[mysql] How can I see the specific value of the sql_mode?

It's only blank for you because you have not set the sql_mode. If you set it, then that query will show you the details:

mysql> SELECT @@sql_mode;
+------------+
| @@sql_mode |
+------------+
|            |
+------------+
1 row in set (0.00 sec)

mysql> set sql_mode=ORACLE;
Query OK, 0 rows affected (0.00 sec)

mysql> SELECT @@sql_mode;
+----------------------------------------------------------------------------------------------------------------------+
| @@sql_mode                                                                                                           |
+----------------------------------------------------------------------------------------------------------------------+
| PIPES_AS_CONCAT,ANSI_QUOTES,IGNORE_SPACE,ORACLE,NO_KEY_OPTIONS,NO_TABLE_OPTIONS,NO_FIELD_OPTIONS,NO_AUTO_CREATE_USER |
+----------------------------------------------------------------------------------------------------------------------+
1 row in set (0.00 sec)