
# q-expansion of newform 2880.3.c.f, downloaded from the LMFDB on 25 April 2024.

# 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 = 2880
weight = 3
poly_data = [121, 0, 24, 0, 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, 0, 0], 1], [[0, 13, 0, 1], 11], [[0, 35, 0, 1], 11], [[12, 0, 1, 0], 1]]

hecke_ring_character_values = [[2431, [1, 0, 0, 0]], [901, [1, 0, 0, 0]], [641, [-1, 0, 0, 0]], [577, [-1, 0, 0, 0]]]
aps_data = [[0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, -1], [0, 0, 1, 0], [0, 7, 0, 0], [0, 0, 3, 0], [0, 0, 0, 4], [12, 0, 0, 0], [0, 0, 0, -2], [0, 6, 0, 0], [38, 0, 0, 0], [0, 0, 1, 0], [0, 49, 0, 0], [0, 0, 10, 0], [0, 0, 0, 16], [0, 0, 0, 0], [0, -59, 0, 0], [70, 0, 0, 0], [0, 0, 16, 0], [0, -84, 0, 0], [0, 0, -2, 0], [-30, 0, 0, 0], [0, 0, 0, -28], [0, 23, 0, 0], [0, 0, -14, 0], [0, -56, 0, 0], [0, 0, 13, 0], [0, 0, 0, 12], [-74, 0, 0, 0], [0, 0, 0, 36], [0, 0, 25, 0], [0, 117, 0, 0], [0, 0, 0, -24], [62, 0, 0, 0], [0, -112, 0, 0], [-70, 0, 0, 0], [0, 0, -7, 0], [0, 0, 14, 0], [0, 0, 0, -42], [0, 0, 0, 56], [0, -95, 0, 0], [22, 0, 0, 0], [0, 138, 0, 0], [0, 0, 40, 0], [0, 0, 0, 34], [-294, 0, 0, 0], [-42, 0, 0, 0], [0, 0, 29, 0], [0, 0, 0, -56], [422, 0, 0, 0], [0, 0, 0, -44], [0, -50, 0, 0], [280, 0, 0, 0], [0, -57, 0, 0], [0, 0, 0, 0], [0, 0, 0, -14], [0, -186, 0, 0], [-322, 0, 0, 0], [0, 0, -5, 0], [0, -231, 0, 0], [0, 0, -16, 0], [0, 0, 0, -42], [0, 0, -24, 0], [0, 126, 0, 0], [0, 0, -8, 0], [0, 0, 0, -58], [40, 0, 0, 0], [0, 0, -46, 0], [0, 0, 0, -84], [406, 0, 0, 0], [0, 0, 0, 112], [0, 114, 0, 0], [0, 0, 37, 0], [0, 0, 15, 0], [538, 0, 0, 0], [0, 0, 0, 56], [0, -350, 0, 0], [0, 0, -41, 0], [0, -175, 0, 0], [-242, 0, 0, 0], [0, -559, 0, 0], [-358, 0, 0, 0], [0, -10, 0, 0], [0, 0, -38, 0], [690, 0, 0, 0], [0, 0, 0, -84], [0, 57, 0, 0], [0, 0, 50, 0], [0, -456, 0, 0], [0, 0, -39, 0], [0, 0, 0, -96], [0, -56, 0, 0], [0, 0, -117, 0], [0, 399, 0, 0], [-72, 0, 0, 0], [0, 0, 0, -48], [0, 348, 0, 0], [0, -49, 0, 0], [0, 0, 50, 0], [590, 0, 0, 0], [0, 0, -34, 0], [0, 0, 0, 144], [0, 0, 0, 4], [0, 77, 0, 0], [-704, 0, 0, 0], [0, 0, -166, 0], [0, 0, 0, 204], [0, 0, 0, 0], [0, 210, 0, 0], [20, 0, 0, 0], [0, 0, -1, 0], [0, 0, -7, 0], [0, 0, 0, -8], [178, 0, 0, 0], [154, 0, 0, 0], [0, 571, 0, 0], [0, 0, -150, 0], [0, 0, 0, -168], [0, 0, 0, -14], [0, -371, 0, 0], [-74, 0, 0, 0], [0, 0, -102, 0], [0, 0, 0, -58], [0, 0, 0, -88], [-68, 0, 0, 0], [0, 92, 0, 0], [210, 0, 0, 0], [0, -86, 0, 0], [0, 0, -3, 0], [0, 0, -209, 0], [416, 0, 0, 0], [0, 0, 0, 168], [-86, 0, 0, 0], [0, 0, 7, 0], [0, 261, 0, 0], [384, 0, 0, 0], [0, 0, 0, 42], [0, 0, -70, 0], [0, 0, 0, 104], [0, -1047, 0, 0], [-602, 0, 0, 0], [0, 994, 