The **dimension** of a space of modular forms is its dimension as a complex vector space; for spaces of newforms $S_k^{\rm new}(N,\chi)$ this is the same as the dimension of the $\Q$-vector space spanned by its eigenforms.

The **dimension** of a newform refers to the dimension of its newform subspace, equivalently, the cardinality of its newform orbit. This is equal to the degree of its coefficient field (as an extension of $\Q$).

The **relative dimension** of $S_k^{\rm new}(N,\chi)$ is its dimension as a $\Q(\chi)$-vector space, where $\Q(\chi)$ is the field generated by the values of $\chi$, and similarly for newform subspaces.

**Authors:**

**Knowl status:**

- Review status: reviewed
- Last edited by John Voight on 2020-02-15 13:57:06

**Referred to by:**

- cmf.23.2.a.a.top
- cmf.983.2.c.a.bottom
- cmf.display_dim
- cmf.galois_conjugate
- cmf.hecke_kernels
- cmf.inner_twist_count
- cmf.trace_bound
- cmf.trace_form
- rcs.cande.cmf
- rcs.cande.lfunction
- rcs.rigor.cmf
- rcs.source.cmf
- lmfdb/classical_modular_forms/main.py (lines 1207-1208)
- lmfdb/classical_modular_forms/main.py (line 1373)
- lmfdb/classical_modular_forms/templates/cmf_full_gamma1_space.html (line 145)
- lmfdb/classical_modular_forms/templates/cmf_newform_common.html (line 51)
- lmfdb/classical_modular_forms/templates/cmf_newform_list.html (line 11)
- lmfdb/classical_modular_forms/templates/cmf_trace_display.html (line 6)
- lmfdb/classical_modular_forms/web_newform.py (line 1057)
- lmfdb/classical_modular_forms/web_newform.py (line 1074)
- lmfdb/classical_modular_forms/web_newform.py (line 1118)
- lmfdb/classical_modular_forms/web_newform.py (line 1135)

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

- 2020-02-15 13:57:06 by John Voight (Reviewed)
- 2020-01-03 05:02:47 by Andrew Sutherland
- 2020-01-03 05:01:25 by Andrew Sutherland
- 2019-01-30 16:01:38 by Andrew Sutherland (Reviewed)

**Differences**(show/hide)