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

• Label: 168.2.j
• Level: $168$
• Weight: $2$
• Character orbit: 168.j
• Rep. character: $\chi_{168}(155,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $4$
• Sturm bound: $64$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.j (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(64\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	36	24	12
Cusp forms	28	24	4
Eisenstein series	8	0	8

Trace form

24 * q + 4 * q^4 - 6 * q^6 - 12 * q^10 - 6 * q^12 - 12 * q^16 + 8 * q^18 - 16 * q^19 + 30 * q^24 + 24 * q^25 - 24 * q^27 - 8 * q^28 - 12 * q^30 - 8 * q^33 - 24 * q^34 + 12 * q^36 - 20 * q^40 - 10 * q^42 + 32 * q^43 - 24 * q^46 + 6 * q^48 - 24 * q^49 + 44 * q^52 - 10 * q^54 - 8 * q^57 - 24 * q^58 + 20 * q^60 + 52 * q^64 + 40 * q^66 - 32 * q^67 - 12 * q^70 - 56 * q^75 - 28 * q^76 + 44 * q^78 + 8 * q^81 + 24 * q^82 + 14 * q^84 - 32 * q^90 + 48 * q^94 + 2 * q^96 + 64 * 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.j.a	$168$	$2$	168.j	24.f	$2$	$4$	$4$	$1.341$	\(\Q(i, \sqrt{5})\)	None		✓			168.2.j.a	$2$	$0$	\(-4\)	\(-2\)	\(4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{2})q^{2}+(\beta _{1}+\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
168.2.j.b	$168$	$2$	168.j	24.f	$2$	$4$	$4$	$1.341$	\(\Q(\zeta_{8})\)	None		✓			168.2.j.b	$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{3} q^{2}+(-\beta_{2}+1)q^{3}+2 q^{4}+\cdots\)
168.2.j.c	$168$	$2$	168.j	24.f	$2$	$4$	$4$	$1.341$	\(\Q(i, \sqrt{5})\)	None		✓			168.2.j.a	$2$	$0$	\(4\)	\(-2\)	\(-4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{2})q^{2}+(-\beta _{2}-\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots\)
168.2.j.d	$168$	$2$	168.j	24.f	$2$	$12$	$12$	$1.341$	12.0.\(\cdots\).2	None		✓	✓		168.2.j.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}-\beta _{6}q^{3}+(-\beta _{2}-\beta _{3})q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(168, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)