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

• Label: 168.2.c
• Level: $168$
• Weight: $2$
• Character orbit: 168.c
• Rep. character: $\chi_{168}(85,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $64$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(64\)
Trace bound:			\(1\)
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	12	24
Cusp forms	28	12	16
Eisenstein series	8	0	8

Trace form

12 * q + 2 * q^2 + 2 * q^4 + 4 * q^6 + 4 * q^7 + 2 * q^8 - 12 * q^9 + 4 * q^10 - 8 * q^12 - 2 * q^14 - 8 * q^15 + 2 * q^16 + 8 * q^17 - 2 * q^18 + 20 * q^20 + 12 * q^22 - 8 * q^23 - 4 * q^24 - 20 * q^25 - 20 * q^26 + 2 * q^28 - 8 * q^30 + 16 * q^31 - 38 * q^32 - 20 * q^34 - 2 * q^36 - 8 * q^38 + 16 * q^39 + 20 * q^40 - 8 * q^41 + 4 * q^44 + 16 * q^48 + 12 * q^49 - 6 * q^50 - 4 * q^52 - 4 * q^54 - 32 * q^55 - 14 * q^56 + 56 * q^58 - 8 * q^60 + 16 * q^62 - 4 * q^63 + 26 * q^64 - 32 * q^65 + 24 * q^66 - 52 * q^68 - 12 * q^70 + 8 * q^71 - 2 * q^72 + 40 * q^73 + 24 * q^74 - 8 * q^76 + 8 * q^78 - 48 * q^79 + 20 * q^80 + 12 * q^81 - 28 * q^82 + 20 * q^86 - 20 * q^88 + 40 * q^89 - 4 * q^90 + 32 * q^92 - 72 * q^94 + 80 * q^95 + 4 * q^96 + 8 * q^97 + 2 * q^98

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.c.a	$168$	$2$	168.c	8.b	$2$	$4$	$4$	$1.341$	\(\Q(\zeta_{12})\)	None		✓			168.2.c.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta_{2}+\beta_1)q^{2}+\beta_{2} q^{3}+(\beta_{3}+\beta_1)q^{4}+\cdots\)
168.2.c.b	$168$	$2$	168.c	8.b	$2$	$8$	$8$	$1.341$	8.0.386672896.3	None		✓	✓		168.2.c.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}-\beta _{2}q^{3}+\beta _{1}q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(168, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)