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

• Label: 2160.2.q
• Level: $2160$
• Weight: $2$
• Character orbit: 2160.q
• Rep. character: $\chi_{2160}(721,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $48$
• Newform subspaces: $12$
• Sturm bound: $864$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2160.q (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(864\)
Trace bound:			\(7\)
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	48	888
Cusp forms	792	48	744
Eisenstein series	144	0	144

Trace form

\( 48 q + O(q^{10}) \)

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.q.a	$2160$	$2$	2160.q	9.c	$3$	$2$	$1$	$17.248$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-1\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots\)
2160.2.q.b	$2160$	$2$	2160.q	9.c	$3$	$2$	$1$	$17.248$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots\)
2160.2.q.c	$2160$	$2$	2160.q	9.c	$3$	$2$	$1$	$17.248$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(5-5\zeta_{6})q^{11}-3q^{17}-5q^{19}+\cdots\)
2160.2.q.d	$2160$	$2$	2160.q	9.c	$3$	$2$	$1$	$17.248$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
2160.2.q.e	$2160$	$2$	2160.q	9.c	$3$	$2$	$1$	$17.248$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+4\zeta_{6}q^{13}+\cdots\)
2160.2.q.f	$2160$	$2$	2160.q	9.c	$3$	$4$	$2$	$17.248$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(1\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1})q^{5}+\beta _{3}q^{7}+(\beta _{1}+\beta _{3})q^{11}+\cdots\)
2160.2.q.g	$2160$	$2$	2160.q	9.c	$3$	$4$	$2$	$17.248$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1})q^{5}+(\beta _{1}-\beta _{2})q^{7}+2q^{17}+\cdots\)
2160.2.q.h	$2160$	$2$	2160.q	9.c	$3$	$4$	$2$	$17.248$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{12}q^{5}+(2-2\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{7}+\cdots\)
2160.2.q.i	$2160$	$2$	2160.q	9.c	$3$	$6$	$3$	$17.248$	6.0.954288.1	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(3\)	$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{2})q^{5}+(-\beta _{2}-\beta _{4})q^{7}+(-\beta _{3}+\cdots)q^{11}+\cdots\)
2160.2.q.j	$2160$	$2$	2160.q	9.c	$3$	$6$	$3$	$17.248$	6.0.954288.1	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(-5\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{3})q^{5}+(-\beta _{1}-\beta _{3}+\beta _{4}-\beta _{5})q^{7}+\cdots\)
2160.2.q.k	$2160$	$2$	2160.q	9.c	$3$	$6$	$3$	$17.248$	6.0.954288.1	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(5\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{3})q^{5}+(2\beta _{3}+\beta _{4}-\beta _{5})q^{7}+\cdots\)
2160.2.q.l	$2160$	$2$	2160.q	9.c	$3$	$8$	$4$	$17.248$	8.0.856615824.2	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(-1\)	$3^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{1})q^{5}-\beta _{3}q^{7}+(\beta _{3}-\beta _{7})q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2160, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)