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

• Label: 552.2.f
• Level: $552$
• Weight: $2$
• Character orbit: 552.f
• Rep. character: $\chi_{552}(277,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $4$
• Sturm bound: $192$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(192\)
Trace bound:			\(1\)
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	44	56
Cusp forms	92	44	48
Eisenstein series	8	0	8

Trace form

44 * q - 12 * q^8 - 44 * q^9 - 4 * q^10 - 8 * q^12 - 4 * q^14 + 24 * q^16 + 8 * q^17 - 4 * q^20 - 20 * q^22 + 12 * q^24 - 52 * q^25 + 16 * q^26 - 8 * q^30 - 24 * q^31 - 20 * q^32 + 8 * q^34 + 4 * q^38 + 16 * q^39 + 36 * q^40 - 8 * q^41 + 12 * q^42 - 24 * q^44 + 48 * q^47 + 60 * q^49 + 16 * q^50 - 12 * q^56 - 16 * q^57 + 24 * q^58 - 24 * q^60 + 48 * q^62 - 32 * q^65 - 16 * q^66 + 44 * q^68 + 16 * q^70 - 64 * q^71 + 12 * q^72 + 24 * q^73 - 64 * q^74 + 60 * q^76 - 16 * q^78 - 28 * q^80 + 44 * q^81 + 24 * q^84 + 12 * q^86 + 24 * q^87 - 68 * q^88 + 40 * q^89 + 4 * q^90 - 8 * q^94 - 48 * q^95 - 20 * q^96 + 8 * q^97 - 56 * 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.f.a	$552$	$2$	552.f	8.b	$2$	$2$	$2$	$4.408$	\(\Q(\sqrt{-1}) \)	None		✓			552.2.f.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(i+1)q^{2}+i q^{3}+2 i q^{4}+2 i q^{5}+\cdots\)
552.2.f.b	$552$	$2$	552.f	8.b	$2$	$4$	$4$	$4.408$	\(\Q(\zeta_{8})\)	None		✓			552.2.f.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{3} q^{2}+\beta_1 q^{3}+2 q^{4}+(\beta_{2}+2\beta_1)q^{5}+\cdots\)
552.2.f.c	$552$	$2$	552.f	8.b	$2$	$18$	$18$	$4.408$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		✓			552.2.f.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}-\beta _{4}q^{3}-\beta _{2}q^{4}+\beta _{9}q^{5}+\cdots\)
552.2.f.d	$552$	$2$	552.f	8.b	$2$	$20$	$20$	$4.408$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓		552.2.f.d	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-8\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+\beta _{5}q^{3}+\beta _{2}q^{4}+\beta _{11}q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(552, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 2}\)