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

• Label: 185.2.f
• Level: $185$
• Weight: $2$
• Character orbit: 185.f
• Rep. character: $\chi_{185}(43,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $34$
• Newform subspaces: $4$
• Sturm bound: $38$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 185 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(38\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

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

	Total	New	Old
Modular forms	42	42	0
Cusp forms	34	34	0
Eisenstein series	8	8	0

Trace form

34 * q + 4 * q^3 - 30 * q^4 - 6 * q^5 - 4 * q^6 - 4 * q^7 - 6 * q^10 - 32 * q^12 + 12 * q^14 + 10 * q^15 + 14 * q^16 - 20 * q^17 - 22 * q^18 + 4 * q^19 - 8 * q^20 + 20 * q^22 + 36 * q^24 + 10 * q^25 - 20 * q^27 - 8 * q^28 + 14 * q^29 - 8 * q^30 + 8 * q^33 - 26 * q^35 - 12 * q^37 - 60 * q^38 + 4 * q^39 + 18 * q^40 + 64 * q^42 + 30 * q^45 + 40 * q^46 + 12 * q^47 + 60 * q^48 + 24 * q^50 - 4 * q^51 - 10 * q^53 + 40 * q^54 + 18 * q^55 - 28 * q^56 - 22 * q^58 - 8 * q^59 - 104 * q^60 - 10 * q^61 - 32 * q^62 + 36 * q^63 - 38 * q^64 + 32 * q^65 + 16 * q^66 + 8 * q^67 + 8 * q^68 - 40 * q^69 - 20 * q^70 + 8 * q^71 + 70 * q^72 + 30 * q^73 + 34 * q^74 + 20 * q^75 - 36 * q^77 - 36 * q^78 - 40 * q^79 - 8 * q^80 - 18 * q^81 - 4 * q^82 - 24 * q^83 - 20 * q^85 + 88 * q^86 - 64 * q^87 - 24 * q^88 - 34 * q^89 - 4 * q^90 + 52 * q^91 + 52 * q^94 + 20 * q^95 - 88 * q^96 + 56 * q^97 - 102 * q^98 - 64 * 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.f.a	$185$	$2$	185.f	185.f	$4$	$2$	$1$	$1.477$	\(\Q(\sqrt{-1}) \)	None		✓			185.2.f.a	$2$	$0$	\(0\)	\(-2\)	\(-4\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-i q^{2}+(-i-1)q^{3}+q^{4}+(i-2)q^{5}+\cdots\)
185.2.f.b	$185$	$2$	185.f	185.f	$4$	$2$	$1$	$1.477$	\(\Q(\sqrt{-1}) \)	None		✓			185.2.f.b	$2$	$0$	\(0\)	\(4\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-i q^{2}+(2 i+2)q^{3}+q^{4}+(i-2)q^{5}+\cdots\)
185.2.f.c	$185$	$2$	185.f	185.f	$4$	$6$	$3$	$1.477$	6.0.350464.1	None		✓			185.2.f.c	$2$	$0$	\(0\)	\(-2\)	\(2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{5}q^{2}+(-1+\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5})q^{3}+\cdots\)
185.2.f.d	$185$	$2$	185.f	185.f	$4$	$24$	$12$	$1.477$		None		✓	✓		185.2.f.d	$2$	$0$	\(0\)	\(4\)	\(0\)	\(6\)		$\mathrm{SU}(2)[C_{4}]$