Space of modular forms of level 3168, weight 2, and Character 3168.d

• Label: 3168.2.d
• Level: $3168$
• Weight: $2$
• Character orbit: 3168.d
• Rep. character: $\chi_{3168}(287,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $4$
• Sturm bound: $1152$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 3168 = 2^{5} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3168.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(1152\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3168, [\chi])\).

	Total	New	Old
Modular forms	608	40	568
Cusp forms	544	40	504
Eisenstein series	64	0	64

Trace form

\( 40 q - 32 q^{13} - 40 q^{25} + 48 q^{37} - 8 q^{49} + 16 q^{61} - 32 q^{73} - 16 q^{85} - 32 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3168, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3168.2.d.a	$3168$	$2$	3168.d	12.b	$2$	$8$	$8$	$25.297$	8.0.110166016.2	None		✓			3168.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{3})q^{5}+(-\beta _{1}+\beta _{3})q^{7}-q^{11}+\cdots\)
3168.2.d.b	$3168$	$2$	3168.d	12.b	$2$	$8$	$8$	$25.297$	8.0.110166016.2	None		✓			3168.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{3})q^{5}+(\beta _{1}-\beta _{3})q^{7}+q^{11}+\cdots\)
3168.2.d.c	$3168$	$2$	3168.d	12.b	$2$	$12$	$12$	$25.297$	12.0.\(\cdots\).1	None		✓			3168.2.d.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{5}-\beta _{10}q^{7}-q^{11}-\beta _{8}q^{13}+\cdots\)
3168.2.d.d	$3168$	$2$	3168.d	12.b	$2$	$12$	$12$	$25.297$	12.0.\(\cdots\).1	None		✓			3168.2.d.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{5}-\beta _{10}q^{7}+q^{11}-\beta _{8}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3168, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3168, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(396, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(528, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1056, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1584, [\chi])\)\(^{\oplus 2}\)