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Modular forms: Fourier coefficients of Eisenstein series

This lecture is part of an online graduate course on modular forms. We calculate the Fourier coefficients of the Eisenstein series introduced in the previous lecture, and use them to construct the elliptic modular function. (Minor typo: in the definition of E10 I wrote 262 instead of 264.) For the other lectures in the course see    • Modular forms  

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Modular forms: Fundamental domain
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Modular forms: Fundamental domain

Modular forms: Eisenstein series
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Modular forms: Eisenstein series

Modular forms: Introduction
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Modular forms: Introduction

The bridge between number theory and complex analysis
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The bridge between number theory and complex analysis

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We're 99.9% sure this pattern is true, but no one can prove it

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Kevin Buzzard (lecture 1/20) Automorphic Forms And The Langlands Program [2017]

Fourier Series Explained (for Beginners)
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Fourier Series Explained (for Beginners)

Modular forms: Classification
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Modular forms: Classification

How Divergence and Curl Were Discovered
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How Divergence and Curl Were Discovered

Counting points on the E8 lattice with modular forms (theta functions) | #SoME2
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Counting points on the E8 lattice with modular forms (theta functions) | #SoME2

Elliptic functions lecture 3. Jacobi functions
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Elliptic functions lecture 3. Jacobi functions

Elliptic functions 1. Weierstrass function.
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Elliptic functions 1. Weierstrass function.

Modular forms: Theta functions
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Modular forms: Theta functions

Complex analysis: Singularities
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Complex analysis: Singularities

Modular forms: Modular functions
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Modular forms: Modular functions

Modular forms: Hecke operators
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Modular forms: Hecke operators

But what is the Fourier Transform?  A visual introduction.
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But what is the Fourier Transform? A visual introduction.

The Mathematical Problem with Music, and How to Solve It
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The Mathematical Problem with Music, and How to Solve It

a formula for the "circumference" of an ellipse.
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a formula for the "circumference" of an ellipse.

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