The Signature of Γ+ 0(n)

The signature of Γ+ 0(eN2), where e is square free, is completely determined if e = 3 or N is odd or e Ψ, where Ψ is the set of all square free integers e such that• (i) if is odd, then admits no divisors of the form 8 + 3,• (ii) if is even, then admits no divisors of the form 8 + 7.In particular, v2 (number of elliptic classes of period 2 of Γ+ 0(n)) is expressed as a linear combination of multiplicative functions.