The **coefficient ring ** of a modular form is the subring 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 $a_n$ are eigenvalues of Hecke operators.

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**Knowl status:**

- Review status: reviewed
- Last edited by David Roe on 2018-09-29 02:33:32

**Referred to by:**

- cmf.hecke_ring_generators
- rcs.cande.cmf
- lmfdb/classical_modular_forms/templates/cmf_browse.html (line 234)
- lmfdb/classical_modular_forms/templates/cmf_newform_common.html (lines 67-71)
- lmfdb/classical_modular_forms/templates/cmf_newform_common.html (lines 80-84)
- lmfdb/classical_modular_forms/templates/cmf_newform_common.html (line 219)
- lmfdb/classical_modular_forms/templates/cmf_refine_search.html (line 139)

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