Newform orbit 92.8.e.a

• Label: 92.8.e.a
• Level: $92$
• Weight: $8$
• Character orbit: 92.e
• Analytic conductor: $28.739$
• Analytic rank: $0$
• Dimension: $140$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	92.e (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(28.7394223445\)
Analytic rank:	\(0\)
Dimension:	\(140\)
Relative dimension:	\(14\) over \(\Q(\zeta_{11})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 140 q + 26 q^{3} + 110 q^{5} + 394 q^{7} - 10856 q^{9}+O(q^{10}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
9.1		0		−50.6801	−	58.4880i		0		−18.4955	−	128.639i		0		−104.219	+	228.208i		0		−541.126	+	3763.62i		0
9.2		0		−46.4379	−	53.5921i		0		60.8697	+	423.358i		0		666.841	−	1460.18i		0		−404.401	+	2812.67i		0
9.3		0		−35.0754	−	40.4791i		0		67.9083	+	472.313i		0		−751.649	+	1645.88i		0		−97.0358	+	674.899i		0
9.4		0		−35.0471	−	40.4465i		0		−48.5188	−	337.456i		0		−247.216	+	541.327i		0		−96.3791	+	670.331i		0
9.5		0		−29.0905	−	33.5722i		0		−4.82427	−	33.5536i		0		340.263	−	745.072i		0		30.4059	−	211.478i		0
9.6		0		−2.04753	−	2.36298i		0		31.8954	+	221.838i		0		−24.3248	+	53.2639i		0		309.851	−	2155.06i		0
9.7		0		0.222562	+	0.256850i		0		−71.7150	−	498.789i		0		502.871	−	1101.13i		0		311.226	−	2164.63i		0
9.8		0		1.45484	+	1.67898i		0		−2.15745	−	15.0054i		0		−217.955	+	477.256i		0		310.540	−	2159.85i		0
9.9		0		6.30894	+	7.28091i		0		39.5529	+	275.096i		0		175.326	−	383.910i		0		298.034	−	2072.87i		0
9.10		0		22.0407	+	25.4364i		0		−52.1222	−	362.518i		0		−639.061	+	1399.35i		0		150.028	−	1043.47i		0
9.11		0		35.8216	+	41.3403i		0		2.20997	+	15.3707i		0		581.322	−	1272.92i		0		−114.593	+	797.011i		0
9.12		0		44.6506	+	51.5295i		0		74.0892	+	515.301i		0		39.6795	−	86.8860i		0		−350.374	+	2436.91i		0
9.13		0		45.1919	+	52.1543i		0		16.0610	+	111.707i		0		−452.924	+	991.765i		0		−366.515	+	2549.16i		0
9.14		0		49.7603	+	57.4264i		0		−39.9710	−	278.004i		0		154.339	−	337.956i		0		−510.467	+	3550.37i		0
13.1		0		−75.6080	−	48.5903i		0		−13.3661	+	29.2676i		0		−360.153	−	105.751i		0		2447.04	+	5358.27i		0
13.2		0		−58.4912	−	37.5900i		0		83.3496	−	182.510i		0		505.796	+	148.515i		0		1099.70	+	2408.00i		0
13.3		0		−38.2886	−	24.6066i		0		−190.677	+	417.525i		0		−1509.64	−	443.271i		0		−47.9791	−	105.060i		0
13.4		0		−37.8122	−	24.3004i		0		−173.633	+	380.203i		0		1064.12	+	312.454i		0		−69.2610	−	151.660i		0
13.5		0		−35.2784	−	22.6720i		0		−24.4830	+	53.6103i		0		204.110	+	59.9322i		0		−177.971	−	389.701i		0
13.6		0		−27.3818	−	17.5972i		0		132.859	−	290.920i		0		−1422.87	−	417.792i		0		−468.412	−	1025.68i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
23.c	even	11	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	92.8.e.a	✓	140
23.c	even	11	1	inner	92.8.e.a	✓	140

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
92.8.e.a	✓	140	1.a	even	1	1	trivial
92.8.e.a	✓	140	23.c	even	11	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{8}^{\mathrm{new}}(92, [\chi])\).