Space of modular forms of level 184, weight 2, and Character 184.b

• Label: 184.2.b
• Level: $184$
• Weight: $2$
• Character orbit: 184.b
• Rep. character: $\chi_{184}(93,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $3$
• Sturm bound: $48$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 184 = 2^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	184.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(48\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(184, [\chi])\).

	Total	New	Old
Modular forms	26	22	4
Cusp forms	22	22	0
Eisenstein series	4	0	4

Trace form

22 * q + 3 * q^6 + 3 * q^8 - 22 * q^9 - 2 * q^10 + q^12 - 8 * q^14 - 16 * q^16 - 4 * q^17 - 7 * q^18 + 16 * q^20 + 20 * q^22 - 6 * q^23 - 18 * q^25 + 5 * q^26 + 6 * q^28 + 26 * q^30 + 12 * q^31 + 8 * q^33 - 10 * q^34 + 7 * q^36 + 12 * q^38 - 4 * q^39 - 22 * q^40 - 4 * q^41 - 44 * q^42 + 18 * q^44 - 4 * q^47 - 39 * q^48 + 6 * q^49 - 28 * q^50 + q^52 + 15 * q^54 + 16 * q^55 - 22 * q^56 + 8 * q^57 - 15 * q^58 + 56 * q^60 - 29 * q^62 - 40 * q^63 + 3 * q^64 + 16 * q^65 + 34 * q^66 - 32 * q^68 + 16 * q^70 + 4 * q^71 - 33 * q^72 - 4 * q^73 - 10 * q^74 - 28 * q^76 + 57 * q^78 + 22 * q^80 + 30 * q^81 - 9 * q^82 + 18 * q^84 - 22 * q^86 + 20 * q^87 + 60 * q^88 - 20 * q^89 + 16 * q^90 - 39 * q^94 + 56 * q^95 + 41 * q^96 - 4 * q^97 - 32 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(184, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
184.2.b.a	$184$	$2$	184.b	8.b	$2$	$2$	$2$	$1.469$	\(\Q(\sqrt{-2}) \)	None		✓			184.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-2\beta q^{3}-2q^{4}-\beta q^{5}+4q^{6}+\cdots\)
184.2.b.b	$184$	$2$	184.b	8.b	$2$	$8$	$8$	$1.469$	8.0.5198736512.1	None		✓			184.2.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}-\beta _{4}q^{3}+\beta _{1}q^{4}-\beta _{6}q^{5}+\cdots\)
184.2.b.c	$184$	$2$	184.b	8.b	$2$	$12$	$12$	$1.469$	12.0.\(\cdots\).1	None		✓	✓		184.2.b.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)