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

• Label: 585.2.cf
• Level: $585$
• Weight: $2$
• Character orbit: 585.cf
• Rep. character: $\chi_{585}(163,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $132$
• Newform subspaces: $3$
• Sturm bound: $168$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.cf (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(168\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	368	148	220
Cusp forms	304	132	172
Eisenstein series	64	16	48

Trace form

132 * q - 62 * q^4 + 2 * q^5 - 6 * q^7 + 12 * q^8 - 10 * q^10 + 8 * q^11 - 10 * q^13 - 58 * q^16 + 2 * q^17 - 12 * q^19 - 2 * q^20 - 6 * q^23 - 10 * q^25 + 24 * q^26 + 6 * q^28 - 16 * q^31 - 2 * q^32 + 30 * q^34 + 20 * q^35 + 6 * q^37 - 8 * q^38 + 32 * q^40 - 6 * q^41 + 18 * q^43 - 76 * q^44 - 28 * q^46 + 22 * q^49 + 8 * q^50 + 14 * q^52 + 6 * q^53 - 6 * q^55 - 72 * q^56 + 42 * q^58 + 48 * q^59 + 4 * q^62 + 92 * q^64 - 4 * q^65 + 38 * q^67 - 76 * q^68 - 104 * q^70 + 32 * q^71 - 64 * q^73 - 18 * q^74 + 20 * q^77 + 70 * q^80 - 54 * q^82 - 62 * q^85 + 4 * q^86 - 110 * q^88 + 6 * q^89 + 24 * q^91 + 72 * q^92 + 26 * q^95 - 38 * q^97 - 112 * q^98

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.cf.a	$585$	$2$	585.cf	65.o	$12$	$20$	$5$	$4.671$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None					65.2.o.a	$2$	$0$	\(4\)	\(0\)	\(6\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\beta _{3}-\beta _{4})q^{2}+(2\beta _{1}+\beta _{2}-\beta _{4}+\beta _{10}+\cdots)q^{4}+\cdots\)
585.2.cf.b	$585$	$2$	585.cf	65.o	$12$	$56$	$14$	$4.671$		None					195.2.bd.a	$2$	$0$	\(-4\)	\(0\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
585.2.cf.c	$585$	$2$	585.cf	65.o	$12$	$56$	$14$	$4.671$		None		✓			585.2.cf.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

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

\( S_{2}^{\mathrm{old}}(585, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)