Space of modular forms of level 185, weight 2, and Character 185.l

• Label: 185.2.l
• Level: $185$
• Weight: $2$
• Character orbit: 185.l
• Rep. character: $\chi_{185}(64,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $32$
• Newform subspaces: $1$
• Sturm bound: $38$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.l (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 185 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(38\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(185, [\chi])\).

	Total	New	Old
Modular forms	40	40	0
Cusp forms	32	32	0
Eisenstein series	8	8	0

Trace form

32 * q - 14 * q^4 + 3 * q^5 + 4 * q^9 + 6 * q^10 + 12 * q^11 + 12 * q^15 - 10 * q^16 - 33 * q^20 - 18 * q^21 - 42 * q^24 + 3 * q^25 - 12 * q^26 + 34 * q^30 + 28 * q^34 - 42 * q^35 + 20 * q^36 - 18 * q^39 - 11 * q^40 - 36 * q^41 - 42 * q^44 + 48 * q^46 + 4 * q^49 - 27 * q^50 + 66 * q^54 + 12 * q^55 + 18 * q^56 - 54 * q^61 + 112 * q^64 + 24 * q^65 - 30 * q^69 + 4 * q^70 + 18 * q^71 - 60 * q^74 - 36 * q^75 - 42 * q^79 - 16 * q^81 + 88 * q^84 + 18 * q^85 + 18 * q^86 + 54 * q^89 - 3 * q^90 - 36 * q^91 + 12 * q^94 - 6 * q^95 - 114 * q^96 - 72 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(185, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
185.2.l.a	$185$	$2$	185.l	185.l	$6$	$32$	$16$	$1.477$		None		✓	✓	✓	185.2.l.a	$4$	$0$	\(0\)	\(0\)	\(3\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$