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

• Label: 552.2.n
• Level: $552$
• Weight: $2$
• Character orbit: 552.n
• Rep. character: $\chi_{552}(91,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.n (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 184 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(2\)
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	48	52
Cusp forms	92	48	44
Eisenstein series	8	0	8

Trace form

48 * q - 4 * q^2 + 8 * q^4 - 4 * q^6 - 4 * q^8 + 48 * q^9 + 8 * q^16 - 4 * q^18 - 4 * q^24 + 48 * q^25 - 4 * q^32 + 8 * q^36 - 40 * q^46 + 48 * q^49 - 84 * q^50 - 4 * q^54 - 80 * q^62 + 8 * q^64 - 4 * q^72 + 48 * q^81 - 80 * q^82 - 12 * q^92 - 8 * q^94 - 4 * q^96 - 20 * q^98

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
552.2.n.a	$552$	$2$	552.n	184.h	$2$	$24$	$24$	$4.408$		None		✓			552.2.n.a	$4$	$0$	\(-4\)	\(24\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
552.2.n.b	$552$	$2$	552.n	184.h	$2$	$24$	$24$	$4.408$		None		✓			552.2.n.b	$4$	$0$	\(0\)	\(-24\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(552, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 2}\)