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 $\text{GL}(2)$ over a number field. Our newforms are more general than those considered in a recent paper by Blomer, Harcos, Maga, and Milićević: we do not require square-free level. Furthermore, we allow for non-trivial central character. Over the rationals we recover the best bounds obtained by Saha.