Space of modular forms of level 288, weight 2, and Character 288.d

• Label: 288.2.d
• Level: $288$
• Weight: $2$
• Character orbit: 288.d
• Rep. character: $\chi_{288}(145,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(288, [\chi])\).

	Total	New	Old
Modular forms	64	6	58
Cusp forms	32	4	28
Eisenstein series	32	2	30

Trace form

\( 4 q + 4 q^{17} + 8 q^{23} - 4 q^{25} + 16 q^{31} - 4 q^{41} - 24 q^{47} - 12 q^{49} - 32 q^{55} - 16 q^{65} + 24 q^{71} + 16 q^{73} + 20 q^{89} - 16 q^{95}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(288, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
288.2.d.a	$288$	$2$	288.d	8.b	$2$	$2$	$2$	$2.300$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-6}) \)					72.2.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{5}-2q^{7}+2\beta q^{11}-3q^{25}+\beta q^{29}+\cdots\)
288.2.d.b	$288$	$2$	288.d	8.b	$2$	$2$	$2$	$2.300$	\(\Q(\sqrt{-1}) \)	None					24.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+2 q^{7}+2\beta q^{13}+2 q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(288, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(288, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)