Space of modular forms of level 552, weight 2, and Character 552.j

• Label: 552.2.j
• Level: $552$
• Weight: $2$
• Character orbit: 552.j
• Rep. character: $\chi_{552}(323,\cdot)$
• Character field: $\Q$
• Dimension: $88$
• Newform subspaces: $4$
• Sturm bound: $192$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.j (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(192\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(552, [\chi])\).

	Total	New	Old
Modular forms	100	88	12
Cusp forms	92	88	4
Eisenstein series	8	0	8

Trace form

\( 88 q - 3 q^{6} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(552, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
552.2.j.a	$552$	$2$	552.j	24.f	$2$	$2$	$2$	$4.408$	\(\Q(\sqrt{-2}) \)	None		$2$	$1$	\(0\)	\(-2\)	\(-8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+(-1+\beta )q^{3}-2q^{4}-4q^{5}+\cdots\)
552.2.j.b	$552$	$2$	552.j	24.f	$2$	$2$	$2$	$4.408$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+(-1+\beta )q^{3}-2q^{4}+4q^{5}+\cdots\)
552.2.j.c	$552$	$2$	552.j	24.f	$2$	$42$	$42$	$4.408$		None		$2$	$0$	\(0\)	\(2\)	\(-8\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
552.2.j.d	$552$	$2$	552.j	24.f	$2$	$42$	$42$	$4.408$		None		$2$	$0$	\(0\)	\(2\)	\(8\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(552, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(552, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)