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

• Label: 585.2.dt
• Level: $585$
• Weight: $2$
• Character orbit: 585.dt
• Rep. character: $\chi_{585}(7,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $320$
• Newform subspaces: $1$
• Sturm bound: $168$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.dt (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 585 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(168\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	352	352	0
Cusp forms	320	320	0
Eisenstein series	32	32	0

Trace form

\( 320 q - 6 q^{2} - 2 q^{3} + 152 q^{4} - 2 q^{5} - 8 q^{6} - 4 q^{7} + 12 q^{9} + O(q^{10}) \)

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.dt.a	$585$	$2$	585.dt	585.ct	$12$	$320$	$80$	$4.671$		None		$2$	$0$	\(-6\)	\(-2\)	\(-2\)	\(-4\)		$\mathrm{SU}(2)[C_{12}]$