0, 0], [0, 0, -189, 0], [0, 0, 0, 244], [-1074, 0, 0, 0], [0, -526, 0, 0], [0, 0, 25, 0], [0, 0, 0, 24], [154, 0, 0, 0], [0, 0, 0, -222], [0, 0, -205, 0], [0, 609, 0, 0], [0, 0, -150, 0], [0, 0, 0, 126], [0, 0, -138, 0], [0, 540, 0, 0], [54, 0, 0, 0], [0, 105, 0, 0], [0, 0, -116, 0], [0, 242, 0, 0], [0, 0, 0, -84], [0, 0, 0, -224], [0, 0, 59, 0], [0, -483, 0, 0], [0, 0, 0, 336], [0, 0, 0, 200], [-1054, 0, 0, 0], [0, 0, 177, 0], [1924, 0, 0, 0], [0, 0, 0, -96], [0, -357, 0, 0], [-1302, 0, 0, 0], [0, 1160, 0, 0], [0, 0, 128, 0], [1306, 0, 0, 0], [0, -357, 0, 0], [566, 0, 0, 0], [0, -60, 0, 0], [0, 0, -7, 0], [-142, 0, 0, 0], [0, 0, -125, 0], [0, -253, 0, 0], [0, 0, 199, 0], [0, 0, 0, -84], [0, 0, 0, 416], [0, 1134, 0, 0], [0, 0, -245, 0], [0, 0, 44, 0], [-1808, 0, 0, 0], [0, 1498, 0, 0], [0, 0, -36, 0], [0, 0, 0, -364], [1186, 0, 0, 0], [0, -336, 0, 0], [0, 0, 0, -228], [0, 0, 0, 444], [1746, 0, 0, 0], [0, 0, -315, 0], [0, 0, 0, -204], [0, 0, 0, 152], [0, 1026, 0, 0], [-498, 0, 0, 0], [0, 0, 273, 0], [1148, 0, 0, 0], [0, -1183, 0, 0], [0, 0, 0, 102], [1974, 0, 0, 0], [0, 0, 0, -16], [0, 1519, 0, 0], [-1700, 0, 0, 0], [0, 0, -176, 0], [0, -792, 0, 0], [0, 0, 175, 0], [0, 0, 0, -336], [0, 704, 0, 0], [-338, 0, 0, 0], [0, 0, -133, 0], [0, 1085, 0, 0], [0, 0, 0, -224], [0, 0, 0, 64], [138, 0, 0, 0], [-1898, 0, 0, 0], [0, -1197, 0, 0], [0, 0, 175, 0], [0, 0, 0, 216], [-210, 0, 0, 0], [0, 0, 0, -28], [0, -634, 0, 0], [0, 0, -181, 0], [0, 1309, 0, 0], [0, 0, 121, 0], [602, 0, 0, 0], [-1490, 0, 0, 0], [0, 1407, 0, 0], [0, 0, -206, 0], [0, 0, 0, -406], [306, 0, 0, 0], [0, 0, 0, 350], [0, -315, 0, 0], [0, -1764, 0, 0], [0, 0, 0, 168], [-1048, 0, 0, 0], [0, 0, -61, 0], [406, 0, 0, 0], [0, 0, 0, -112], [0, -84, 0, 0], [0, 0, 375, 0], [0, 903, 0, 0], [-392, 0, 0, 0], [0, 0, 0, -266], [0, 0, -123, 0], [0, -35, 0, 0], [0, 0, 0, 514], [2318, 0, 0, 0], [0, 0, 0, -112], [0, -975, 0, 0], [-934, 0, 0, 0], [0, 0, 100, 0], [0, 0, 0, -56], [0, 0, 418, 0], [0, 0, 243, 0], [0, 0, 0, 112], [634, 0, 0, 0], [0, 0, -227, 0], [0, 0, 0, -444], [2056, 0, 0, 0], [0, 1890, 0, 0], [0, -461, 0, 0], [0, 0, 238, 0], [0, 0, 0, 378], [-506, 0, 0, 0], [0, 0, 112, 0], [0, 0, 464, 0], [-1850, 0, 0, 0], [0, 0, 308, 0], [0, 0, 175, 0], [0, 0, 0, 476], [242, 0, 0, 0], [-562, 0, 0, 0], [0, 1533, 0, 0], [0, 0, 0, 462], [1774, 0, 0, 0], [0, 0, 0, -680], [1646, 0, 0, 0], [0, 0, 334, 0], [0, 1694, 0, 0], [0, 0, -240, 0], [0, 0, 0, 490], [-802, 0, 0, 0], [0, -931, 0, 0], [0, -322, 0, 0], [0, 0, 0, -252], [0, 0, 0, -336], [0, 1329, 0, 0], [0, 0, -283, 0], [0, -108, 0, 0], [-3390, 0, 0, 0], [0, 0, 0, -216], [0, -91, 0, 0], [0, 0, 354, 0], [0, 0, -460, 0], [0, 0, 0, -54], [1022, 0, 0, 0]]
