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

• Label: 550.2.bh
• Level: $550$
• Weight: $2$
• Character orbit: 550.bh
• Rep. character: $\chi_{550}(7,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $144$
• Newform subspaces: $3$
• Sturm bound: $180$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.bh (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(180\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	816	144	672
Cusp forms	624	144	480
Eisenstein series	192	0	192

Trace form

\( 144 q + 4 q^{3} + 20 q^{7} + O(q^{10}) \)

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.bh.a	$550$	$2$	550.bh	55.l	$20$	$32$	$4$	$4.392$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$
550.2.bh.b	$550$	$2$	550.bh	55.l	$20$	$48$	$6$	$4.392$		None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(20\)		$\mathrm{SU}(2)[C_{20}]$
550.2.bh.c	$550$	$2$	550.bh	55.l	$20$	$64$	$8$	$4.392$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$

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

\( S_{2}^{\mathrm{old}}(550, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)