The **coefficient ring ** of a modular form is the subring $\Z[a_1,a_2,a_3,\ldots]$ 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.

**Authors:**

**Knowl status:**

- Review status: reviewed
- Last edited by Andrew Sutherland on 2019-06-14 04:42:55

**Referred to by:**

- cmf.1.250.a.a.bottom
- cmf.hecke_ring_generators
- rcs.cande.cmf
- lmfdb/classical_modular_forms/main.py (line 1439)
- lmfdb/classical_modular_forms/templates/cmf_newform_common.html (line 71)
- lmfdb/classical_modular_forms/templates/cmf_newform_common.html (line 80)
- lmfdb/classical_modular_forms/templates/cmf_newform_common.html (line 86)
- lmfdb/classical_modular_forms/templates/cmf_newform_common.html (line 226)

**History:**(expand/hide all)

- 2019-06-14 04:42:55 by Andrew Sutherland (Reviewed)
- 2018-09-29 02:33:32 by David Roe (Reviewed)

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