**Nikoloz Kachakhidze**

## On the Fourier Expansions of
Eisenstein Series of Some Types

**Abstract:**

Bases of the spaces of Eisenstein series $E_k(\Gamma_0(4N),\chi)$ $(k\in \mathbb{N}$,
$k\geq 3$, $N$ is an odd natural and square-free) and $E_{k/2}(\wt\Gamma_0(4N),\chi)$
$(k\in \mathbb{N}$, $2\dag k$, $k\geq 5$, $N$ is an odd natural and square-free)
are constructed for any Dirichlet character mod $4N$ and Fourier expansions of
these series are obtained.

**Keywords:**

Entire modular form, Eisenstein series, congruence subgroup.

**MSC 2000:** 11F11