Space of modular forms of level 561, weight 2, and Character 561.t

• Label: 561.2.t
• Level: $561$
• Weight: $2$
• Character orbit: 561.t
• Rep. character: $\chi_{561}(35,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $256$
• Newform subspaces: $2$
• Sturm bound: $144$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 561 = 3 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	561.t (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(144\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(561, [\chi])\).

	Total	New	Old
Modular forms	304	256	48
Cusp forms	272	256	16
Eisenstein series	32	0	32

Trace form

\( 256 q + 2 q^{3} - 64 q^{4} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(561, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
561.2.t.a	$561$	$2$	561.t	33.f	$10$	$128$	$32$	$4.480$		None		$2$	$0$	\(0\)	\(1\)	\(-5\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$
561.2.t.b	$561$	$2$	561.t	33.f	$10$	$128$	$32$	$4.480$		None		$2$	$0$	\(0\)	\(1\)	\(5\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(561, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(561, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)