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

• Label: 192.3.h
• Level: $192$
• Weight: $3$
• Character orbit: 192.h
• Rep. character: $\chi_{192}(161,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $3$
• Sturm bound: $96$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	192.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(96\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	76	16	60
Cusp forms	52	16	36
Eisenstein series	24	0	24

Trace form

\( 16 q + 80 q^{25} - 48 q^{33} + 80 q^{49} - 240 q^{57} - 160 q^{73} - 240 q^{81} - 128 q^{97}+O(q^{100}) \)

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.h.a	$192$	$3$	192.h	24.h	$2$	$4$	$4$	$5.232$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)		✓			192.3.h.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{U}(1)[D_{2}]$	\(q+3\beta_1 q^{3}-\beta_{3} q^{7}-9 q^{9}-\beta_{2} q^{13}+\cdots\)
192.3.h.b	$192$	$3$	192.h	24.h	$2$	$4$	$4$	$5.232$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-2}) \)		✓			192.3.h.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta_{2} q^{3}+(-\beta_{3}+7)q^{9}+(-6\beta_{2}-3\beta_1)q^{11}+\cdots\)
192.3.h.c	$192$	$3$	192.h	24.h	$2$	$8$	$8$	$5.232$	8.0.12960000.1	None		✓	✓		192.3.h.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}-\beta _{4}q^{5}-\beta _{1}q^{7}+(1-\beta _{5}+\cdots)q^{9}+\cdots\)

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

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