Diamond operator

This article is about ⋄. For <> following a type name in the Java programming language, see Generics in Java § Diamond operator.

In number theory, the diamond operators 〈d〉 are operators acting on the space of modular forms for the 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 and commute with the Hecke operators.

Unicode

In Unicode, the diamond operator is represented by the character U+22C4 ⋄ DIAMOND OPERATOR.

References

• Diamond, Fred; Shurman, Jerry (2005), A first course in modular forms, Graduate Texts in Mathematics, vol. 228, Berlin, New York: Springer-Verlag, ISBN 978-0-387-23229-4, MR 2112196