Non-optimal levels of a reducible mod l modular representation

Let $ell>3$ be a prime and $N$ is a square-free integer prime to $\ell$. For each prime divisor $p$ of $N$, let $a_p$ is either 1 or -1. We give a sufficient criterion for the existence of a newform $f$ of weight 2 for $\Gamma_0(N)$ such that the mod $\ell$ Galois representation attached to $f$ is reducible and $U_p f= a_p f$ for prime divisors $p$ of $N$. The main techniques used are level raising methods based on an exact sequence due to Ribet.