Here is a simple query that shows metadata about all the tables in your dataset:
SELECT * FROM <dataset>.__TABLES__;
You can add
WHERE table_id='<table_name>'
if you want to limit it to a specific table.
These are the returned columns:
project_id, dataset_id, table_id, creation_time, last_modified_time, row_count, size_bytes, type
The web interface says this request processes 0 bytes, so I think it is free to run.