Embedded newform 23.11.d.a.5.17

• Label: 23.11.d.a.5.17
• Level: $23$
• Weight: $11$
• Character: 23.5
• Analytic conductor: $14.613$
• Analytic rank: $0$
• Dimension: $190$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	23.d (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.6132168115\)
Analytic rank:	\(0\)
Dimension:	\(190\)
Relative dimension:	\(19\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.17
Character	\(\chi\)	\(=\)	23.5
Dual form			23.11.d.a.14.17

$q$-expansion

\(f(q)\)	\(=\)	\(q+(47.0781 + 13.8234i) q^{2} +(169.037 - 195.079i) q^{3} +(1163.81 + 747.938i) q^{4} +(3647.86 + 524.483i) q^{5} +(10654.6 - 6847.29i) q^{6} +(-5261.26 + 2402.74i) q^{7} +(11548.9 + 13328.1i) q^{8} +(-1078.80 - 7503.20i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 190 q + 13 q^{2} - 71 q^{3} - 11699 q^{4} - 11 q^{5} + 3346 q^{6} - 11 q^{7} - 50582 q^{8} - 394850 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/23\mathbb{Z}\right)^\times\).

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

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	47.0781	+	13.8234i	1.47119	+	0.431980i	0.916486	−	0.400068i	\(-0.131013\pi\)
							0.554704	+	0.832048i	\(0.312832\pi\)
\(3\)	169.037	−	195.079i	0.695625	−	0.802795i	−0.292529	−	0.956257i	\(-0.594497\pi\)
							0.988155	+	0.153462i	\(0.0490423\pi\)
\(5\)	3647.86	+	524.483i	1.16731	+	0.167834i	0.698598	−	0.715514i	\(-0.253808\pi\)
							0.468716	+	0.883349i	\(0.344717\pi\)
\(7\)	−5261.26	+	2402.74i	−0.313040	+	0.142960i	−0.565739	−	0.824584i	\(-0.691409\pi\)
							0.252699	+	0.967545i	\(0.418682\pi\)
\(11\)	−11038.3	−	37592.9i	−0.0685390	−	0.233423i	0.918099	−	0.396352i	\(-0.129724\pi\)
							−0.986638	+	0.162929i	\(0.947906\pi\)
\(13\)	141890.	−	310695.i	0.382150	−	0.836792i	−0.616622	−	0.787259i	\(-0.711499\pi\)
							0.998772	−	0.0495331i	\(-0.0157733\pi\)
\(17\)	785502.	+	1.22227e6i	0.553226	+	0.860837i	0.999418	−	0.0341003i	\(-0.0108566\pi\)
							−0.446192	+	0.894937i	\(0.647220\pi\)
\(19\)	−1.19522e6	+	1.85979e6i	−0.482702	+	0.751098i	−0.994126	−	0.108230i	\(-0.965482\pi\)
							0.511424	+	0.859328i	\(0.329118\pi\)
\(23\)	−6.34633e6	−	1.07265e6i	−0.986015	−	0.166655i
							\(29\)	−4.61873e6	+	2.96828e6i	−0.225182	+	0.144715i	−0.648368	−	0.761327i	\(-0.724548\pi\)
0.423186	+	0.906043i	\(0.360912\pi\)
\(31\)	6.12995e6	+	7.07434e6i	0.214116	+	0.247103i	0.852640	−	0.522499i	\(-0.175000\pi\)
							−0.638524	+	0.769602i	\(0.720455\pi\)
\(37\)	−7.46237e7	+	1.07293e7i	−1.07614	+	0.154725i	−0.657521	−	0.753437i	\(-0.728395\pi\)
							−0.418619	+	0.908162i	\(0.637486\pi\)
\(41\)	−6.55909e6	+	4.56195e7i	−0.0566140	+	0.393759i	0.941737	+	0.336351i	\(0.109193\pi\)
							−0.998351	+	0.0574084i	\(0.981716\pi\)
\(43\)	−1.32408e8	−	1.14732e8i	−0.900681	−	0.780444i	0.0755581	−	0.997141i	\(-0.475926\pi\)
							−0.976239	+	0.216697i	\(0.930472\pi\)
\(47\)	−2.59367e8			−1.13090			−0.565451	−	0.824782i	\(-0.691298\pi\)
							−0.565451	+	0.824782i	\(0.691298\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.11.d.a.5.17	✓	190
23.14	odd	22	inner	23.11.d.a.14.17	yes	190

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.11.d.a.5.17	✓	190	1.1	even	1	trivial
23.11.d.a.14.17	yes	190	23.14	odd	22	inner