Space of modular forms of level 288, weight 3, and Character 288.x

• Label: 288.3.x
• Level: $288$
• Weight: $3$
• Character orbit: 288.x
• Rep. character: $\chi_{288}(53,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $128$
• Newform subspaces: $2$
• Sturm bound: $144$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	288.x (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 96 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(144\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(288, [\chi])\).

	Total	New	Old
Modular forms	400	128	272
Cusp forms	368	128	240
Eisenstein series	32	0	32

Trace form

\( 128 q + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(288, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
288.3.x.a	$288$	$3$	288.x	96.p	$8$	$64$	$16$	$7.847$		None		$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$
288.3.x.b	$288$	$3$	288.x	96.p	$8$	$64$	$16$	$7.847$		None		$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{3}^{\mathrm{old}}(288, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(288, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)