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

• Label: 185.2.d
• Level: $185$
• Weight: $2$
• Character orbit: 185.d
• Rep. character: $\chi_{185}(184,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $38$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 185 \)
Character field:			\(\Q\)
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	20	20	0
Cusp forms	16	16	0
Eisenstein series	4	4	0

Trace form

16 * q + 8 * q^4 - 16 * q^9 - 12 * q^10 - 8 * q^16 + 24 * q^21 - 12 * q^25 - 4 * q^30 + 8 * q^34 - 8 * q^36 - 16 * q^40 + 24 * q^46 - 16 * q^49 - 88 * q^64 + 12 * q^65 + 44 * q^70 - 24 * q^71 + 48 * q^74 + 12 * q^75 - 56 * q^81 + 80 * q^84 + 60 * q^85 - 72 * q^86 + 12 * q^95 + 24 * 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.d.a	$185$	$2$	185.d	185.d	$2$	$16$	$16$	$1.477$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓	✓	✓	185.2.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{2}-\beta _{9}q^{3}+(1-\beta _{2})q^{4}-\beta _{1}q^{5}+\cdots\)