Ok I have found how to do it on my own.
For people interested, to change the default value of the search bar, it is the following code:
add_filter(“asp_print_search_query”, “asp_change_print_search_query”, 10, 2);
function asp_change_print_search_query($query, $search_id) {
// Edit query (string that is the default value)
return $query;
}