Space of modular forms of level 184, weight 2, and trivial character

• Label: 184.2.a
• Level: $184$
• Weight: $2$
• Character orbit: 184.a
• Rep. character: $\chi_{184}(1,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $5$
• Sturm bound: $48$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 184 = 2^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	184.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(48\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(184))\).

	Total	New	Old
Modular forms	28	6	22
Cusp forms	21	6	15
Eisenstein series	7	0	7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(23\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(1\)
\(+\)	\(-\)	\(-\)	\(2\)
\(-\)	\(+\)	\(-\)	\(2\)
\(-\)	\(-\)	\(+\)	\(1\)
Plus space		\(+\)	\(2\)
Minus space		\(-\)	\(4\)

Trace form

6 * q - 2 * q^5 + 2 * q^9 + 2 * q^11 + 4 * q^15 - 4 * q^17 + 2 * q^19 - 4 * q^21 - 2 * q^25 + 12 * q^27 + 12 * q^29 - 12 * q^31 - 12 * q^33 - 18 * q^37 - 28 * q^39 + 4 * q^41 - 10 * q^43 + 18 * q^45 + 4 * q^47 - 2 * q^49 + 4 * q^51 - 6 * q^53 + 24 * q^55 - 26 * q^61 - 20 * q^63 + 16 * q^65 + 6 * q^67 + 4 * q^69 + 4 * q^71 - 20 * q^73 - 24 * q^75 + 24 * q^77 + 4 * q^79 + 6 * q^81 + 14 * q^83 + 20 * q^85 + 28 * q^87 + 12 * q^89 - 36 * q^91 + 28 * q^93 - 8 * q^95 - 12 * q^97 + 14 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(184))\) 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					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	23
184.2.a.a	$184$	$2$	184.a	1.a	$1$	$1$	$1$	$1.469$	\(\Q\)	None	✓	✓	✓	✓	184.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}+2q^{7}-2q^{9}-4q^{11}+\cdots\)
184.2.a.b	$184$	$2$	184.a	1.a	$1$	$1$	$1$	$1.469$	\(\Q\)	None	✓	✓	✓	✓	184.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}-4q^{7}-2q^{9}-2q^{11}+\cdots\)
184.2.a.c	$184$	$2$	184.a	1.a	$1$	$1$	$1$	$1.469$	\(\Q\)	None	✓	✓			184.2.a.c	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}-3q^{9}+6q^{11}-2q^{13}+6q^{17}+\cdots\)
184.2.a.d	$184$	$2$	184.a	1.a	$1$	$1$	$1$	$1.469$	\(\Q\)	None	✓	✓			184.2.a.d	$1$	$0$	\(0\)	\(3\)	\(0\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-2q^{7}+6q^{9}-5q^{13}-6q^{17}+\cdots\)
184.2.a.e	$184$	$2$	184.a	1.a	$1$	$2$	$2$	$1.469$	\(\Q(\sqrt{17}) \)	None	✓	✓	✓	✓	184.2.a.e	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+2q^{5}+(1+\beta )q^{9}+2\beta q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(184))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(184)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 2}\)