The zeros of even period polynomials for newforms on Γ₀(𝑁)

We prove that for even integer k ≥ k 0 k\geq k_0 , almost all of zeros of the even period polynomial associated to a newform of weight k k on Γ 0 ( N ) \Gamma _0(N) are on the circle | z | = 1 / N |z|=1/\sqrt {N} .