Space of modular forms of level 5544, weight 2, and Character 5544.f

• Label: 5544.2.f
• Level: $5544$
• Weight: $2$
• Character orbit: 5544.f
• Rep. character: $\chi_{5544}(2969,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $2$
• Sturm bound: $2304$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 5544 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5544.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(2304\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5544, [\chi])\).

	Total	New	Old
Modular forms	1184	72	1112
Cusp forms	1120	72	1048
Eisenstein series	64	0	64

Trace form

\( 72 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5544, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5544.2.f.a	$5544$	$2$	5544.f	33.d	$2$	$36$	$36$	$44.269$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
5544.2.f.b	$5544$	$2$	5544.f	33.d	$2$	$36$	$36$	$44.269$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(5544, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5544, [\chi]) \cong \)