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

• Label: 576.2.be
• Level: $576$
• Weight: $2$
• Character orbit: 576.be
• Rep. character: $\chi_{576}(35,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $256$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $8$

Defining parameters

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.be (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 192 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(8\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	800	256	544
Cusp forms	736	256	480
Eisenstein series	64	0	64

Trace form

\( 256 q + O(q^{10}) \)

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.be.a	$576$	$2$	576.be	192.s	$16$	$128$	$16$	$4.599$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$
576.2.be.b	$576$	$2$	576.be	192.s	$16$	$128$	$16$	$4.599$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$

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

\( S_{2}^{\mathrm{old}}(576, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)