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

• Label: 288.3.e
• Level: $288$
• Weight: $3$
• Character orbit: 288.e
• Rep. character: $\chi_{288}(161,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $4$
• Sturm bound: $144$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	288.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(144\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	112	8	104
Cusp forms	80	8	72
Eisenstein series	32	0	32

Trace form

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

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.e.a	$288$	$3$	288.e	3.b	$2$	$2$	$2$	$7.847$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-8q^{7}-8\beta q^{11}-8q^{13}-9\beta q^{17}+\cdots\)
288.3.e.b	$288$	$3$	288.e	3.b	$2$	$2$	$2$	$7.847$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+7\beta q^{5}-24q^{13}-7\beta q^{17}-73q^{25}+\cdots\)
288.3.e.c	$288$	$3$	288.e	3.b	$2$	$2$	$2$	$7.847$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{5}+24q^{13}+23\beta q^{17}+23q^{25}+\cdots\)
288.3.e.d	$288$	$3$	288.e	3.b	$2$	$2$	$2$	$7.847$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+8q^{7}+8\beta q^{11}-8q^{13}-9\beta q^{17}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(288, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)