Dirichlet character
Modular forms and functions

Dirichlet characters appear several places in the theory of modular forms and functions. A typical example is

Let χ ∈ (Z / M Z) × ^ {\displaystyle \chi \in {\widehat {(\mathbb {Z} /M\mathbb {Z})^{\times }}}} and let χ 1 ∈ (Z / N Z) × ^ {\displaystyle \chi _{1}\in {\widehat {(\mathbb {Z} /N\mathbb {Z})^{\times }}}} be primitive.

If

define

Then

See theta series of a Dirichlet character for another example.
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