A sample of low energy bursts from FRB 121102

We present 41 bursts from the first repeating fast radio burst discovered (FRB 121102). A deep search has allowed us to probe unprecedentedly low burst energies during two consecutive observations (separated by one day) using the Arecibo telescope at 1.4 GHz. The bursts are generally detected in less than a third of the 580-MHz observing bandwidth, demonstrating that narrow-band FRB signals may be more common than previously thought. We show that the bursts are likely faint versions of previously reported multi-component bursts. There is a striking lack of bursts detected below 1.35 GHz and simultaneous VLA observations at 3 GHz did not detect any of the 41 bursts, but did detect one that was not seen with Arecibo, suggesting preferred radio emission frequencies that vary with epoch. A power law approximation of the cumulative distribution of burst energies yields an index $-1.8\pm0.3$ that is much steeper than the previously reported value of $\sim-0.7$. The discrepancy may be evidence for a more complex energy distribution. We place constraints on the possibility that the associated persistent radio source is generated by the emission of many faint bursts ($\sim700$ ms$^{-1}$). We do not see a connection between burst fluence and wait time. The distribution of wait times follows a log-normal distribution centered around $\sim200$ s; however, some bursts have wait times below 1 s and as short as 26 ms, which is consistent with previous reports of a bimodal distribution. We caution against exclusively integrating over the full observing band during FRB searches, because this can lower signal-to-noise.