I try to chmod some files and I get the error "disk quota exceeded":

It's true that I don't have that much space remaining in the filesystem where I use chmod, namelynfs.mit.edu:/export/evodesign/beatdb (which is an NFS), either in terms of bytes or in terms of inodes:

But why does chmod need more space?
I use Ubuntu 12.04.
Edit: Some more info following the comments:
1) I don't know the OS of the NFS server (nmap -O nfs-server-ip didn't return anything)
2) The NFS protocol in use by a mounted NFS filesystem is NFSv3:

3) quota -v:

4) I don't have any /var/log/messages logs, I do have some /var/log/syslog logs but nothing looks weird there.