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

• Label: 185.2.p
• Level: $185$
• Weight: $2$
• Character orbit: 185.p
• Rep. character: $\chi_{185}(82,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $68$
• Newform subspaces: $1$
• Sturm bound: $38$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.p (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 185 \)
Character field:			\(\Q(\zeta_{12})\)
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	84	84	0
Cusp forms	68	68	0
Eisenstein series	16	16	0

Trace form

68 * q - 4 * q^2 - 8 * q^3 - 30 * q^4 - 10 * q^5 - 8 * q^6 - 2 * q^7 + 12 * q^8 - 6 * q^10 + 14 * q^12 - 6 * q^13 - 8 * q^15 - 26 * q^16 + 12 * q^17 + 18 * q^18 + 4 * q^19 + 48 * q^20 - 12 * q^21 + 6 * q^22 - 12 * q^23 + 10 * q^25 - 24 * q^26 - 68 * q^27 - 26 * q^28 + 14 * q^29 + 10 * q^30 - 24 * q^31 - 16 * q^32 - 2 * q^33 - 10 * q^35 - 16 * q^37 - 36 * q^38 + 52 * q^39 + 42 * q^40 - 18 * q^41 + 132 * q^42 + 8 * q^43 - 36 * q^44 - 32 * q^45 - 52 * q^46 - 24 * q^47 - 60 * q^48 - 36 * q^49 - 8 * q^50 - 8 * q^51 - 26 * q^52 + 82 * q^53 + 40 * q^54 + 18 * q^55 + 16 * q^56 - 6 * q^57 + 86 * q^58 - 8 * q^59 + 36 * q^60 + 4 * q^61 + 10 * q^62 - 48 * q^63 - 20 * q^64 + 8 * q^65 + 80 * q^66 - 40 * q^67 + 8 * q^69 - 82 * q^70 + 4 * q^71 - 90 * q^72 - 60 * q^73 - 44 * q^74 + 64 * q^75 + 72 * q^76 + 66 * q^77 - 24 * q^78 + 56 * q^79 + 34 * q^80 - 6 * q^81 + 24 * q^83 - 20 * q^85 - 4 * q^86 - 84 * q^87 - 22 * q^89 - 50 * q^90 + 44 * q^91 + 44 * q^92 - 34 * q^93 - 20 * q^94 - 28 * q^95 - 8 * q^96 + 42 * q^98 + 32 * 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.p.a	$185$	$2$	185.p	185.p	$12$	$68$	$17$	$1.477$		None		✓	✓	✓	185.2.p.a	$2$	$0$	\(-4\)	\(-8\)	\(-10\)	\(-2\)		$\mathrm{SU}(2)[C_{12}]$