Space of modular forms of level 264, weight 3, and Character 264.e

• Label: 264.3.e
• Level: $264$
• Weight: $3$
• Character orbit: 264.e
• Rep. character: $\chi_{264}(109,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $144$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 264 = 2^{3} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	264.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 88 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(144\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(264, [\chi])\).

	Total	New	Old
Modular forms	100	48	52
Cusp forms	92	48	44
Eisenstein series	8	0	8

Trace form

\( 48 q - 12 q^{4} - 144 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(264, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
264.3.e.a	$264$	$3$	264.e	88.b	$2$	$48$	$48$	$7.193$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(264, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(264, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 2}\)