Space of modular forms of level 547, weight 2, and Character 547.j

• Label: 547.2.j
• Level: $547$
• Weight: $2$
• Character orbit: 547.j
• Rep. character: $\chi_{547}(11,\cdot)$
• Character field: $\Q(\zeta_{39})$
• Dimension: $1080$
• Newform subspaces: $1$
• Sturm bound: $91$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.j (of order \(39\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 547 \)
Character field:			\(\Q(\zeta_{39})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(91\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(547, [\chi])\).

	Total	New	Old
Modular forms	1128	1128	0
Cusp forms	1080	1080	0
Eisenstein series	48	48	0

Trace form

\( 1080 q - 25 q^{2} - 74 q^{3} + 21 q^{4} - 27 q^{5} - 75 q^{6} - 28 q^{7} + 4 q^{8} + 1010 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(547, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
547.2.j.a	$547$	$2$	547.j	547.j	$39$	$1080$	$45$	$4.368$		None		$2$	$0$	\(-25\)	\(-74\)	\(-27\)	\(-28\)		$\mathrm{SU}(2)[C_{39}]$