Let $f(z)=\sum_{n\ge 1}a(n)n^{(k-1/2)/2}e(nz)\in S_{k+1/2}(\Gamma_0(4N))$ be a cuspidal Hecke eigenform. Let 
$$M(s)=\sum_{p\ge 2, \text{prime}}\frac{|a(p)|^2}{p^s}$$ and
$$R_f(s)=\sum_{n\ge 1}\frac{|a(n)|^2}{n^s}$$
Is there a functional equation link the two series ?