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

• Label: 666.2.bs
• Level: $666$
• Weight: $2$
• Character orbit: 666.bs
• Rep. character: $\chi_{666}(17,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $168$
• Newform subspaces: $2$
• Sturm bound: $228$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.bs (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 111 \)
Character field:			\(\Q(\zeta_{36})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(228\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	1464	168	1296
Cusp forms	1272	168	1104
Eisenstein series	192	0	192

Trace form

\( 168 q + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
666.2.bs.a	$666$	$2$	666.bs	111.q	$36$	$72$	$6$	$5.318$		None		✓			666.2.bs.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{36}]$
666.2.bs.b	$666$	$2$	666.bs	111.q	$36$	$96$	$8$	$5.318$		None		✓	✓		666.2.bs.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{36}]$

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

\( S_{2}^{\mathrm{old}}(666, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 2}\)