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

• Label: 185.2.k
• Level: $185$
• Weight: $2$
• Character orbit: 185.k
• Rep. character: $\chi_{185}(68,\cdot)$
• 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.k (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 - 2 * q^2 - 4 * q^3 + 30 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 6 * q^8 - 6 * q^10 - 32 * q^12 - 12 * q^14 + 2 * q^15 + 14 * q^16 - 4 * q^19 + 18 * q^20 - 36 * q^24 - 10 * q^25 + 20 * q^27 + 8 * q^28 - 14 * q^29 + 8 * q^30 - 14 * q^32 + 8 * q^33 + 10 * q^35 + 34 * q^37 - 60 * q^38 - 4 * q^39 - 18 * q^40 - 20 * q^43 - 4 * q^45 + 40 * q^46 + 12 * q^47 - 60 * q^48 - 10 * q^50 - 4 * q^51 - 52 * q^52 - 10 * q^53 - 40 * q^54 + 6 * q^55 - 28 * q^56 - 48 * q^57 + 22 * q^58 + 8 * q^59 + 36 * q^60 - 10 * q^61 + 32 * q^62 + 36 * q^63 + 38 * q^64 - 32 * q^65 + 16 * q^66 - 8 * q^67 + 40 * q^69 - 20 * q^70 + 8 * q^71 - 30 * q^73 - 34 * q^74 + 20 * q^75 + 36 * q^77 + 36 * q^78 + 40 * q^79 + 38 * q^80 - 18 * q^81 - 24 * q^83 + 20 * q^85 + 88 * q^86 + 34 * q^89 - 4 * q^90 + 52 * q^91 + 64 * q^92 + 28 * q^93 - 52 * q^94 - 20 * q^95 - 88 * q^96 + 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.k.a	$185$	$2$	185.k	185.k	$4$	$2$	$1$	$1.477$	\(\Q(\sqrt{-1}) \)	None		✓			185.2.f.b	$2$	$1$	\(-2\)	\(-4\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-q^{2}+(2 i-2)q^{3}-q^{4}+(2 i-1)q^{5}+\cdots\)
185.2.k.b	$185$	$2$	185.k	185.k	$4$	$2$	$1$	$1.477$	\(\Q(\sqrt{-1}) \)	None		✓			185.2.f.a	$2$	$0$	\(-2\)	\(2\)	\(-2\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-q^{2}+(-i+1)q^{3}-q^{4}+(2 i-1)q^{5}+\cdots\)
185.2.k.c	$185$	$2$	185.k	185.k	$4$	$6$	$3$	$1.477$	6.0.350464.1	None		✓			185.2.f.c	$2$	$0$	\(-2\)	\(2\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{3}q^{2}+(1-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5})q^{3}+\cdots\)
185.2.k.d	$185$	$2$	185.k	185.k	$4$	$24$	$12$	$1.477$		None		✓	✓		185.2.f.d	$2$	$0$	\(4\)	\(-4\)	\(8\)	\(6\)		$\mathrm{SU}(2)[C_{4}]$