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

• Label: 168.2.p
• Level: $168$
• Weight: $2$
• Character orbit: 168.p
• Rep. character: $\chi_{168}(139,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• 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.p (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
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	36	16	20
Cusp forms	28	16	12
Eisenstein series	8	0	8

Trace form

16 * q + 2 * q^2 + 2 * q^4 - 10 * q^8 - 16 * q^9 - 8 * q^11 - 14 * q^14 + 18 * q^16 - 2 * q^18 + 8 * q^22 + 16 * q^25 - 10 * q^28 - 16 * q^30 - 18 * q^32 + 24 * q^35 - 2 * q^36 - 4 * q^42 - 8 * q^43 + 52 * q^46 - 8 * q^49 - 34 * q^50 + 50 * q^56 - 16 * q^57 + 24 * q^58 + 32 * q^60 + 2 * q^64 - 40 * q^67 - 24 * q^70 + 10 * q^72 - 32 * q^74 - 24 * q^78 + 16 * q^81 + 8 * q^84 - 32 * q^86 - 88 * q^88 - 56 * q^91 + 44 * q^92 + 66 * q^98 + 8 * q^99

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.p.a	$168$	$2$	168.p	56.e	$2$	$16$	$16$	$1.341$	16.0.\(\cdots\).1	None		✓	✓	✓	168.2.p.a	$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}-\beta _{3}q^{3}+\beta _{1}q^{4}+(\beta _{6}-\beta _{11}+\cdots)q^{5}+\cdots\)

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

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