Space of modular forms of level 192, weight 3, and Character 192.i

• Label: 192.3.i
• Level: $192$
• Weight: $3$
• Character orbit: 192.i
• Rep. character: $\chi_{192}(17,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $28$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	192.i (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 48 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(192, [\chi])\).

	Total	New	Old
Modular forms	144	36	108
Cusp forms	112	28	84
Eisenstein series	32	8	24

Trace form

\( 28 q + 2 q^{3} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(192, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
192.3.i.a	$192$	$3$	192.i	48.i	$4$	$8$	$4$	$5.232$	8.0.629407744.1	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{6}-\beta _{7})q^{3}+\cdots\)
192.3.i.b	$192$	$3$	192.i	48.i	$4$	$20$	$10$	$5.232$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$2^{23}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{4}q^{3}+(\beta _{8}-\beta _{9}-\beta _{10})q^{5}-\beta _{6}q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(192, [\chi])\) into lower level spaces

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