**Background:**
Let $M_{f_i}, i=1,2$ be two modular motives associated to cusp forms
$f_i \in S_{w_i}(\Gamma_0(N_i))$ of weight $w_i$ and level $N_i$ respectively.
The Rankin-Selberg convolution associates an L-series
$L(f_1\otimes f_2,s)$ to this pair of modular forms.
In the framework of automorphic motives a natural question is
whether the L-series $L(M,s)$ of a motive $M$ can be represented in
terms of modular submotives $M_{f_i}$ as $L(M,s) \stackrel{?}{=}
L(f_1\otimes f_2,s)$.

**Question:**
Is there a (practical) test that can be applied to a given
(motivic) L-series as to whether it admits a Rankin-Selberg
product representation?