We report the detection of 72 new pulses from the repeating fast radio burst FRB 121102 in Breakthrough Listen C-band (4–8 GHz) observations at the Green Bank Telescope. The new pulses were found with a convolutional neural network in data taken on 2017 August 26, where 21 bursts have been previously detected. Our technique combines neural network detection with dedispersion verification. For the current application, we demonstrate its advantage over a traditional brute-force dedispersion algorithm in terms of higher sensitivity, lower false-positive rates, and faster computational speed. Together with the 21 previously reported pulses, this observation marks the highest number of FRB 121102 pulses from a single observation, totaling 93 pulses in five hours, including 45 pulses within the first 30 minutes. The number of data points reveals trends in pulse fluence, pulse detection rate, and pulse frequency structure. We introduce a new periodicity search technique, based on the Rayleigh test, to analyze the time of arrivals (TOAs), with which we exclude with 99% confidence periodicity in TOAs with periods larger than 5.1 times the model-dependent timestamp uncertainty. In particular, we rule out constant periods≳ 10 ms in the barycentric arrival times, though intrinsic periodicity in the time of emission remains plausible.