Space of modular forms of level 585, weight 2, and Character 585.l

• Label: 585.2.l
• Level: $585$
• Weight: $2$
• Character orbit: 585.l
• Rep. character: $\chi_{585}(16,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $112$
• Newform subspaces: $2$
• Sturm bound: $168$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.l (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 117 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(168\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(585, [\chi])\).

	Total	New	Old
Modular forms	176	112	64
Cusp forms	160	112	48
Eisenstein series	16	0	16

Trace form

\( 112 q + 112 q^{4} + 6 q^{6} - 4 q^{7} + 12 q^{8} + 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(585, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
585.2.l.a	$585$	$2$	585.l	117.h	$3$	$56$	$28$	$4.671$		None		$2$	$0$	\(0\)	\(-1\)	\(28\)	\(6\)		$\mathrm{SU}(2)[C_{3}]$
585.2.l.b	$585$	$2$	585.l	117.h	$3$	$56$	$28$	$4.671$		None		$2$	$0$	\(0\)	\(1\)	\(-28\)	\(-10\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(585, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(585, [\chi]) \cong \)