Space of modular forms of level 2160, weight 3, and Character 2160.bs

• Label: 2160.3.bs
• Level: $2160$
• Weight: $3$
• Character orbit: 2160.bs
• Rep. character: $\chi_{2160}(881,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $5$
• Sturm bound: $1296$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2160.bs (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(1296\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2160, [\chi])\).

	Total	New	Old
Modular forms	1800	96	1704
Cusp forms	1656	96	1560
Eisenstein series	144	0	144

Trace form

\( 96 q + 240 q^{25} - 72 q^{29} + 48 q^{31} - 72 q^{41} - 96 q^{43} - 336 q^{49} - 432 q^{59} + 48 q^{73} + 288 q^{77} + 720 q^{83} - 384 q^{91} + 120 q^{97}+O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2160, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2160.3.bs.a	$2160$	$3$	2160.bs	9.d	$6$	$4$	$2$	$58.856$	\(\Q(\sqrt{-3}, \sqrt{-5})\)	None					180.3.o.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{5}+(-2\beta _{1}-4\beta _{2}-2\beta _{3})q^{7}+\cdots\)
2160.3.bs.b	$2160$	$3$	2160.bs	9.d	$6$	$12$	$6$	$58.856$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					180.3.o.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$3^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{4}q^{5}+(1+\beta _{2}+\beta _{3}-2\beta _{4}-\beta _{9}+\cdots)q^{7}+\cdots\)
2160.3.bs.c	$2160$	$3$	2160.bs	9.d	$6$	$16$	$8$	$58.856$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					45.3.i.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$3^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{9}q^{5}+(-\beta _{1}+\beta _{10})q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
2160.3.bs.d	$2160$	$3$	2160.bs	9.d	$6$	$16$	$8$	$58.856$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					90.3.h.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{4}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{8}q^{5}+(\beta _{1}-\beta _{4}+\beta _{5}+\beta _{7}-\beta _{13}+\cdots)q^{7}+\cdots\)
2160.3.bs.e	$2160$	$3$	2160.bs	9.d	$6$	$48$	$24$	$58.856$		None			✓		360.3.bc.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(2160, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2160, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 20}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)