Space of modular forms of level 549, weight 2, and Character 549.bp

• Label: 549.2.bp
• Level: $549$
• Weight: $2$
• Character orbit: 549.bp
• Rep. character: $\chi_{549}(4,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $480$
• Newform subspaces: $1$
• Sturm bound: $124$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 549 = 3^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	549.bp (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 549 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(124\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(549, [\chi])\).

	Total	New	Old
Modular forms	512	512	0
Cusp forms	480	480	0
Eisenstein series	32	32	0

Trace form

\( 480 q - 2 q^{2} - 6 q^{3} - 64 q^{4} + 5 q^{5} - q^{6} + 5 q^{7} - 20 q^{8} + 12 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(549, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
549.2.bp.a	$549$	$2$	549.bp	549.ap	$30$	$480$	$60$	$4.384$		None		$2$	$0$	\(-2\)	\(-6\)	\(5\)	\(5\)		$\mathrm{SU}(2)[C_{30}]$