Okay so first of all, the website is stored on a server that I don't own, so I can't run such commands.
The data the program uses is stored in a DBM database, and it's only the beginning so it's quite small really.

I've used the following memory test script I got from a certain website. It tries to use about 8MB of memory. It fails to do so:

#!/usr/bin/perl
$| = 1;
print "Content-type: text/html\n\n";
print "Memory/Resource Test<BR>\n";
print "Number is the amount of memory used<BR>\n";
print "If you don't see 'Completed Test!' at the bottom, the test fail
+ed<P><HR>\n";
for ($i = 10000; $i <= 8000000; $i += 100000) {
        $x = " " x $i;
        print "-";
        print "| $i ; Time (secs): ", (time - $^T), "<BR>\n" if $i % 1
+000000 == 0;
}
print "Completed Test!\n";
exit(0);
[download]

So I guess my host limits the ammount of memory my CGI programs can use...