So all the monomials ((m))a j–b arising in the equation E((m), j−1) = 0 have exp-type
(Θl2 (m + 1), Θl2(l + m + 1)2, 4),
and the coefficients in their q-expansions up to order
2 deg((m)) × deg(j–1 ≤ Θ(m + 1)l4
are rational integers bounded in absolute value by
exp(Θl24(m + 1)8).
Since the coefficients in E(x, y) are solutions of the homogeneous system given by these truncated q-expansions, they are bounded in absolute value by
exp(Θl28(m + 1)9).