1796 Draped Bust Dollar - Fake?

Yes. Conforms to no known die variety, and the denticles stop at a raised rim instead of carrying to the edge. Let's see how many things wrong we can find, though...

I just bought this yesterday. It has the Heraldic Eagle,
but it shares similarities to your coin.





On both of the "coins" the legends around the circumference
are sharp, but as one looks towards the center the details
become blurred. This is more obvious on the reverse.

The horizontal bars on the shield are completely missing,
perhaps because the word "copy" was removed. The breasts on both eagles are lacking any definition.

I bought my example just after having negotiated for a genuine 1799 Dollar. Side by side they will be an interesting learning tool.

My point is this: sometimes a coin will not look quite
right. Before examining the details for die characteristics
the initial reaction that you have to a coin is your first
and most valuable guide.

I hope that this reply complements philadelphian's
technical analysis.

Welcome, lux73!

The surfaces on the OP's coin indicate modern manufacturing techniques, versus a screw press.

Shouldn't it say $1 on it somewhere?

I think I would not trust a coin like that in that grade not being slabbed. Too expensive of a mistake and looks like something someone would fake.

Some of the things I noticed include the off center bust which I believe was only used in 1795, the mushiness in some of the details, and the general appearance of the coin which looks very typical of many modern Chinese counterfeits.