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

• Label: 585.2.dd
• Level: $585$
• Weight: $2$
• Character orbit: 585.dd
• Rep. character: $\chi_{585}(41,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $224$
• 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.dd (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 117 \)
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	224	128
Cusp forms	320	224	96
Eisenstein series	32	0	32

Trace form

224 * q - 12 * q^6 - 8 * q^7 + 36 * q^8 - 12 * q^11 - 4 * q^15 + 112 * q^16 + 44 * q^18 - 8 * q^19 - 36 * q^21 - 8 * q^24 - 48 * q^26 + 24 * q^27 - 16 * q^28 - 48 * q^30 - 16 * q^31 - 72 * q^32 + 4 * q^33 - 4 * q^37 + 8 * q^39 - 24 * q^41 - 128 * q^42 - 16 * q^45 - 72 * q^47 - 56 * q^48 - 4 * q^52 + 8 * q^54 + 36 * q^57 + 36 * q^58 - 72 * q^59 + 32 * q^60 + 36 * q^62 - 8 * q^63 - 108 * q^66 + 28 * q^67 - 48 * q^71 - 204 * q^72 + 28 * q^73 + 16 * q^76 + 144 * q^77 - 60 * q^78 - 12 * q^79 - 48 * q^80 + 12 * q^81 - 36 * q^83 - 16 * q^84 - 12 * q^85 - 108 * q^86 - 88 * q^87 + 60 * q^89 + 16 * q^91 - 120 * q^92 + 108 * q^93 + 16 * q^96 - 4 * q^97 + 96 * q^98 + 116 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
585.2.dd.a	$585$	$2$	585.dd	117.ac	$12$	$224$	$56$	$4.671$		None		✓	✓	✓	585.2.cm.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{12}]$

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

\( S_{2}^{\mathrm{old}}(585, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)