741 amplification factor doesn't change
Here is your schematic:



This shows a + and - supply, and the left end of R1 grounded.  But they you say:

 My negative input terminal on the op-amp is grounded to the power supplies negative terminal

There two statements contradict each other, so now we don't know what you really have connected to what.

It should be connected as your schematic shows.  You want the input signal amplified about ground, which should also be near the center of the power supply range.  The scope trace you show hints that the amp is clipping on the negative portion of the square wave:



This shows no noise ripple at the bottom level, but does at the top.

Further discussion is pointless while you're contradicting yourself.  A better answer requires a better question.