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

• Label: 185.2.bc
• Level: $185$
• Weight: $2$
• Character orbit: 185.bc
• Rep. character: $\chi_{185}(2,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $204$
• Newform subspaces: $1$
• Sturm bound: $38$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.bc (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 185 \)
Character field:			\(\Q(\zeta_{36})\)
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	252	252	0
Cusp forms	204	204	0
Eisenstein series	48	48	0

Trace form

204 * q - 12 * q^2 - 18 * q^3 - 12 * q^5 - 24 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 + 24 * q^14 - 12 * q^15 - 24 * q^16 + 12 * q^17 + 66 * q^18 - 108 * q^20 - 24 * q^21 - 24 * q^22 - 18 * q^23 - 36 * q^24 - 48 * q^25 - 12 * q^26 + 6 * q^27 - 24 * q^28 + 36 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^33 + 84 * q^35 + 12 * q^37 + 60 * q^38 - 24 * q^39 + 42 * q^40 - 18 * q^41 - 150 * q^42 + 180 * q^44 + 72 * q^45 - 24 * q^46 - 6 * q^47 - 30 * q^48 - 36 * q^49 - 102 * q^50 - 24 * q^51 + 60 * q^52 + 30 * q^53 - 42 * q^55 - 24 * q^56 - 36 * q^57 - 138 * q^58 + 138 * q^60 + 60 * q^61 + 72 * q^62 - 6 * q^63 + 18 * q^64 - 30 * q^65 + 120 * q^66 + 30 * q^67 - 24 * q^68 - 132 * q^69 + 156 * q^70 + 24 * q^71 - 192 * q^72 - 90 * q^73 + 66 * q^74 - 120 * q^75 + 36 * q^76 - 132 * q^77 + 150 * q^78 + 96 * q^79 - 132 * q^80 + 132 * q^81 - 6 * q^82 + 48 * q^83 - 18 * q^85 + 96 * q^86 + 258 * q^87 - 174 * q^88 + 12 * q^89 + 60 * q^90 - 96 * q^91 - 102 * q^92 - 42 * q^93 - 72 * q^94 - 66 * q^95 + 60 * q^96 - 18 * q^97 + 36 * q^98 - 192 * 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.bc.a	$185$	$2$	185.bc	185.ac	$36$	$204$	$17$	$1.477$		None		✓	✓	✓	185.2.z.a	$2$	$0$	\(-12\)	\(-18\)	\(-12\)	\(-12\)		$\mathrm{SU}(2)[C_{36}]$