# Harmonic Eisenstein Series of Weight One

## TL;DR

This paper constructs a harmonic Eisenstein series of weight one and explores its relation to a known Eisenstein series via the $\xi$-operator, contributing to the understanding of modular forms of weight one.

## Contribution

It introduces a new harmonic Eisenstein series of weight one and analyzes its connection to classical Eisenstein series through the $\xi$-operator.

## Key findings

- Constructed a harmonic Eisenstein series of weight one.
- Established the relationship between the new series and Hecke's Eisenstein series.
- Enhanced understanding of weight one modular forms.

## Abstract

In this short note, we will construct a harmonic Eisenstein series of weight one, whose image under the $\xi$-operator is a weight one Eisenstein series studied by Hecke.