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 - 4 * q^10 + 4 * q^11 + 2 * q^12 - 30 * q^13 - 20 * q^16 + 30 * q^18 - 2 * q^21 - 30 * q^22 + 30 * q^24 + 14 * q^25 + 12 * q^26 + 32 * q^27 + 2 * q^28 - 12 * q^30 + 18 * q^32 + 18 * q^33 + 2 * q^34 + 6 * q^35 - 72 * q^36 + 6 * q^37 - 36 * q^38 - 18 * q^39 - 6 * q^40 + 10 * q^41 - 12 * q^42 - 2 * q^44 - 12 * q^46 - 44 * q^47 + 16 * q^48 - 6 * q^49 - 6 * q^50 - 54 * q^52 - 6 * q^54 - 12 * q^55 + 30 * q^56 + 18 * q^57 - 12 * q^58 + 12 * q^59 + 10 * q^62 - 64 * q^63 - 4 * q^64 - 2 * q^65 - 60 * q^67 + 18 * q^69 + 28 * q^70 + 18 * q^71 + 222 * q^72 + 44 * q^73 - 56 * q^74 - 8 * q^75 - 36 * q^76 + 6 * q^77 + 24 * q^78 + 66 * q^79 - 38 * q^81 + 20 * q^83 + 104 * q^84 + 12 * q^85 - 14 * q^86 + 24 * q^87 - 12 * q^89 + 2 * q^90 - 132 * q^92 - 42 * q^93 - 60 * q^94 - 20 * q^95 + 78 * q^96 + 126 * q^98 - 60 * 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.m.a	$185$	$2$	185.m	37.e	$6$	$28$	$14$	$1.477$		None		✓	✓	✓	185.2.m.a	$2$	$0$	\(-6\)	\(-4\)	\(0\)	\(-2\)		$\mathrm{SU}(2)[C_{6}]$

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

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