Space of modular forms of level 550, weight 2, and Character 550.bj

• Label: 550.2.bj
• Level: $550$
• Weight: $2$
• Character orbit: 550.bj
• Rep. character: $\chi_{550}(13,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $240$
• Newform subspaces: $1$
• Sturm bound: $180$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.bj (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 275 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(180\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(550, [\chi])\).

	Total	New	Old
Modular forms	752	240	512
Cusp forms	688	240	448
Eisenstein series	64	0	64

Trace form

\( 240 q - 4 q^{3} + 12 q^{5} + 20 q^{7} - 20 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(550, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
550.2.bj.a	$550$	$2$	550.bj	275.ag	$20$	$240$	$30$	$4.392$		None		$2$	$0$	\(0\)	\(-4\)	\(12\)	\(20\)		$\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{2}^{\mathrm{old}}(550, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(550, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)