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

• Label: 185.2.o
• Level: $185$
• Weight: $2$
• Character orbit: 185.o
• Rep. character: $\chi_{185}(16,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $72$
• Newform subspaces: $2$
• Sturm bound: $38$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.o (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(38\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	120	72	48
Cusp forms	96	72	24
Eisenstein series	24	0	24

Trace form

72 * q - 6 * q^2 - 6 * q^4 + 6 * q^7 + 6 * q^8 - 6 * q^10 - 30 * q^12 + 30 * q^13 + 6 * q^14 - 42 * q^16 - 30 * q^18 + 6 * q^19 - 36 * q^21 - 30 * q^22 - 36 * q^23 - 30 * q^24 - 24 * q^27 - 30 * q^28 + 6 * q^29 - 24 * q^30 - 36 * q^31 + 72 * q^32 + 60 * q^33 + 6 * q^34 - 6 * q^35 + 12 * q^36 + 48 * q^37 + 96 * q^38 + 12 * q^39 - 30 * q^41 + 12 * q^42 + 24 * q^43 + 12 * q^44 + 12 * q^45 + 54 * q^46 - 54 * q^47 - 24 * q^48 - 6 * q^50 + 60 * q^51 - 18 * q^52 - 24 * q^53 - 126 * q^54 - 12 * q^55 + 12 * q^56 - 54 * q^57 - 30 * q^58 + 6 * q^59 - 24 * q^61 + 48 * q^62 + 24 * q^63 + 12 * q^64 - 18 * q^65 - 6 * q^66 + 18 * q^67 - 60 * q^68 - 18 * q^69 - 36 * q^71 + 30 * q^72 + 72 * q^73 + 78 * q^74 + 12 * q^75 - 60 * q^76 + 6 * q^77 + 24 * q^78 - 48 * q^79 + 48 * q^81 + 48 * q^82 - 72 * q^83 + 72 * q^84 - 12 * q^85 - 144 * q^86 + 36 * q^87 + 6 * q^88 - 48 * q^89 - 24 * q^90 - 60 * q^91 + 78 * q^92 + 54 * q^93 + 30 * q^94 + 24 * q^95 + 54 * q^96 + 24 * q^97 + 42 * q^98 - 84 * 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.o.a	$185$	$2$	185.o	37.f	$9$	$36$	$6$	$1.477$		None		✓			185.2.o.a	$2$	$0$	\(-3\)	\(0\)	\(0\)	\(6\)		$\mathrm{SU}(2)[C_{9}]$
185.2.o.b	$185$	$2$	185.o	37.f	$9$	$36$	$6$	$1.477$		None		✓			185.2.o.b	$2$	$0$	\(-3\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$

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

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