##  [Eichler–Shimura Correspondence](/eichler-shimura-correspondence) 

  ##  [Eichler–Shimura Correspondence](https://puremath.quantumdictionary.io/eichler-shimura-correspondence-0) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The relationship that associates weight-two modular forms (newforms) with algebraic geometric objects: it identifies certain newforms with factors of the Jacobian of modular curves (or with abelian varieties A_f) and relates Hecke eigenvalues to Frobenius traces in cohomology, linking analytic modular forms and algebraic geometry.

 

 

 

 

 





 

 



 ##  [Eichler–Shimura Correspondence](https://algebra.quantumdictionary.io/eichler-shimura-correspondence-1) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A relationship between classical modular forms (especially weight two eigenforms), two-dimensional l-adic Galois representations, and the cohomology (or Jacobians) of modular curves that connects complex-analytic objects and arithmetic representations.