Space of modular forms of level 2160, weight 2, and Character 2160.br

• Label: 2160.2.br
• Level: $2160$
• Weight: $2$
• Character orbit: 2160.br
• Rep. character: $\chi_{2160}(719,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $72$
• Newform subspaces: $4$
• Sturm bound: $864$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2160.br (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 180 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(864\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2160, [\chi])\).

	Total	New	Old
Modular forms	936	72	864
Cusp forms	792	72	720
Eisenstein series	144	0	144

Trace form

\( 72 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2160, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2160.2.br.a	$2160$	$2$	2160.br	180.n	$6$	$8$	$4$	$17.248$	8.0.3317760000.3	\(\Q(\sqrt{-5}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{U}(1)[D_{6}]$	\(q+\beta _{1}q^{5}+(\beta _{6}-\beta _{7})q^{7}+(-\beta _{2}-\beta _{3}+\cdots)q^{23}+\cdots\)
2160.2.br.b	$2160$	$2$	2160.br	180.n	$6$	$16$	$8$	$17.248$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{2}+\beta _{3}-\beta _{5})q^{5}+(\beta _{10}+\beta _{11}+\beta _{12}+\cdots)q^{7}+\cdots\)
2160.2.br.c	$2160$	$2$	2160.br	180.n	$6$	$24$	$12$	$17.248$		None		$4$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
2160.2.br.d	$2160$	$2$	2160.br	180.n	$6$	$24$	$12$	$17.248$		None		$4$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2160, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2160, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)