Space of modular forms of level 192, weight 3, and Character 192.b

• Label: 192.3.b
• Level: $192$
• Weight: $3$
• Character orbit: 192.b
• Rep. character: $\chi_{192}(31,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	192.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(192, [\chi])\).

	Total	New	Old
Modular forms	76	8	68
Cusp forms	52	8	44
Eisenstein series	24	0	24

Trace form

\( 8 q + 24 q^{9} + 48 q^{17} + 104 q^{25} - 240 q^{41} - 24 q^{49} + 96 q^{57} - 384 q^{65} - 304 q^{73} + 72 q^{81} + 240 q^{89} + 112 q^{97}+O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(192, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
192.3.b.a	$192$	$3$	192.b	8.d	$2$	$4$	$4$	$5.232$	\(\Q(\zeta_{12})\)	None		✓			192.3.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_1 q^{3}-\beta_{2} q^{5}+\beta_{3} q^{7}+3 q^{9}+\cdots\)
192.3.b.b	$192$	$3$	192.b	8.d	$2$	$4$	$4$	$5.232$	\(\Q(\zeta_{12})\)	None		✓			192.3.b.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_1 q^{3}-\beta_{2} q^{5}+5\beta_{3} q^{7}+3 q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(192, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)