On non-vanishing of the Fourier coefficients of primitive forms

TL;DR

This paper explores conditions under which the Fourier coefficients of primitive forms do not vanish, clarifying a discrepancy in previous literature and contributing to the understanding of their non-vanishing properties.

Contribution

It provides a semi-expository discussion on non-vanishing of Fourier coefficients and addresses a specific discrepancy in earlier results.

Findings

Clarification of non-vanishing conditions for Fourier coefficients

Identification of a discrepancy in previous literature

Insights into the properties of primitive forms

Abstract

In this semi-expository article, we discuss about the non-vanishing of the Fourier coefficients of primitive forms. Also, we shall make a note of a discrepancy in the statement of [KRW07, Lemma 2.2].