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

• Label: 185.2.e
• Level: $185$
• Weight: $2$
• Character orbit: 185.e
• Rep. character: $\chi_{185}(26,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $28$
• Newform subspaces: $2$
• Sturm bound: $38$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(38\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	40	28	12
Cusp forms	32	28	4
Eisenstein series	8	0	8

Trace form

28 * q + 2 * q^2 - 4 * q^3 - 16 * q^4 + 2 * q^7 - 18 * q^9 + 4 * q^10 - 12 * q^11 - 2 * q^12 + 10 * q^13 - 16 * q^14 - 12 * q^16 - 4 * q^17 - 10 * q^18 - 8 * q^19 + 14 * q^21 + 6 * q^22 + 12 * q^23 - 6 * q^24 - 14 * q^25 - 20 * q^26 + 8 * q^27 + 22 * q^28 - 24 * q^29 + 4 * q^30 - 8 * q^31 + 22 * q^32 - 10 * q^33 + 22 * q^34 - 2 * q^35 + 32 * q^36 + 30 * q^37 + 12 * q^38 - 2 * q^39 - 6 * q^40 - 10 * q^41 + 6 * q^44 + 16 * q^45 - 4 * q^46 + 12 * q^47 + 16 * q^48 - 2 * q^49 + 2 * q^50 + 44 * q^51 + 38 * q^52 - 8 * q^53 + 14 * q^54 - 4 * q^55 - 6 * q^56 - 22 * q^57 - 24 * q^58 - 16 * q^59 - 28 * q^60 - 24 * q^61 - 46 * q^62 + 56 * q^63 - 12 * q^64 - 2 * q^65 - 44 * q^66 - 28 * q^67 + 136 * q^68 + 6 * q^69 - 28 * q^70 + 22 * q^71 + 14 * q^72 - 36 * q^73 - 48 * q^74 + 8 * q^75 + 28 * q^76 - 6 * q^77 - 16 * q^78 + 14 * q^79 - 32 * q^80 - 6 * q^81 + 128 * q^82 - 20 * q^83 - 72 * q^84 + 4 * q^85 + 14 * q^86 - 72 * q^87 - 76 * q^88 - 28 * q^89 - 2 * q^90 - 12 * q^91 - 40 * q^92 - 22 * q^93 + 32 * q^94 - 20 * q^95 - 82 * q^96 - 32 * q^97 + 30 * 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.e.a	$185$	$2$	185.e	37.c	$3$	$14$	$7$	$1.477$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓			185.2.e.a	$2$	$0$	\(0\)	\(-2\)	\(-7\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{4})q^{2}-\beta _{6}q^{3}+(\beta _{2}+\beta _{9}+\cdots)q^{4}+\cdots\)
185.2.e.b	$185$	$2$	185.e	37.c	$3$	$14$	$7$	$1.477$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓			185.2.e.b	$2$	$0$	\(2\)	\(-2\)	\(7\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{8}q^{2}+\beta _{6}q^{3}+(-1+\beta _{5}-\beta _{7}+\cdots)q^{4}+\cdots\)

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

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