Space of modular forms of level 576, weight 2, and Character 576.f

• Label: 576.2.f
• Level: $576$
• Weight: $2$
• Character orbit: 576.f
• Rep. character: $\chi_{576}(287,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $192$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(192\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(576, [\chi])\).

	Total	New	Old
Modular forms	120	8	112
Cusp forms	72	8	64
Eisenstein series	48	0	48

Trace form

\( 8 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(576, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
576.2.f.a	$576$	$2$	576.f	24.f	$2$	$8$	$8$	$4.599$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{24}^{2}q^{5}-\zeta_{24}q^{7}-\zeta_{24}^{6}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(576, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(576, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)