Embedded newform 23.11.d.a.5.16

• Label: 23.11.d.a.5.16
• 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			5.16
Character	\(\chi\)	\(=\)	23.5
Dual form			23.11.d.a.14.16

$q$-expansion

\(f(q)\)	\(=\)	\(q+(43.9370 + 12.9011i) q^{2} +(-46.3131 + 53.4482i) q^{3} +(902.580 + 580.053i) q^{4} +(-2494.45 - 358.647i) q^{5} +(-2724.40 + 1750.87i) q^{6} +(-21084.8 + 9629.08i) q^{7} +(1466.36 + 1692.27i) q^{8} +(7691.74 + 53497.3i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 190 q + 13 q^{2} - 71 q^{3} - 11699 q^{4} - 11 q^{5} + 3346 q^{6} - 11 q^{7} - 50582 q^{8} - 394850 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	43.9370	+	12.9011i	1.37303	+	0.403159i	0.883338	−	0.468736i	\(-0.155290\pi\)
							0.489694	+	0.871895i	\(0.337109\pi\)
\(3\)	−46.3131	+	53.4482i	−0.190589	+	0.219952i	−0.843000	−	0.537914i	\(-0.819212\pi\)
							0.652410	+	0.757866i	\(0.273758\pi\)
\(5\)	−2494.45	−	358.647i	−0.798223	−	0.114767i	−0.268878	−	0.963174i	\(-0.586653\pi\)
							−0.529344	+	0.848407i	\(0.677562\pi\)
\(7\)	−21084.8	+	9629.08i	−1.25452	+	0.572921i	−0.928110	−	0.372307i	\(-0.878567\pi\)
							−0.326412	+	0.945228i	\(0.605840\pi\)
\(11\)	−20438.4	−	69606.7i	−0.126906	−	0.432203i	0.871387	−	0.490596i	\(-0.163221\pi\)
							−0.998294	+	0.0583924i	\(0.981403\pi\)
\(13\)	−161273.	+	353138.i	−0.434355	+	0.951104i	0.558246	+	0.829676i	\(0.311475\pi\)
							−0.992600	+	0.121428i	\(0.961253\pi\)
\(17\)	270455.	+	420836.i	0.190480	+	0.296393i	0.923338	−	0.383989i	\(-0.125450\pi\)
							−0.732857	+	0.680383i	\(0.761814\pi\)
\(19\)	709491.	−	1.10399e6i	0.286536	−	0.445858i	−0.667910	−	0.744242i	\(-0.732811\pi\)
							0.954446	+	0.298383i	\(0.0964474\pi\)
\(23\)	6.19487e6	+	1.74645e6i	0.962483	+	0.271341i
							\(29\)	−3.16463e7	+	2.03379e7i	−1.54288	+	0.991552i	−0.555806	+	0.831312i	\(0.687590\pi\)
−0.987078	+	0.160240i	\(0.948773\pi\)
\(31\)	1.45955e7	+	1.68442e7i	0.509814	+	0.588357i	0.951051	−	0.309034i	\(-0.100006\pi\)
							−0.441237	+	0.897391i	\(0.645460\pi\)
\(37\)	9.57465e7	−	1.37663e7i	1.38075	−	0.198522i	0.588390	−	0.808578i	\(-0.299762\pi\)
							0.792358	+	0.610056i	\(0.208853\pi\)
\(41\)	793094.	−	5.51609e6i	0.00684550	−	0.0476115i	−0.986112	−	0.166079i	\(-0.946889\pi\)
							0.992958	+	0.118468i	\(0.0377983\pi\)
\(43\)	1.57681e8	+	1.36632e8i	1.07260	+	0.929414i	0.997700	−	0.0677771i	\(-0.0215907\pi\)
							0.0749003	+	0.997191i	\(0.476136\pi\)
\(47\)	−8.38897e7			−0.365779			−0.182890	−	0.983133i	\(-0.558545\pi\)
							−0.182890	+	0.983133i	\(0.558545\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.11.d.a.5.16	✓	190
23.14	odd	22	inner	23.11.d.a.14.16	yes	190

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.11.d.a.5.16	✓	190	1.1	even	1	trivial
23.11.d.a.14.16	yes	190	23.14	odd	22	inner