Space of modular forms of level 168, weight 2, and Character 168.ba

• Label: 168.2.ba
• Level: $168$
• Weight: $2$
• Character orbit: 168.ba
• Rep. character: $\chi_{168}(5,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $56$
• Newform subspaces: $3$
• Sturm bound: $64$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.ba (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 168 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(64\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(168, [\chi])\).

	Total	New	Old
Modular forms	72	72	0
Cusp forms	56	56	0
Eisenstein series	16	16	0

Trace form

\( 56 q - 2 q^{4} - 8 q^{7} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(168, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
168.2.ba.a	$168$	$2$	168.ba	168.aa	$6$	$4$	$2$	$1.341$	\(\Q(\sqrt{2}, \sqrt{-3})\)	\(\Q(\sqrt{-6}) \)		✓			168.2.ba.a	$4$	$0$	\(0\)	\(-6\)	\(6\)	\(-2\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
168.2.ba.b	$168$	$2$	168.ba	168.aa	$6$	$4$	$2$	$1.341$	\(\Q(\sqrt{2}, \sqrt{-3})\)	\(\Q(\sqrt{-6}) \)		✓			168.2.ba.a	$4$	$0$	\(0\)	\(6\)	\(-6\)	\(-2\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{3}+2\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
168.2.ba.c	$168$	$2$	168.ba	168.aa	$6$	$48$	$24$	$1.341$		None		✓	✓		168.2.ba.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{6}]$