# q-expansion of newform 150.4.a.h, 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
    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 = 150
weight = 4
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 = [[2], [3], [0], [1], [42], [67], [-54], [-115], [162], [-210], [-193], [286], [12], [-263], [-414], [192], [690], [-733], [-299], [-228], [-938], [-160], [462], [-240], [511], [912], [-668], [1296], [-1735], [1092], [16], [1992], [2346], [2900], [-2070], [2237], [241], [3547], [-984], [-3618], [-150], [197], [1302], [-4163], [-3054], [3425], [-2443], [-23], [1956], [1805], [-3468], [2640], [-5383], [-5028], [-564], [1812], [-5190], [4592], [2191], [7842], [247], [5442], [3871], [-5718], [3637], [1296], [5132], [6751], [5226], [-6190], [-6618], [-3420], [871], [-6383], [-9865], [-9828], [12540], [1381], [14232], [2645], [3000], [-11338], [-3258], [-1163], [6695], [-16368], [16380], [13786], [11832], [-3008], [-4434], [7410], [8671], [-19368], [-8875], [10452], [-19770], [-11238], [7447], [-17623], [10096], [-14514], [10242], [-6750], [17117], [301], [15456], [9492], [1500], [14627], [-16184], [18502], [13896], [-9895], [467], [30612], [1852], [21156], [9702], [1980], [-20158], [16882], [-20934], [8712], [-14128], [-28278], [8885], [-7530], [1801], [7882], [33860], [20652], [7472], [32251], [16812], [-34645], [8412], [-18329], [-16044], [-24000], [5117], [13542], [-1283], [-16344], [-790], [-9990], [-24743], [23556], [-34000], [37032], [-2519], [43992], [19177], [-44994], [52396], [7242], [4085], [-3030], [-5759], [-258], [-1374], [-9288], [21616], [-19098], [18246], [38772], [-23053], [10366]]