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

• Label: 666.2.bb
• Level: $666$
• Weight: $2$
• Character orbit: 666.bb
• Rep. character: $\chi_{666}(191,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $152$
• Newform subspaces: $1$
• Sturm bound: $228$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.bb (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 333 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(228\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	472	152	320
Cusp forms	440	152	288
Eisenstein series	32	0	32

Trace form

152 * q + 12 * q^5 + 8 * q^9 - 8 * q^12 - 4 * q^13 - 12 * q^15 + 76 * q^16 - 8 * q^19 + 12 * q^20 + 36 * q^23 - 36 * q^29 - 16 * q^31 + 16 * q^37 + 8 * q^39 - 56 * q^42 + 4 * q^43 - 48 * q^47 - 68 * q^49 - 48 * q^50 + 20 * q^51 + 4 * q^52 - 36 * q^54 - 24 * q^55 + 28 * q^57 - 12 * q^59 - 28 * q^61 - 72 * q^63 + 32 * q^66 - 56 * q^69 + 36 * q^74 + 52 * q^75 - 4 * q^76 + 4 * q^79 - 104 * q^81 - 48 * q^82 + 228 * q^83 - 80 * q^87 + 48 * q^91 + 36 * q^92 - 72 * q^93 + 32 * q^97

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.bb.a	$666$	$2$	666.bb	333.ac	$12$	$152$	$38$	$5.318$		None		✓	✓	✓	666.2.bb.a	$4$	$0$	\(0\)	\(0\)	\(12\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

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

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