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

• Label: 550.2.j
• Level: $550$
• Weight: $2$
• Character orbit: 550.j
• Rep. character: $\chi_{550}(81,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $120$
• 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.j (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 275 \)
Character field:			\(\Q(\zeta_{5})\)
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	376	120	256
Cusp forms	344	120	224
Eisenstein series	32	0	32

Trace form

\( 120 q + 6 q^{3} - 30 q^{4} + 4 q^{5} + 16 q^{6} - 6 q^{7} - 24 q^{9} + O(q^{10}) \)

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.j.a	$550$	$2$	550.j	275.j	$5$	$12$	$3$	$4.392$	12.0.\(\cdots\).1	None		$2$	$0$	\(3\)	\(-2\)	\(0\)	\(-7\)	$5$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{3}q^{2}+(-\beta _{6}-\beta _{9})q^{3}-\beta _{8}q^{4}+\cdots\)
550.2.j.b	$550$	$2$	550.j	275.j	$5$	$48$	$12$	$4.392$		None		$2$	$0$	\(12\)	\(7\)	\(4\)	\(4\)		$\mathrm{SU}(2)[C_{5}]$
550.2.j.c	$550$	$2$	550.j	275.j	$5$	$60$	$15$	$4.392$		None		$2$	$0$	\(-15\)	\(1\)	\(0\)	\(-3\)		$\mathrm{SU}(2)[C_{5}]$

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

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