You can query Composer to find where it has set the user $COMPOSER_HOME directory.
composer config --list --global
The [home] ... line refers to the default value of $COMPOSER_HOME.
The word home can be used as a single parameter as well to show the configuration value.
Example (Windows):
> composer -n config --global home
C:\Users\<user>\AppData\Roaming\Composer
Example (Linux):
$ composer -n config --global home
/home/<user>/.composer
Just as a final confirmation – the ‘yourname’ part in the configuration, would very likely need to be updated with your own Windows username – composer config will say where it puts the files.