On modular forms for some noncongruence subgroups of SL_2(Z) II

TL;DR

This paper proves that certain noncongruence subgroups of SL_2(Z) have the unbounded denominator property, confirming a conjecture for specific character groups of Gamma^0(11).

Contribution

It establishes the unbounded denominator property for two classes of noncongruence subgroups, confirming a prior conjecture for Gamma^0(11).

Findings

Two classes of noncongruence subgroups satisfy the unbounded denominator property.

Confirmed the conjecture for all type II noncongruence character groups of Gamma^0(11).

Abstract

In this paper we show two classes of noncongruence subgroups satisfy the so-called unbounded denominator property. In particular, we establish our conjecture in [KL08] which says that every type II noncongruence character group of Gamma^0(11) satisfies the unbounded denominator property.