  Let $f(z)=\sum_{n=1}^{\infty}a(n) e^{2\pi i nz}$ be a normalized Hecke
eigenform in $S_{2k}^{\text{new}}(\Gamma_0(N))$ with integer Fourier
coefficients. We prove that there exists a constant $C(f)>0$ such that any
integer is a sum of at most $C(f)$ coefficients $a(n) $. It holds
$C(f)\ll_{\varepsilon,k}N^{\frac{6k-3}{16}+\varepsilon}$.
