SCHEMA:
CREATE TABLE table_name_42 (total_atms INTEGER, bank_type VARCHAR, on_site_atms VARCHAR)
USER:
What is the minimum total ATMs with new private sector banks as the bank type, and the on-site ATMs are greater than 1883?

QUERY:
SELECT MIN(total_atms) FROM table_name_42 WHERE bank_type = "new private sector banks" AND on_site_atms > 1883