There Exist Non-CM Hilbert Modular Forms of Partial Weight 1

TL;DR

This paper demonstrates the existence of non-CM Hilbert modular cusp forms of partial weight one over Q(√5), challenging prior assumptions that such forms are always induced from CM extensions.

Contribution

It proves the existence of classical Hilbert modular cusp forms of partial weight one that are not derived from CM extensions, a novel result in the field.

Findings

Existence of non-CM Hilbert modular forms of partial weight one over Q(√5)

Contradicts the assumption that all such forms are induced from CM extensions

Provides new insights into the structure of Hilbert modular forms

Abstract

In this note, we prove that there exists a classical Hilbert modular cusp form over Q(\sqrt{5}) of partial weight one which does not arise from the induction of a Grossencharacter from a CM extension of Q(\sqrt{5}).