Space of modular forms of level 182, weight 4, and Character 182.h

• Label: 182.4.h
• Level: $182$
• Weight: $4$
• Character orbit: 182.h
• Rep. character: $\chi_{182}(9,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $56$
• Newform subspaces: $2$
• Sturm bound: $112$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 182 = 2 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	182.h (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(112\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(182, [\chi])\).

	Total	New	Old
Modular forms	176	56	120
Cusp forms	160	56	104
Eisenstein series	16	0	16

Trace form

56 * q - 112 * q^4 + 32 * q^7 + 568 * q^9 - 80 * q^10 - 60 * q^11 - 118 * q^13 + 24 * q^14 + 128 * q^15 - 448 * q^16 + 134 * q^17 + 48 * q^18 - 540 * q^19 - 116 * q^21 + 28 * q^22 + 140 * q^23 - 636 * q^25 + 116 * q^26 + 276 * q^27 - 184 * q^28 + 294 * q^29 - 104 * q^30 - 356 * q^31 + 1528 * q^33 + 50 * q^35 - 1136 * q^36 - 812 * q^37 + 580 * q^38 - 1148 * q^39 + 160 * q^40 - 52 * q^41 - 56 * q^42 - 364 * q^43 + 120 * q^44 + 80 * q^45 + 272 * q^46 + 90 * q^47 + 494 * q^49 + 8 * q^50 - 994 * q^51 - 16 * q^52 - 1310 * q^53 - 60 * q^54 - 396 * q^55 - 144 * q^56 + 256 * q^57 + 448 * q^58 - 1096 * q^59 + 512 * q^60 - 5164 * q^61 + 1296 * q^62 + 1148 * q^63 + 3584 * q^64 + 2378 * q^65 + 2496 * q^66 + 4220 * q^67 + 536 * q^68 + 2076 * q^69 - 1776 * q^70 + 1728 * q^71 - 384 * q^72 - 674 * q^73 - 576 * q^74 - 1172 * q^75 + 1080 * q^76 + 3064 * q^77 + 296 * q^78 - 3130 * q^79 + 8680 * q^81 - 1600 * q^82 - 2320 * q^83 + 616 * q^84 - 3544 * q^85 - 1044 * q^86 + 3356 * q^87 - 224 * q^88 - 228 * q^89 - 5592 * q^90 - 2972 * q^91 - 1120 * q^92 - 1366 * q^93 - 5392 * q^94 + 1728 * q^95 - 3254 * q^97 - 1368 * q^98 - 5476 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(182, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
182.4.h.a	$182$	$4$	182.h	91.g	$3$	$28$	$14$	$10.738$		None		✓			182.4.e.b	$2$	$0$	\(-28\)	\(0\)	\(10\)	\(7\)		$\mathrm{SU}(2)[C_{3}]$
182.4.h.b	$182$	$4$	182.h	91.g	$3$	$28$	$14$	$10.738$		None		✓			182.4.e.a	$2$	$0$	\(28\)	\(0\)	\(-10\)	\(25\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{4}^{\mathrm{old}}(182, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(182, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)