Every fingering that fits a hand
2030
open · no 5
2033
open · no 5
203x
open · no 5
2433
moderate
x98a
easy · no 5
What is true of it
Am7 is A, C, E and G — 1, b3, 5 and b7 counted from A.
These are also the notes of C6/A. Which name is right depends on what is underneath and what came before — the notes alone do not decide.
On an instrument that cannot reach all 4, the 5 goes first, in that order.
The easiest of the 5 fingerings below is 2030: 2 fingers, held at the 2nd fret.
3 of them use open strings, which is what makes a shape quiet to change to.
It leaves out the 5. 4 strings cannot carry 4 notes, and the 5 is the one this chord can lose without changing what it is.
Where its notes are on the neck
The brass dots are A, the root. Everything else is a chord tone with its degree printed in it.
With a different note underneath
Am7/C
x030
Am7/E
998a
Am7/G
0000
An inversion is the same chord with a different note lowest. The name changes to a slash name because the bass is what a listener hears as the foundation.