Space of modular forms of level 192, weight 7, and Character 192.g

• Label: 192.7.g
• Level: $192$
• Weight: $7$
• Character orbit: 192.g
• Rep. character: $\chi_{192}(127,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $6$
• Sturm bound: $224$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
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:			\(224\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(192, [\chi])\).

	Total	New	Old
Modular forms	204	24	180
Cusp forms	180	24	156
Eisenstein series	24	0	24

Trace form

\( 24 q - 5832 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(192, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
192.7.g.a	$192$	$7$	192.g	4.b	$2$	$2$	$2$	$44.170$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-300\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-9\zeta_{6}q^{3}-150q^{5}-188\zeta_{6}q^{7}-3^{5}q^{9}+\cdots\)
192.7.g.b	$192$	$7$	192.g	4.b	$2$	$2$	$2$	$44.170$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-9\zeta_{6}q^{3}-6q^{5}+116\zeta_{6}q^{7}-3^{5}q^{9}+\cdots\)
192.7.g.c	$192$	$7$	192.g	4.b	$2$	$2$	$2$	$44.170$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(180\)	\(0\)	$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{3}+90q^{5}-12\zeta_{6}q^{7}-3^{5}q^{9}+\cdots\)
192.7.g.d	$192$	$7$	192.g	4.b	$2$	$4$	$4$	$44.170$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(200\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3\zeta_{12}^{2}q^{3}+(50-5\zeta_{12}^{3})q^{5}+(-73\zeta_{12}+\cdots)q^{7}+\cdots\)
192.7.g.e	$192$	$7$	192.g	4.b	$2$	$6$	$6$	$44.170$	6.0.50898483.1	None		$2$	$0$	\(0\)	\(0\)	\(44\)	\(0\)	$2^{27}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(7+\beta _{2})q^{5}+(-7\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
192.7.g.f	$192$	$7$	192.g	4.b	$2$	$8$	$8$	$44.170$	8.0.\(\cdots\).5	None		$2$	$0$	\(0\)	\(0\)	\(-112\)	\(0\)	$2^{38}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(-14+\beta _{2})q^{5}+(-7\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(192, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)