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

• Label: 185.2.m
• Level: $185$
• Weight: $2$
• Character orbit: 185.m
• Rep. character: $\chi_{185}(11,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $28$
• Newform subspaces: $1$
• Sturm bound: $38$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.m (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
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	44	28	16
Cusp forms	36	28	8
Eisenstein series	8	0	8

Trace form

\( 28 q - 6 q^{2} - 4 q^{3} + 20 q^{4} - 2 q^{7} - 18 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
185.2.m.a	$185$	$2$	185.m	37.e	$6$	$28$	$14$	$1.477$		None		$2$	$0$	\(-6\)	\(-4\)	\(0\)	\(-2\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(185, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(185, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 2}\)