A Note on Hecke's absolute Invariants

Let Jq be Hecke's absolute invariant. The n-th Fourier coefficient of J_q is written in the form α_q(n)r where α_q(n) ∈ Q, r_q∈ R. We regard α_q(n) as a rational function of q. In § 3, it is proved that α_q(n) is divisible by q²-4 for n > 2. This implies the conjecture of J. Raleigh [4]. Prime divisors of the denominator of α_q (n) are also treated in § 4. In the last section, we propose interesting conjectures concerning α_q (n).