Space of modular forms of level 184, weight 4, and Character 184.i

• Label: 184.4.i
• Level: $184$
• Weight: $4$
• Character orbit: 184.i
• Rep. character: $\chi_{184}(9,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $180$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 184 = 2^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	184.i (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{11})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(184, [\chi])\).

	Total	New	Old
Modular forms	760	180	580
Cusp forms	680	180	500
Eisenstein series	80	0	80

Trace form

180 * q - 10 * q^5 - 134 * q^9 + 38 * q^11 - 100 * q^15 - 68 * q^17 + 182 * q^19 + 252 * q^21 + 56 * q^23 - 522 * q^25 - 444 * q^27 - 84 * q^29 - 196 * q^31 + 116 * q^33 - 1766 * q^35 - 1214 * q^37 + 176 * q^39 + 1306 * q^41 + 1606 * q^43 + 2532 * q^45 + 1008 * q^47 + 1176 * q^49 + 1152 * q^51 + 416 * q^53 - 1828 * q^55 - 2580 * q^57 - 2198 * q^59 - 690 * q^61 + 1508 * q^63 - 832 * q^65 - 270 * q^67 + 52 * q^69 + 1276 * q^71 - 244 * q^73 + 7730 * q^75 + 1704 * q^77 + 4446 * q^79 + 3402 * q^81 - 1644 * q^83 + 498 * q^85 - 13222 * q^87 - 5646 * q^89 - 10744 * q^91 - 1476 * q^93 - 7476 * q^95 - 1846 * q^97 - 5128 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(184, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
184.4.i.a	$184$	$4$	184.i	23.c	$11$	$90$	$9$	$10.856$		None		✓			184.4.i.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-87\)		$\mathrm{SU}(2)[C_{11}]$
184.4.i.b	$184$	$4$	184.i	23.c	$11$	$90$	$9$	$10.856$		None		✓			184.4.i.b	$2$	$0$	\(0\)	\(2\)	\(-10\)	\(87\)		$\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{4}^{\mathrm{old}}(184, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(184, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 2}\)