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The coefficient ring of a Siegel modular form is the subring $\Z[{a_n}]$ of $\C$ generated by the coefficients $a_n$ of its $q$-expansion $\sum a_nq^n$. In the case of a newform the coefficients $a_n$ are algebraic integers and the coefficient ring is a finite index subring of the ring of integers of the coefficient field of the newform. It is also known as the Hecke ring, since the $a_n$ generate the same ring as the eigenvalues of the Hecke operators.

Knowl status:
  • Review status: beta
  • Last edited by Eran Assaf on 2022-08-31 11:05:24
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