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

• Label: 168.2.k
• Level: $168$
• Weight: $2$
• Character orbit: 168.k
• Rep. character: $\chi_{168}(41,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $64$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(64\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	40	8	32
Cusp forms	24	8	16
Eisenstein series	16	0	16

Trace form

\( 8 q - 4 q^{7} + 4 q^{9} + 4 q^{15} - 8 q^{21} - 16 q^{37} + 4 q^{39} - 32 q^{43} + 16 q^{49} - 24 q^{51} - 28 q^{57} + 32 q^{63} + 16 q^{67} + 56 q^{79} + 32 q^{85} - 24 q^{91} + 56 q^{93} + 64 q^{99}+O(q^{100}) \)

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.k.a	$168$	$2$	168.k	21.c	$2$	$8$	$8$	$1.341$	8.0.342102016.5	None		✓	✓	✓	168.2.k.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-1-\beta _{5}-\beta _{6}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(168, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(168, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)