On sup-norm bounds part I: ramified Maaß newforms over number fields

Abstract

We prove new upper bounds for the sup-norm of Hecke Maaß newforms on $GL(2)$ over a number field. Our newforms are more general than those considered in a recent paper by Blomer, Harcos, Maga, and Milicevic: we do not require square free level. Furthermore, we allow for non-trivial central character. Over the rationals we cover the best bounds as obtained by Saha.