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

• Label: 585.2.bs
• Level: $585$
• Weight: $2$
• Character orbit: 585.bs
• Rep. character: $\chi_{585}(289,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $68$
• Newform subspaces: $3$
• Sturm bound: $168$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bs (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(168\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	184	76	108
Cusp forms	152	68	84
Eisenstein series	32	8	24

Trace form

68 * q + 32 * q^4 + 2 * q^5 - 3 * q^10 - 4 * q^11 + 20 * q^14 - 28 * q^16 - 12 * q^19 + 17 * q^20 + 10 * q^25 + 24 * q^26 - 6 * q^29 - 24 * q^34 - 20 * q^35 + 2 * q^40 + 26 * q^41 - 36 * q^44 - 22 * q^46 + 34 * q^49 + 11 * q^50 + 14 * q^55 + 40 * q^56 - 8 * q^59 - 30 * q^61 - 100 * q^64 - 37 * q^65 - 116 * q^70 + 8 * q^71 + 4 * q^74 + 86 * q^76 - 40 * q^79 - 29 * q^80 - 33 * q^85 - 44 * q^86 + 44 * q^89 - 12 * q^91 + 56 * q^94 + 8 * q^95

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.bs.a	$585$	$2$	585.bs	65.n	$6$	$12$	$6$	$4.671$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					65.2.n.a	$4$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{4}q^{2}+(-\beta _{2}-\beta _{6}-\beta _{10})q^{4}+(1+\cdots)q^{5}+\cdots\)
585.2.bs.b	$585$	$2$	585.bs	65.n	$6$	$24$	$12$	$4.671$		None					195.2.ba.a	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
585.2.bs.c	$585$	$2$	585.bs	65.n	$6$	$32$	$16$	$4.671$		None		✓	✓		585.2.bs.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

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