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

• Label: 585.2.bm
• Level: $585$
• Weight: $2$
• Character orbit: 585.bm
• Rep. character: $\chi_{585}(166,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $112$
• 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.bm (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 117 \)
Character field:			\(\Q(\zeta_{6})\)
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	176	112	64
Cusp forms	160	112	48
Eisenstein series	16	0	16

Trace form

112 * q + 56 * q^4 - 2 * q^9 + 12 * q^12 + 2 * q^13 - 56 * q^16 - 16 * q^17 + 24 * q^18 + 6 * q^19 - 6 * q^21 + 48 * q^23 - 60 * q^24 + 56 * q^25 - 12 * q^26 - 24 * q^27 + 10 * q^29 + 8 * q^30 - 24 * q^31 + 36 * q^32 - 18 * q^33 + 16 * q^35 + 8 * q^36 - 6 * q^37 - 44 * q^38 - 22 * q^39 + 8 * q^42 - 16 * q^43 + 36 * q^47 + 64 * q^48 - 104 * q^49 - 20 * q^51 + 34 * q^52 - 32 * q^53 - 36 * q^54 - 80 * q^56 - 18 * q^57 + 24 * q^59 + 24 * q^60 + 28 * q^61 - 26 * q^62 - 76 * q^64 + 4 * q^65 - 18 * q^66 - 148 * q^68 - 56 * q^69 - 24 * q^71 + 16 * q^74 - 56 * q^77 + 104 * q^78 - 8 * q^79 + 34 * q^81 + 18 * q^82 + 18 * q^83 + 30 * q^84 + 18 * q^85 + 6 * q^86 - 12 * q^87 - 36 * q^89 - 34 * q^90 + 12 * q^92 - 30 * q^93 + 72 * q^94 - 28 * q^95 - 48 * q^96 + 48 * q^98 + 6 * 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.bm.a	$585$	$2$	585.bm	117.r	$6$	$112$	$56$	$4.671$		None		✓	✓	✓	585.2.ba.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

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