Space of modular forms of level 144, weight 4, and Character 144.x

• Label: 144.4.x
• Level: $144$
• Weight: $4$
• Character orbit: 144.x
• Rep. character: $\chi_{144}(13,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $280$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	144.x (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 144 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(96\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(144, [\chi])\).

	Total	New	Old
Modular forms	296	296	0
Cusp forms	280	280	0
Eisenstein series	16	16	0

Trace form

\( 280 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 2 q^{5} + 26 q^{6} - 8 q^{8} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(144, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
144.4.x.a	$144$	$4$	144.x	144.x	$12$	$280$	$70$	$8.496$		None		$4$	$0$	\(-2\)	\(-4\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$