Space of modular forms of level 192, weight 9, and Character 192.g

• Label: 192.9.g
• Level: $192$
• Weight: $9$
• Character orbit: 192.g
• Rep. character: $\chi_{192}(127,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $6$
• Sturm bound: $288$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	192.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(288\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(192, [\chi])\).

	Total	New	Old
Modular forms	268	32	236
Cusp forms	244	32	212
Eisenstein series	24	0	24

Trace form

32 * q - 69984 * q^9 + 51392 * q^13 + 154560 * q^17 + 243648 * q^21 + 3208288 * q^25 - 2132352 * q^29 - 431552 * q^37 + 4374720 * q^41 - 26353376 * q^49 + 5358720 * q^53 - 40770240 * q^61 - 45233664 * q^65 + 8636544 * q^69 + 7613760 * q^73 + 248209152 * q^77 + 153055008 * q^81 - 28343552 * q^85 + 60889920 * q^89 - 34696512 * q^93 + 140979520 * q^97

Decomposition of \(S_{9}^{\mathrm{new}}(192, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
192.9.g.a	$192$	$9$	192.g	4.b	$2$	$2$	$2$	$78.217$	\(\Q(\sqrt{-3}) \)	None					48.9.g.b	$2$	$0$	\(0\)	\(0\)	\(-1452\)	\(0\)	$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3\beta q^{3}-726 q^{5}-196\beta q^{7}-2187 q^{9}+\cdots\)
192.9.g.b	$192$	$9$	192.g	4.b	$2$	$2$	$2$	$78.217$	\(\Q(\sqrt{-3}) \)	None					48.9.g.a	$2$	$0$	\(0\)	\(0\)	\(180\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+27\beta q^{3}+90 q^{5}-532\beta q^{7}-2187 q^{9}+\cdots\)
192.9.g.c	$192$	$9$	192.g	4.b	$2$	$4$	$4$	$78.217$	\(\Q(\sqrt{-3}, \sqrt{1801})\)	None					48.9.g.c	$2$	$0$	\(0\)	\(0\)	\(264\)	\(0\)	$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3^{3}\beta _{1}q^{3}+(66+\beta _{2})q^{5}+(-772\beta _{1}+\cdots)q^{7}+\cdots\)
192.9.g.d	$192$	$9$	192.g	4.b	$2$	$8$	$8$	$78.217$	8.0.3468738816.6	None					96.9.g.b	$2$	$0$	\(0\)	\(0\)	\(-560\)	\(0\)	$2^{40}\cdot 3^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(-70-\beta _{4})q^{5}+(7\beta _{1}+7\beta _{3}+\cdots)q^{7}+\cdots\)
192.9.g.e	$192$	$9$	192.g	4.b	$2$	$8$	$8$	$78.217$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None					12.9.d.a	$2$	$0$	\(0\)	\(0\)	\(336\)	\(0\)	$2^{52}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(42+\beta _{2})q^{5}+(-7\beta _{1}-\beta _{6}+\cdots)q^{7}+\cdots\)
192.9.g.f	$192$	$9$	192.g	4.b	$2$	$8$	$8$	$78.217$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None					96.9.g.a	$2$	$0$	\(0\)	\(0\)	\(1232\)	\(0\)	$2^{40}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(154-\beta _{6})q^{5}+(-17\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(192, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)