Space of modular forms of level 576, weight 4, and Character 576.l

• Label: 576.4.l
• Level: $576$
• Weight: $4$
• Character orbit: 576.l
• Rep. character: $\chi_{576}(143,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $384$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	576.l (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 48 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(384\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(576, [\chi])\).

	Total	New	Old
Modular forms	608	48	560
Cusp forms	544	48	496
Eisenstein series	64	0	64

Trace form

\( 48 q + 48 q^{19} - 864 q^{43} + 2352 q^{49} + 576 q^{55} + 1824 q^{61} - 816 q^{67} - 480 q^{85} + 3600 q^{91}+O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(576, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
576.4.l.a	$576$	$4$	576.l	48.k	$4$	$48$	$24$	$33.985$		None			✓	✓	144.4.l.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{4}^{\mathrm{old}}(576, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(576, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)