Space of modular forms of level 192, weight 4, and Character 192.d

• Label: 192.4.d
• Level: $192$
• Weight: $4$
• Character orbit: 192.d
• Rep. character: $\chi_{192}(97,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $3$
• Sturm bound: $128$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	192.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(128\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(192, [\chi])\).

	Total	New	Old
Modular forms	108	12	96
Cusp forms	84	12	72
Eisenstein series	24	0	24

Trace form

\( 12 q - 108 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(192, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
192.4.d.a	$192$	$4$	192.d	8.b	$2$	$4$	$4$	$11.328$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\zeta_{12}q^{3}-3\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}+\cdots\)
192.4.d.b	$192$	$4$	192.d	8.b	$2$	$4$	$4$	$11.328$	\(\Q(i, \sqrt{11})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\beta _{1}q^{3}-\beta _{3}q^{5}+\beta _{2}q^{7}-9q^{9}+\cdots\)
192.4.d.c	$192$	$4$	192.d	8.b	$2$	$4$	$4$	$11.328$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}-7\zeta_{12}^{3}q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(192, [\chi]) \cong \)