Let k be an even positive integer and N a squarefree positive integer. Denote by \(S_k^{\text {new}}(N)\) the newspace of weight k and level \(\Gamma _0(N)\) . Let \( S = \bigoplus _{k \in 2\mathbb {N}} S_k^{\text {new}}(N)\) . Given any two nonzero elements \(f, g \in S\) , we define the set \( R(f, g) := \left\{ x \in \mathbb {P}^1(\mathbb {C}) \mid x = [a_f(p): a_g(p)]\;\text {for prime}\; p \right\} \) . For level \(N = 1\) , Choi and Lim (J Number Theory 202:298–315, 2019) proved that if the set R(f, g) is finite, then f is a constant multiple of g. In this article, our aim is to extend the results of Choi and Lim to higher levels. We also obtain analogous results for the Kohnen plus space of half-integral weight modular forms.
