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

• Label: 185.2.c
• Level: $185$
• Weight: $2$
• Character orbit: 185.c
• Rep. character: $\chi_{185}(36,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $2$
• Sturm bound: $38$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(38\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	22	14	8
Cusp forms	18	14	4
Eisenstein series	4	0	4

Trace form

14 * q + 4 * q^3 - 14 * q^4 - 16 * q^7 + 18 * q^9 - 2 * q^10 - 4 * q^11 - 32 * q^12 + 38 * q^16 - 4 * q^21 - 14 * q^25 - 12 * q^26 + 16 * q^27 + 28 * q^28 - 12 * q^30 - 24 * q^33 + 4 * q^34 - 30 * q^36 + 12 * q^37 + 12 * q^38 + 6 * q^40 - 16 * q^41 + 32 * q^44 - 24 * q^46 - 4 * q^47 + 68 * q^48 + 18 * q^49 - 24 * q^53 - 24 * q^58 + 44 * q^62 - 20 * q^63 - 110 * q^64 + 20 * q^65 + 24 * q^67 - 28 * q^70 + 60 * q^71 - 32 * q^73 + 50 * q^74 - 4 * q^75 + 24 * q^77 + 132 * q^78 - 10 * q^81 - 32 * q^83 - 80 * q^84 - 64 * q^86 - 26 * q^90 + 32 * q^95 - 72 * 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.c.a	$185$	$2$	185.c	37.b	$2$	$2$	$2$	$1.477$	\(\Q(\sqrt{-1}) \)	None		✓			185.2.c.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+2 q^{4}+i q^{5}+q^{7}-2 q^{9}+\cdots\)
185.2.c.b	$185$	$2$	185.c	37.b	$2$	$12$	$12$	$1.477$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓	✓		185.2.c.b	$2$	$0$	\(0\)	\(2\)	\(0\)	\(-18\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{9}q^{3}+(-1+\beta _{9}+\beta _{10}+\cdots)q^{4}+\cdots\)

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

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