Why does the smartphone turn off?

Question

Android

Recently, the battery on the nexus 4 was replaced with a new one, since the old one did not hold a charge at all. But there were problems:
The phone began to turn off at 48% of the charge. If you put it back on charge, then it does not immediately show that the charge is in progress. Only the red light is on. When enabled, 0% is shown.
I read on the forums that you need to calibrate the battery. I made the phone root charged up to 100% and did the calibration. and instead of 100% showed 90% and now the phone began to turn off at 38%. But that is not all.
Yesterday the phone died by 58%. After I put it on charge and turned it on, it showed ~ 2%, and after rebooting 40% and as soon as the charge reached 38%, it turned off again.
How to win it. already tired of fighting with him. no more thoughts.