Space of modular forms of level 192, weight 2, and Character 192.c

• Label: 192.2.c
• Level: $192$
• Weight: $2$
• Character orbit: 192.c
• Rep. character: $\chi_{192}(191,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $64$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(64\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(192, [\chi])\).

	Total	New	Old
Modular forms	44	10	34
Cusp forms	20	6	14
Eisenstein series	24	4	20

Trace form

\( 6 q - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(192, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
192.2.c.a	$192$	$2$	192.c	12.b	$2$	$2$	$2$	$1.533$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)					48.2.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{3}-2\beta q^{7}-3 q^{9}+2 q^{13}+\cdots\)
192.2.c.b	$192$	$2$	192.c	12.b	$2$	$4$	$4$	$1.533$	\(\Q(\zeta_{8})\)	None			✓		96.2.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_1 q^{3}-\beta_{3} q^{5}+(-\beta_{2}+\beta_1)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

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