Space of modular forms of level 168, weight 4, and Character 168.bc

• Label: 168.4.bc
• Level: $168$
• Weight: $4$
• Character orbit: 168.bc
• Rep. character: $\chi_{168}(37,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $1$
• Sturm bound: $128$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	168.bc (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(128\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(168, [\chi])\).

	Total	New	Old
Modular forms	200	96	104
Cusp forms	184	96	88
Eisenstein series	16	0	16

Trace form

\( 96 q - 2 q^{2} - 10 q^{4} + 16 q^{8} + 432 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(168, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
168.4.bc.a	$168$	$4$	168.bc	56.p	$6$	$96$	$48$	$9.912$		None		$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(168, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(168, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)