Space of modular forms of level 666, weight 2, and Character 666.bj

• Label: 666.2.bj
• Level: $666$
• Weight: $2$
• Character orbit: 666.bj
• Rep. character: $\chi_{666}(289,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $96$
• Newform subspaces: $6$
• Sturm bound: $228$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.bj (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(228\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(666, [\chi])\).

	Total	New	Old
Modular forms	732	96	636
Cusp forms	636	96	540
Eisenstein series	96	0	96

Trace form

\( 96 q - 12 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(666, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
666.2.bj.a	$666$	$2$	666.bj	37.h	$18$	$12$	$2$	$5.318$	\(\Q(\zeta_{36})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{18}]$	\(q+\zeta_{36}q^{2}+\zeta_{36}^{2}q^{4}+(-\zeta_{36}^{2}-\zeta_{36}^{3}+\cdots)q^{5}+\cdots\)
666.2.bj.b	$666$	$2$	666.bj	37.h	$18$	$12$	$2$	$5.318$	\(\Q(\zeta_{36})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{18}]$	\(q+\zeta_{36}q^{2}+\zeta_{36}^{2}q^{4}+(\zeta_{36}^{2}-\zeta_{36}^{3}+\cdots)q^{5}+\cdots\)
666.2.bj.c	$666$	$2$	666.bj	37.h	$18$	$12$	$2$	$5.318$	\(\Q(\zeta_{36})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{18}]$	\(q+\zeta_{36}q^{2}+\zeta_{36}^{2}q^{4}+(-\zeta_{36}+\zeta_{36}^{2}+\cdots)q^{5}+\cdots\)
666.2.bj.d	$666$	$2$	666.bj	37.h	$18$	$12$	$2$	$5.318$	\(\Q(\zeta_{36})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(24\)	$1$	$\mathrm{SU}(2)[C_{18}]$	\(q+\zeta_{36}q^{2}+\zeta_{36}^{2}q^{4}+(\zeta_{36}+\zeta_{36}^{3}+\cdots)q^{5}+\cdots\)
666.2.bj.e	$666$	$2$	666.bj	37.h	$18$	$24$	$4$	$5.318$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)		$\mathrm{SU}(2)[C_{18}]$
666.2.bj.f	$666$	$2$	666.bj	37.h	$18$	$24$	$4$	$5.318$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)		$\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(666, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(666, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 2}\)