Space of modular forms of level 192, weight 5, and Character 192.g

• Label: 192.5.g
• Level: $192$
• Weight: $5$
• Character orbit: 192.g
• Rep. character: $\chi_{192}(127,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $5$
• Sturm bound: $160$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	192.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(160\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(192, [\chi])\).

	Total	New	Old
Modular forms	140	16	124
Cusp forms	116	16	100
Eisenstein series	24	0	24

Trace form

\( 16 q - 432 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(192, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
192.5.g.a	$192$	$5$	192.g	4.b	$2$	$2$	$2$	$19.847$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{3}-6q^{5}+12\zeta_{6}q^{7}-3^{3}q^{9}+\cdots\)
192.5.g.b	$192$	$5$	192.g	4.b	$2$	$2$	$2$	$19.847$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(84\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\zeta_{6}q^{3}+42q^{5}-44\zeta_{6}q^{7}-3^{3}q^{9}+\cdots\)
192.5.g.c	$192$	$5$	192.g	4.b	$2$	$4$	$4$	$19.847$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(-88\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}^{2}q^{3}+(-22-\zeta_{12}^{3})q^{5}+(-\zeta_{12}+\cdots)q^{7}+\cdots\)
192.5.g.d	$192$	$5$	192.g	4.b	$2$	$4$	$4$	$19.847$	\(\Q(\sqrt{-3}, \sqrt{13})\)	None		$2$	$0$	\(0\)	\(0\)	\(-24\)	\(0\)	$2^{10}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-6-\beta _{2})q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots\)
192.5.g.e	$192$	$5$	192.g	4.b	$2$	$4$	$4$	$19.847$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(40\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\zeta_{12}^{2}q^{3}+(10-\zeta_{12}^{3})q^{5}+(-11\zeta_{12}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

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