Space of modular forms of level 184, weight 4, and trivial character

• Label: 184.4.a
• Level: $184$
• Weight: $4$
• Character orbit: 184.a
• Rep. character: $\chi_{184}(1,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $6$
• Sturm bound: $96$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 184 = 2^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	184.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(96\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(184))\).

	Total	New	Old
Modular forms	76	16	60
Cusp forms	68	16	52
Eisenstein series	8	0	8

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		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(23\)	\(4\)	\(19\)		\(21\)	\(4\)	\(17\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)		\(15\)	\(3\)	\(12\)		\(13\)	\(3\)	\(10\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)		\(21\)	\(4\)	\(17\)		\(19\)	\(4\)	\(15\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)		\(17\)	\(5\)	\(12\)		\(15\)	\(5\)	\(10\)		\(2\)	\(0\)	\(2\)
Plus space		\(+\)		\(40\)	\(9\)	\(31\)		\(36\)	\(9\)	\(27\)		\(4\)	\(0\)	\(4\)
Minus space		\(-\)		\(36\)	\(7\)	\(29\)		\(32\)	\(7\)	\(25\)		\(4\)	\(0\)	\(4\)

Trace form

16 * q + 8 * q^3 + 14 * q^5 - 48 * q^7 + 156 * q^9 + 50 * q^11 - 44 * q^13 + 84 * q^15 - 32 * q^17 - 270 * q^19 - 60 * q^21 + 764 * q^25 + 140 * q^27 - 312 * q^29 + 516 * q^31 - 468 * q^33 + 432 * q^35 + 350 * q^37 + 132 * q^39 - 360 * q^41 + 6 * q^43 + 394 * q^45 - 172 * q^47 + 536 * q^49 - 92 * q^51 - 174 * q^53 - 328 * q^55 - 896 * q^57 + 520 * q^59 - 410 * q^61 - 980 * q^63 + 920 * q^65 - 106 * q^67 - 276 * q^69 - 2732 * q^71 - 64 * q^73 + 3248 * q^75 + 408 * q^77 + 1156 * q^79 - 272 * q^81 - 82 * q^83 - 3532 * q^85 + 748 * q^87 - 1392 * q^89 - 2324 * q^91 + 196 * q^93 - 2776 * q^95 - 1224 * q^97 - 2770 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(184))\) 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
184.4.a.a	$184$	$4$	184.a	1.a	$1$	$1$	$1$	$10.856$	\(\Q\)	None	✓	✓			184.4.a.a	$1$	$0$	\(0\)	\(-4\)	\(22\)	\(8\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{3}+22q^{5}+8q^{7}-11q^{9}-20q^{11}+\cdots\)
184.4.a.b	$184$	$4$	184.a	1.a	$1$	$1$	$1$	$10.856$	\(\Q\)	None	✓	✓			184.4.a.b	$1$	$0$	\(0\)	\(8\)	\(-4\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+8q^{3}-4q^{5}-4q^{7}+37q^{9}+26q^{11}+\cdots\)
184.4.a.c	$184$	$4$	184.a	1.a	$1$	$3$	$3$	$10.856$	3.3.761.1	None	✓	✓	✓	✓	184.4.a.c	$1$	$1$	\(0\)	\(-3\)	\(2\)	\(-28\)		$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{2})q^{3}+(1-\beta _{1}-\beta _{2})q^{5}+\cdots\)
184.4.a.d	$184$	$4$	184.a	1.a	$1$	$3$	$3$	$10.856$	3.3.761.1	None	✓	✓	✓		184.4.a.d	$1$	$0$	\(0\)	\(1\)	\(16\)	\(18\)		$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(5+2\beta _{1}+\beta _{2})q^{5}+(5+3\beta _{1}+\cdots)q^{7}+\cdots\)
184.4.a.e	$184$	$4$	184.a	1.a	$1$	$4$	$4$	$10.856$	4.4.167313.1	None	✓	✓	✓	✓	184.4.a.e	$1$	$1$	\(0\)	\(1\)	\(-20\)	\(-10\)		$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+(-5+\beta _{2}+\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
184.4.a.f	$184$	$4$	184.a	1.a	$1$	$4$	$4$	$10.856$	4.4.2822449.1	None	✓	✓	✓		184.4.a.f	$1$	$0$	\(0\)	\(5\)	\(-2\)	\(-32\)		$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(-1-\beta _{1}+\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(184))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(184)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 2}\)