It is hoster's job, to solve such errors. So it's always nice to disturb them, because the money is paid for that.
This is what they replied:
The forbidden message you are seeing is due to the search script that is being used hitting our Mod Security rule set. The mod security rule is in place to protect against common PHP injection attacks. In some cases it returns false positives due to the manner in which the script operates. Unfortunately, we can disclose the exact rule for security reasons.
They also suggested to whitelist our domain for this rule so that when searching for those variables, it will be allowed through the rule set
I disagreed with that. There is nothing critical comes regarding this point comparing to security.
So like I replied above, do not use major PHP functions in search. Skipping parentheses and other system symbols, leaving the phrase characters clean, will help.