Please note: I have not done any benchmarks, these are just my calculations. I have also not factored the Java overhead into my calculations, so the memory usage will probably be slightly higher.

What you need to know beforehand:
The JVM stores a single Java byte using 4 "real" bytes in memory.¹ (This of course depends on the JVM you're using)

The graphics buffer of a ClientsideMap holds 128*128 Java bytes. This roughly equates to 64 KB of memory usage.

A MapScreen is built using an array of width*height ClientsideMaps, so it takes up width*height*128*128 of Java bytes. This equates to a memory usage of 2048 KB (2 MB) for a 8*4 MapScreen.

If you now enable the Advanced Content Change optimization algorithm, a MapScreen will double its usual memory usage. (4096 KB or 4 MB for a 8*4 MapScreen)