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

• Label: 585.2.ca
• Level: $585$
• Weight: $2$
• Character orbit: 585.ca
• Rep. character: $\chi_{585}(58,\cdot)$
• 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.ca (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 - 2 * q^3 - 304 * q^4 - 2 * q^5 - 8 * q^6 + 2 * q^7 + 12 * q^9 - 16 * q^10 - 12 * q^11 - 14 * q^12 - 2 * q^13 + 48 * q^14 - 6 * q^15 + 264 * q^16 - 12 * q^17 + 4 * q^18 - 30 * q^20 - 16 * q^21 - 4 * q^22 + 2 * q^23 + 56 * q^24 - 20 * q^27 - 24 * q^28 - 2 * q^30 - 4 * q^31 - 6 * q^33 + 8 * q^34 - 46 * q^35 - 60 * q^36 - 4 * q^37 - 40 * q^38 - 4 * q^39 + 28 * q^40 + 4 * q^41 + 22 * q^42 - 6 * q^43 + 8 * q^44 + 4 * q^45 - 16 * q^46 - 14 * q^47 + 2 * q^48 - 112 * q^49 + 56 * q^50 - 30 * q^52 - 16 * q^53 - 4 * q^55 - 108 * q^56 - 72 * q^57 + 28 * q^58 - 16 * q^59 + 10 * q^60 + 4 * q^61 - 28 * q^62 - 18 * q^63 - 192 * q^64 + 58 * q^65 - 6 * q^67 + 62 * q^68 + 24 * q^69 + 10 * q^70 - 2 * q^72 - 34 * q^75 - 20 * q^76 - 44 * q^77 - 42 * q^78 + 4 * q^80 + 8 * q^81 + 20 * q^82 + 8 * q^83 + 124 * q^84 - 16 * q^85 + 68 * q^86 + 38 * q^87 - 8 * q^88 + 64 * q^90 - 16 * q^91 - 32 * q^92 - 70 * q^93 + 48 * q^94 - 64 * q^96 - 6 * q^97 - 282 * q^98 - 20 * 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.ca.a	$585$	$2$	585.ca	585.ba	$12$	$320$	$80$	$4.671$		None		✓	✓	✓	585.2.ca.a	$2$	$0$	\(0\)	\(-2\)	\(-2\)	\(2\)		$\mathrm{SU}(2)[C_{12}]$