Embedded newform 23.11.d.a.5.14

• Label: 23.11.d.a.5.14
• 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			5.14
Character	\(\chi\)	\(=\)	23.5
Dual form			23.11.d.a.14.14

$q$-expansion

\(f(q)\)	\(=\)	\(q+(30.3985 + 8.92579i) q^{2} +(-183.914 + 212.248i) q^{3} +(-17.0475 - 10.9558i) q^{4} +(-1508.74 - 216.924i) q^{5} +(-7485.18 + 4810.43i) q^{6} +(12346.2 - 5638.33i) q^{7} +(-21665.5 - 25003.3i) q^{8} +(-2821.33 - 19622.8i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 190 q + 13 q^{2} - 71 q^{3} - 11699 q^{4} - 11 q^{5} + 3346 q^{6} - 11 q^{7} - 50582 q^{8} - 394850 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	30.3985	+	8.92579i	0.949952	+	0.278931i	0.719767	−	0.694216i	\(-0.244249\pi\)
							0.230185	+	0.973147i	\(0.426067\pi\)
\(3\)	−183.914	+	212.248i	−0.756848	+	0.873449i	−0.995213	−	0.0977267i	\(-0.968843\pi\)
							0.238366	+	0.971175i	\(0.423388\pi\)
\(5\)	−1508.74	−	216.924i	−0.482798	−	0.0694158i	−0.103381	−	0.994642i	\(-0.532966\pi\)
							−0.379416	+	0.925226i	\(0.623875\pi\)
\(7\)	12346.2	−	5638.33i	0.734588	−	0.335475i	−0.0127502	−	0.999919i	\(-0.504059\pi\)
							0.747339	+	0.664443i	\(0.231331\pi\)
\(11\)	−21949.7	−	74753.7i	−0.136290	−	0.464162i	0.862857	−	0.505448i	\(-0.168673\pi\)
							−0.999147	+	0.0412860i	\(0.986855\pi\)
\(13\)	241692.	−	529231.i	0.650946	−	1.42537i	−0.239777	−	0.970828i	\(-0.577074\pi\)
							0.890723	−	0.454546i	\(-0.150198\pi\)
\(17\)	−111314.	−	173208.i	−0.0783981	−	0.121990i	0.799840	−	0.600213i	\(-0.204917\pi\)
							−0.878238	+	0.478223i	\(0.841281\pi\)
\(19\)	−1.03763e6	+	1.61458e6i	−0.419058	+	0.652067i	−0.985035	−	0.172354i	\(-0.944863\pi\)
							0.565977	+	0.824421i	\(0.308499\pi\)
\(23\)	−112686.	−	6.43536e6i	−0.0175078	−	0.999847i
							\(29\)	3.78887e6	−	2.43496e6i	0.184723	−	0.118714i	−0.445011	−	0.895525i	\(-0.646800\pi\)
0.629734	+	0.776811i	\(0.283164\pi\)
\(31\)	−1.25716e7	−	1.45084e7i	−0.439120	−	0.506772i	0.492446	−	0.870343i	\(-0.336103\pi\)
							−0.931566	+	0.363571i	\(0.881557\pi\)
\(37\)	−7.96348e7	+	1.14498e7i	−1.14840	+	0.165115i	−0.690123	−	0.723692i	\(-0.742443\pi\)
							−0.458280	+	0.888808i	\(0.651534\pi\)
\(41\)	−1.11064e7	+	7.72464e7i	−0.0958633	+	0.666744i	0.884061	+	0.467372i	\(0.154799\pi\)
							−0.979924	+	0.199372i	\(0.936110\pi\)
\(43\)	1.48955e7	+	1.29070e7i	0.101324	+	0.0877978i	0.704050	−	0.710151i	\(-0.251373\pi\)
							−0.602726	+	0.797948i	\(0.705919\pi\)
\(47\)	1.47231e8			0.641965			0.320982	−	0.947085i	\(-0.395987\pi\)
							0.320982	+	0.947085i	\(0.395987\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.11.d.a.5.14	✓	190
23.14	odd	22	inner	23.11.d.a.14.14	yes	190

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.11.d.a.5.14	✓	190	1.1	even	1	trivial
23.11.d.a.14.14	yes	190	23.14	odd	22	inner