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

• Label: 552.2.t
• Level: $552$
• Weight: $2$
• Character orbit: 552.t
• Rep. character: $\chi_{552}(19,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $480$
• 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.t (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 184 \)
Character field:			\(\Q(\zeta_{22})\)
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	1000	480	520
Cusp forms	920	480	440
Eisenstein series	80	0	80

Trace form

\( 480 q + 4 q^{2} - 8 q^{4} + 4 q^{6} + 4 q^{8} - 48 q^{9} + O(q^{10}) \)

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.t.a	$552$	$2$	552.t	184.j	$22$	$240$	$24$	$4.408$		None		$4$	$0$	\(0\)	\(24\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$
552.2.t.b	$552$	$2$	552.t	184.j	$22$	$240$	$24$	$4.408$		None		$4$	$0$	\(4\)	\(-24\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$

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

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