# Diamond operator

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This article is about ⋄. For <> following a type name in the [Java programming language](/source/Java_programming_language), see [Generics in Java § Diamond operator](/source/Generics_in_Java#Diamond_operator).

In [number theory](/source/Number_theory), the **diamond operators** 〈*d*〉 are operators acting on the space of [modular forms](/source/Modular_form) for the [congruence subgroup](/source/Congruence_subgroup) Γ1(*N*), given by the action of a matrix (a b c δ) in Γ0(*N*) where δ ≈ d mod N. The diamond operators form an [abelian group](/source/Abelian_group) and commute with the [Hecke operators](/source/Hecke_operator).

## Unicode

In [Unicode](/source/Unicode), the diamond operator is represented by the character U+22C4 ⋄ DIAMOND OPERATOR.[1]

## Notes

1. **[^](#cite_ref-1)** ["Mathematical Operators – Unicode"](https://www.unicode.org/charts/PDF/U2200.pdf) (PDF). Retrieved 2013-04-22.

## References

- Diamond, Fred; Shurman, Jerry (2005), [*A first course in modular forms*](https://books.google.com/books?id=He6nwjGdlG4C), [Graduate Texts in Mathematics](/source/Graduate_Texts_in_Mathematics), vol. 228, Berlin, New York: [Springer-Verlag](/source/Springer-Verlag), [ISBN](/source/ISBN_(identifier)) [978-0-387-23229-4](https://en.wikipedia.org/wiki/Special:BookSources/978-0-387-23229-4), [MR](/source/MR_(identifier)) [2112196](https://mathscinet.ams.org/mathscinet-getitem?mr=2112196)

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