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

• Label: 550.2.bb
• Level: $550$
• Weight: $2$
• Character orbit: 550.bb
• Rep. character: $\chi_{550}(119,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $120$
• 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.bb (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 275 \)
Character field:			\(\Q(\zeta_{10})\)
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	376	120	256
Cusp forms	344	120	224
Eisenstein series	32	0	32

Trace form

\( 120 q + 10 q^{3} - 120 q^{4} - 2 q^{5} + 4 q^{6} - 20 q^{7} + 36 q^{9} + O(q^{10}) \)

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.bb.a	$550$	$2$	550.bb	275.n	$10$	$120$	$30$	$4.392$		None		$2$	$0$	\(0\)	\(10\)	\(-2\)	\(-20\)		$\mathrm{SU}(2)[C_{10}]$

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

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