Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Atkin–Lehner theory | Statement: [Hecke operators, appearIn, Atkin–Lehner theory]

Target entity: Atkin–Lehner theory
Context triple: [Hecke operators, appearIn, Atkin–Lehner theory]

• A. Hecke theory
  Hecke theory is a branch of number theory centered on Hecke operators and modular forms, providing powerful tools to study arithmetic properties of modular forms and related objects.
• B. Eichler–Shimura theory
  Eichler–Shimura theory is a foundational framework in number theory and arithmetic geometry that connects modular forms with the cohomology of modular curves and the theory of elliptic curves.
• C. Automorphic Forms and Representations
  Automorphic Forms and Representations is a foundational mathematical monograph that develops the theory of automorphic forms and their connections to representation theory and number theory.
• D. Hecke operators
  Hecke operators are algebraic operators acting on modular forms that play a central role in number theory, particularly in understanding congruences, L-functions, and the arithmetic of modular forms.
• E. Shimura correspondence
  The Shimura correspondence is a fundamental result in number theory that establishes a deep link between modular forms of half-integral weight and modular forms of integral weight, with important applications to L-functions and arithmetic geometry.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Atkin–Lehner theory
Target entity description: Atkin–Lehner theory is a framework in the theory of modular forms that studies their symmetries and decompositions using certain involutions and operators, refining the structure of spaces of modular forms and newforms.

• A. Hecke theory
  Hecke theory is a branch of number theory centered on Hecke operators and modular forms, providing powerful tools to study arithmetic properties of modular forms and related objects.
• B. Eichler–Shimura theory
  Eichler–Shimura theory is a foundational framework in number theory and arithmetic geometry that connects modular forms with the cohomology of modular curves and the theory of elliptic curves.
• C. Automorphic Forms and Representations
  Automorphic Forms and Representations is a foundational mathematical monograph that develops the theory of automorphic forms and their connections to representation theory and number theory.
• D. Hecke operators
  Hecke operators are algebraic operators acting on modular forms that play a central role in number theory, particularly in understanding congruences, L-functions, and the arithmetic of modular forms.
• E. Shimura correspondence
  The Shimura correspondence is a fundamental result in number theory that establishes a deep link between modular forms of half-integral weight and modular forms of integral weight, with important applications to L-functions and arithmetic geometry.
• F. None of above. chosen