, -4], [19, -10], [-10, 12], [27, 7], [18, -3], [-2, -23], [12, 16], [19, 2], [8, -5], [8, 12], [32, 5], [-3, -6], [14, 12], [-8, 20], [-12, -6], [-4, 0], [-6, 16], [10, -11], [10, 8], [-3, -7], [15, 12], [-6, 5], [28, 6], [-17, -13], [7, 19], [-27, 3], [-34, 0], [2, 12], [16, -6], [-27, -9], [-3, -7], [20, 11], [-20, -16], [-28, 6], [-11, 13], [-3, -1], [0, 25], [-18, 6], [26, -6], [8, -8], [-6, -15], [-1, -8], [3, -18], [-7, -11], [-12, 18], [-8, 11], [-3, -7], [-32, 2], [-12, -18], [2, -14], [-18, 11], [22, 20], [2, 9], [26, -14], [-22, 6], [25, -11], [20, -9], [-17, 10], [-17, 4], [-6, -16], [-18, 12], [4, -3], [-12, 2], [-25, 6], [-49, 1], [-3, -12], [30, -10], [6, 22], [1, -12], [12, -19], [10, 30], [15, 5], [9, 24], [-20, 2], [0, 0], [-32, 14], [-11, 4], [18, -5], [-13, 10], [20, -16], [8, -1], [-5, -29], [-10, 4], [44, 7], [14, -1], [-19, -19], [36, -12], [30, -16], [-18, -28], [12, -21], [18, 12], [25, -11], [-9, -1], [-30, -5], [20, -6], [14, -1], [3, -12], [-6, -14], [6, -12], [12, -18], [10, 28], [-29, -12], [20, 20], [21, -7], [20, 9], [30, 14], [44, -3], [-38, -4], [-7, -22], [-2, -32], [24, -12], [-6, 0], [14, 32], [-6, 3], [-16, 0], [-34, -4], [-6, 3], [-23, 23], [-19, 6], [-24, -10], [2, -18], [-46, -10], [-12, 1], [-12, 12], [-18, -18], [2, -37], [-10, -20], [-39, 15], [0, -4], [15, 30], [32, 3], [30, 24], [-9, 3], [-21, 1], [-26, 2], [39, 23], [-12, 29], [-45, -12], [2, -9], [39, 15], [14, -10], [-12, -22], [23, 17], [23, 6], [-22, -27], [24, 21], [-39, 21], [6, 2], [-12, 33], [-31, -20], [-49, -1], [-20, -13], [-22, -37], [24, 9], [-30, 8], [-2, -49], [-16, -6], [16, -23], [-34, 20], [10, 35], [27, -12], [32, 25], [24, -15], [6, 32], [-14, 9], [-6, -6], [-16, 20], [-45, -13], [0, -10], [-28, -16], [-10, -26], [-61, -2], [8, -40], [-34, 25], [-22, 26], [-3, 7], [-29, -34], [-30, 34], [41, -6], [-8, 17], [42, -10], [-1, 12], [-30, 18], [2, -16], [-52, 5], [0, -27], [-15, 33], [24, -27], [11, 4], [15, 19], [-6, -6], [-40, -10], [30, 5], [-33, -12], [-27, -29], [6, -2], [14, 32], [13, 43], [16, 20], [51, 0], [-13, -6], [-3, 42], [-6, -12], [-16, 36], [15, 45], [16, -34], [-36, 27], [-33, -15], [-9, -19], [-6, -51], [-6, -12], [8, 2], [-40, 30], [11, -19], [0, -45], [62, 2], [50, 3], [-23, 17], [15, -9], [-6, -20], [27, 25], [-20, 37], [-40, 21], [27, 13], [12, -6], [2, -38], [-36, 0], [30, -3], [28, 30], [42, -8], [1, -44], [1, 47], [19, 2], [-10, 32], [-36, -19], [-41, -12], [30, 12], [-4, -49], [9, -15], [6, -6], [-8, -38], [-43, 22], [22, -23], [24, 12], [6, 40], [24, 45], [2, -10], [-1, -47], [2, -30], [12, 18], [6, 19], [46, 19], [48, 15], [62, 0], [-46, 5], [-14, 5], [27, 27], [-18, 10], [-28, -34], [6, 36], [0, 0], [-24, -42], [-11, 16], [67, 1], [46, -3], [-58, 1], [-26, 11], [-29, 38], [-16, 0], [-84, 4], [-28, -14], [78, 6], [-16, 16], [24, -12], [56, 6], [-11, 12], [36, 16], [56, -2], [-18, -45], [53, 26], [-3, -51], [-81, 0], [0, -6], [-24, 50], [-18, 29], [72, -4], [-6, 1], [-28, 17], [23, -14], [66, 4], [-35, 25], [0, -34], [14, 22], [-30, -3], [-62, -26], [23, 28], [71, -16], [32, -16], [32, -36], [0, -62], [55, 23], [66, 0], [36, 3], [-8, -17], [66, 9], [-84, 6], [-75, 9], [20, 33], [-15, 41], [56, 25], [31, -32], [24, -12], [-2, 38], [-66, 0], [18, -3], [-48, -6], [63, 6], [12, -32], [18, 18], [-33, 37], [0, 18], [36, 0], [24, 28], [8, 48], [20, 27], [-30, -18], [31, -18], [-30, 6], [39, -18], [-42, 6], [-53, 26], [42, -2], [-12, -9], [-48, 21], [-15, -12], [-3, -37], [40, 25], [-52, 31], [1, -38], [-24, 28], [4, -10], [-20, 22], [44, -21], [36, 35], [-30, 39], [-24, -33], [21, 35], [-66, 24], [-16, 41], [90, 0], [-18, -19], [51, -3], [7, 0], [12, 39], [-37, -31], [-33, -27], [44, 19], [-3, -21]]