Space of modular forms of level 192, weight 12, and Character 192.c

• Label: 192.12.c
• Level: $192$
• Weight: $12$
• Character orbit: 192.c
• Rep. character: $\chi_{192}(191,\cdot)$
• Character field: $\Q$
• Dimension: $86$
• Newform subspaces: $5$
• Sturm bound: $384$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	192.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(384\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(192, [\chi])\).

	Total	New	Old
Modular forms	364	90	274
Cusp forms	340	86	254
Eisenstein series	24	4	20

Trace form

\( 86 q - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(192, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
192.12.c.a	$192$	$12$	192.c	12.b	$2$	$2$	$2$	$147.522$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)					48.12.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+3^{5}\zeta_{6}q^{3}-51346\zeta_{6}q^{7}-3^{11}q^{9}+\cdots\)
192.12.c.b	$192$	$12$	192.c	12.b	$2$	$8$	$8$	$147.522$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None					48.12.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{30}\cdot 3^{19}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(6\beta _{1}-\beta _{3})q^{7}+(-9171+\cdots)q^{9}+\cdots\)
192.12.c.c	$192$	$12$	192.c	12.b	$2$	$12$	$12$	$147.522$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					48.12.c.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{68}\cdot 3^{20}\cdot 13^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+\beta _{4}q^{5}+(-52\beta _{1}+7^{2}\beta _{2}+\cdots)q^{7}+\cdots\)
192.12.c.d	$192$	$12$	192.c	12.b	$2$	$20$	$20$	$147.522$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None					12.12.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{194}\cdot 3^{42}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{3}q^{5}+(-3\beta _{1}+\beta _{2})q^{7}+\cdots\)
192.12.c.e	$192$	$12$	192.c	12.b	$2$	$44$	$44$	$147.522$		None			✓		96.12.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{12}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(192, [\chi]) \simeq \) \(S_{12}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)