Space of modular forms of level 192, weight 8, and Character 192.f

• Label: 192.8.f
• Level: $192$
• Weight: $8$
• Character orbit: 192.f
• Rep. character: $\chi_{192}(95,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $4$
• Sturm bound: $256$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	192.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(256\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(192, [\chi])\).

	Total	New	Old
Modular forms	236	56	180
Cusp forms	212	56	156
Eisenstein series	24	0	24

Trace form

\( 56 q + 875000 q^{25} + 297048 q^{33} - 5566248 q^{49} + 2059032 q^{57} - 2534128 q^{73} - 38530440 q^{81} - 48537152 q^{97}+O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(192, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
192.8.f.a	$192$	$8$	192.f	24.f	$2$	$4$	$4$	$59.978$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-6}) \)		✓			192.8.f.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+27\beta_{2} q^{3}+13\beta_{3} q^{5}+377\beta_1 q^{7}+\cdots\)
192.8.f.b	$192$	$8$	192.f	24.f	$2$	$4$	$4$	$59.978$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)		✓			192.8.f.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{U}(1)[D_{2}]$	\(q-27\beta_1 q^{3}-127\beta_{3} q^{7}+2187 q^{9}+\cdots\)
192.8.f.c	$192$	$8$	192.f	24.f	$2$	$16$	$16$	$59.978$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			192.8.f.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{60}\cdot 3^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}-\beta _{8}q^{5}+(6^{2}\beta _{4}+\beta _{11})q^{7}+\cdots\)
192.8.f.d	$192$	$8$	192.f	24.f	$2$	$32$	$32$	$59.978$		None		✓	✓		192.8.f.d	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{8}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

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