Embedded newform 92.4.h.a.79.28

• Label: 92.4.h.a.79.28
• Level: $92$
• Weight: $4$
• Character: 92.79
• Analytic conductor: $5.428$
• Analytic rank: $0$
• Dimension: $340$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	92.h (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.42817572053\)
Analytic rank:	\(0\)
Dimension:	\(340\)
Relative dimension:	\(34\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			79.28
Character	\(\chi\)	\(=\)	92.79
Dual form			92.4.h.a.7.28

$q$-expansion

\(f(q)\)	\(=\)	\(q+(2.29918 - 1.64735i) q^{2} +(2.24967 - 3.50055i) q^{3} +(2.57248 - 7.57511i) q^{4} +(15.6896 + 7.16519i) q^{5} +(-0.594234 - 11.7544i) q^{6} +(-8.54748 - 2.50977i) q^{7} +(-6.56426 - 21.6543i) q^{8} +(4.02336 + 8.80993i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 340 q - 11 q^{2} + 13 q^{4} - 22 q^{5} + 2 q^{6} + 22 q^{8} + 252 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/92\mathbb{Z}\right)^\times\).

\(n\)	\(5\)	\(47\)
\(\chi(n)\)	\(e\left(\frac{3}{22}\right)\)	\(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

(See \(a_n\) instead)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	2.29918	−	1.64735i	0.812884	−	0.582426i
							\(3\)	2.24967	−	3.50055i	0.432948	−	0.673681i	−0.554399	−	0.832251i	\(-0.687052\pi\)
0.987348	+	0.158570i	\(0.0506883\pi\)
\(5\)	15.6896	+	7.16519i	1.40332	+	0.640874i	0.966026	−	0.258446i	\(-0.0832103\pi\)
							0.437292	+	0.899320i	\(0.355938\pi\)
\(7\)	−8.54748	−	2.50977i	−0.461520	−	0.135515i	0.0427031	−	0.999088i	\(-0.486403\pi\)
							−0.504224	+	0.863573i	\(0.668221\pi\)
\(11\)	−9.60234	+	11.0817i	−0.263201	+	0.303750i	−0.871933	−	0.489626i	\(-0.837133\pi\)
							0.608731	+	0.793376i	\(0.291679\pi\)
\(13\)	−30.9800	+	9.09654i	−0.660946	+	0.194071i	−0.594967	−	0.803750i	\(-0.702835\pi\)
							−0.0659783	+	0.997821i	\(0.521017\pi\)
\(17\)	−45.3388	+	6.51873i	−0.646839	+	0.0930014i	−0.457923	−	0.888992i	\(-0.651406\pi\)
							−0.188916	+	0.981993i	\(0.560497\pi\)
\(19\)	13.6286	−	94.7890i	0.164559	−	1.14453i	−0.725346	−	0.688385i	\(-0.758320\pi\)
							0.889905	−	0.456147i	\(-0.150771\pi\)
\(23\)	−55.9300	+	95.0728i	−0.507053	+	0.861915i
							\(29\)	28.4308	+	197.741i	0.182051	+	1.26619i	0.851905	+	0.523697i	\(0.175448\pi\)
−0.669854	+	0.742493i	\(0.733643\pi\)
\(31\)	−21.9905	−	34.2179i	−0.127407	−	0.198249i	0.771690	−	0.635999i	\(-0.219412\pi\)
							−0.899097	+	0.437750i	\(0.855775\pi\)
\(37\)	296.672	−	135.486i	1.31818	−	0.601991i	0.372783	−	0.927919i	\(-0.378404\pi\)
							0.945395	+	0.325927i	\(0.105676\pi\)
\(41\)	−104.334	+	228.459i	−0.397420	+	0.870228i	0.600105	+	0.799921i	\(0.295125\pi\)
							−0.997525	+	0.0703074i	\(0.977602\pi\)
\(43\)	−16.8020	−	10.7980i	−0.0595880	−	0.0382949i	0.510508	−	0.859873i	\(-0.329458\pi\)
							−0.570096	+	0.821578i	\(0.693094\pi\)
\(47\)			385.676i			1.19695i	0.801141	+	0.598475i	\(0.204226\pi\)
							−0.801141	+	0.598475i	\(0.795774\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.4.h.a.79.28	yes	340
4.3	odd	2	inner	92.4.h.a.79.9	yes	340
23.7	odd	22	inner	92.4.h.a.7.9	✓	340
92.7	even	22	inner	92.4.h.a.7.28	yes	340

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.4.h.a.7.9	✓	340	23.7	odd	22	inner
92.4.h.a.7.28	yes	340	92.7	even	22	inner
92.4.h.a.79.9	yes	340	4.3	odd	2	inner
92.4.h.a.79.28	yes	340	1.1	even	1	trivial