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

• Label: 2160.2.by
• Level: $2160$
• Weight: $2$
• Character orbit: 2160.by
• Rep. character: $\chi_{2160}(289,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $68$
• Newform subspaces: $6$
• 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.by (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
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	76	860
Cusp forms	792	68	724
Eisenstein series	144	8	136

Trace form

\( 68 q + q^{5} + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2160.2.by.a	$2160$	$2$	2160.by	45.j	$6$	$4$	$2$	$17.248$	\(\Q(\zeta_{12})\)	None					360.2.bi.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2\zeta_{12}-\zeta_{12}^{2}-2\zeta_{12}^{3})q^{5}+\zeta_{12}q^{7}+\cdots\)
2160.2.by.b	$2160$	$2$	2160.by	45.j	$6$	$4$	$2$	$17.248$	\(\Q(\zeta_{12})\)	None					90.2.i.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2\zeta_{12}-\zeta_{12}^{2}+2\zeta_{12}^{3})q^{5}+\zeta_{12}q^{7}+\cdots\)
2160.2.by.c	$2160$	$2$	2160.by	45.j	$6$	$8$	$4$	$17.248$	\(\Q(\zeta_{24})\)	None					45.2.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{24}-\zeta_{24}^{3}+\zeta_{24}^{4}+\zeta_{24}^{6}+\cdots)q^{5}+\cdots\)
2160.2.by.d	$2160$	$2$	2160.by	45.j	$6$	$8$	$4$	$17.248$	\(\Q(\zeta_{24})\)	None					90.2.i.b	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{24}-\zeta_{24}^{2}-\zeta_{24}^{6})q^{5}+(-2\zeta_{24}+\cdots)q^{7}+\cdots\)
2160.2.by.e	$2160$	$2$	2160.by	45.j	$6$	$12$	$6$	$17.248$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					180.2.r.a	$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{9}q^{5}+(-\beta _{4}+\beta _{5}-\beta _{6}-\beta _{7}+\beta _{9}+\cdots)q^{7}+\cdots\)
2160.2.by.f	$2160$	$2$	2160.by	45.j	$6$	$32$	$16$	$17.248$		None			✓		360.2.bi.b	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(2160, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)