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

• Label: 168.2.q
• Level: $168$
• Weight: $2$
• Character orbit: 168.q
• Rep. character: $\chi_{168}(25,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $8$
• 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.q (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
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	80	8	72
Cusp forms	48	8	40
Eisenstein series	32	0	32

Trace form

8 * q + 2 * q^3 - 4 * q^9 + 4 * q^11 + 12 * q^13 - 4 * q^15 + 4 * q^17 + 14 * q^19 - 4 * q^21 - 12 * q^23 - 14 * q^25 - 4 * q^27 - 8 * q^29 - 10 * q^33 - 36 * q^35 - 2 * q^37 - 2 * q^39 + 24 * q^41 - 4 * q^43 - 12 * q^49 - 4 * q^51 - 28 * q^53 + 28 * q^55 + 12 * q^57 - 20 * q^61 + 6 * q^63 - 16 * q^65 + 2 * q^67 + 8 * q^69 + 16 * q^71 + 10 * q^73 + 22 * q^75 + 36 * q^77 - 20 * q^79 - 4 * q^81 + 40 * q^83 + 24 * q^85 + 2 * q^87 + 32 * q^89 - 26 * q^91 + 10 * q^93 + 32 * q^95 - 12 * q^97 - 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.q.a	$168$	$2$	168.q	7.c	$3$	$2$	$1$	$1.341$	\(\Q(\sqrt{-3}) \)	None		✓			168.2.q.a	$2$	$0$	\(0\)	\(-1\)	\(1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{3}+(1-\zeta_{6})q^{5}+(2-3\zeta_{6})q^{7}+\cdots\)
168.2.q.b	$168$	$2$	168.q	7.c	$3$	$2$	$1$	$1.341$	\(\Q(\sqrt{-3}) \)	None		✓			168.2.q.b	$2$	$0$	\(0\)	\(1\)	\(-2\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{5}+(3-\zeta_{6})q^{7}+\cdots\)
168.2.q.c	$168$	$2$	168.q	7.c	$3$	$4$	$2$	$1.341$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None		✓	✓		168.2.q.c	$2$	$0$	\(0\)	\(2\)	\(1\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{2})q^{3}+(-1+2\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(168, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)