Additive bases with coefficients of newforms

Victor Cuauhtemoc Garcia, Florin Nicolae

Let $f(z)={\sum }_{n=1}^{\infty }a(n)e^{2\pi inz}$ be a normalized Hecke eigenform in $S_{2k}^{\text{new}}({\Gamma }_0(N))$ with integer Fourier coefficients. We prove that there exists a const…