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

• Label: 3168.2.m
• Level: $3168$
• Weight: $2$
• Character orbit: 3168.m
• Rep. character: $\chi_{3168}(593,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $3$
• Sturm bound: $1152$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 3168 = 2^{5} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3168.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 264 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(1152\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	608	48	560
Cusp forms	544	48	496
Eisenstein series	64	0	64

Trace form

\( 48 q + 48 q^{25} - 48 q^{49} + 32 q^{55} - 32 q^{97}+O(q^{100}) \)

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.m.a	$3168$	$2$	3168.m	264.m	$2$	$4$	$4$	$25.297$	\(\Q(\sqrt{-2}, \sqrt{-11})\)	\(\Q(\sqrt{-22}) \)					792.2.m.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{3}q^{11}+(-2-\beta _{1})q^{13}+(-4+\beta _{1}+\cdots)q^{19}+\cdots\)
3168.2.m.b	$3168$	$2$	3168.m	264.m	$2$	$4$	$4$	$25.297$	\(\Q(\sqrt{-2}, \sqrt{-11})\)	\(\Q(\sqrt{-22}) \)					792.2.m.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{3}q^{11}+(2+\beta _{1})q^{13}+(4-\beta _{1})q^{19}+\cdots\)
3168.2.m.c	$3168$	$2$	3168.m	264.m	$2$	$40$	$40$	$25.297$		None			✓		792.2.m.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(3168, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(792, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1056, [\chi])\)\(^{\oplus 2}\)