Embedded newform 23.11.d.a.7.1

• Label: 23.11.d.a.7.1
• Level: $23$
• Weight: $11$
• Character: 23.7
• 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			7.1
Character	\(\chi\)	\(=\)	23.7
Dual form			23.11.d.a.10.1

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-40.8007 + 47.0865i) q^{2} +(-166.294 + 106.871i) q^{3} +(-406.713 - 2828.75i) q^{4} +(-2779.67 + 1269.43i) q^{5} +(1752.75 - 12190.6i) q^{6} +(-4308.90 - 14674.8i) q^{7} +(96118.5 + 61771.6i) q^{8} +(-8297.48 + 18168.9i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 190 q + 13 q^{2} - 71 q^{3} - 11699 q^{4} - 11 q^{5} + 3346 q^{6} - 11 q^{7} - 50582 q^{8} - 394850 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(5\)
\(\chi(n)\)	\(e\left(\frac{19}{22}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−40.8007	+	47.0865i	−1.27502	+	1.47145i	−0.464702	+	0.885467i	\(0.653838\pi\)
							−0.810321	+	0.585987i	\(0.800707\pi\)
\(3\)	−166.294	+	106.871i	−0.684338	+	0.439797i	−0.836069	−	0.548625i	\(-0.815152\pi\)
							0.151731	+	0.988422i	\(0.451515\pi\)
\(5\)	−2779.67	+	1269.43i	−0.889493	+	0.406218i	−0.807123	−	0.590384i	\(-0.798976\pi\)
							−0.0823706	+	0.996602i	\(0.526249\pi\)
\(7\)	−4308.90	−	14674.8i	−0.256376	−	0.873135i	−0.982609	−	0.185687i	\(-0.940549\pi\)
							0.726233	−	0.687448i	\(-0.241269\pi\)
\(11\)	158384.	−	137241.i	0.983443	−	0.852158i	−0.00557045	−	0.999984i	\(-0.501773\pi\)
							0.989013	+	0.147826i	\(0.0472277\pi\)
\(13\)	−321287.	−	94338.4i	−0.865320	−	0.254081i	−0.181196	−	0.983447i	\(-0.557997\pi\)
							−0.684124	+	0.729366i	\(0.739815\pi\)
\(17\)	−1.63835e6	−	235559.i	−1.15388	−	0.165903i	−0.461302	−	0.887243i	\(-0.652618\pi\)
							−0.692581	+	0.721340i	\(0.743527\pi\)
\(19\)	−634715.	+	91258.2i	−0.256337	+	0.0368556i	−0.269285	−	0.963061i	\(-0.586787\pi\)
							0.0129484	+	0.999916i	\(0.495878\pi\)
\(23\)	2.34713e6	−	5.99312e6i	0.364668	−	0.931138i
							\(29\)	−3.75924e6	+	2.61461e7i	−0.183278	+	1.27473i	0.665669	+	0.746247i	\(0.268146\pi\)
−0.848947	+	0.528478i	\(0.822763\pi\)
\(31\)	2.18379e7	+	1.40344e7i	0.762787	+	0.490213i	0.863281	−	0.504724i	\(-0.168406\pi\)
							−0.100494	+	0.994938i	\(0.532042\pi\)
\(37\)	−3.90480e7	−	1.78326e7i	−0.563106	−	0.257162i	0.113461	−	0.993542i	\(-0.463806\pi\)
							−0.676568	+	0.736380i	\(0.736533\pi\)
\(41\)	2.37202e7	+	5.19400e7i	0.204738	+	0.448314i	0.983950	−	0.178447i	\(-0.0571073\pi\)
							−0.779211	+	0.626761i	\(0.784380\pi\)
\(43\)	1.10539e8	+	1.72002e8i	0.751921	+	1.17001i	0.980506	+	0.196488i	\(0.0629536\pi\)
							−0.228586	+	0.973524i	\(0.573410\pi\)
\(47\)	−8.55292e7			−0.372928			−0.186464	−	0.982462i	\(-0.559703\pi\)
							−0.186464	+	0.982462i	\(0.559703\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.11.d.a.7.1	✓	190
23.10	odd	22	inner	23.11.d.a.10.1	yes	190

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.11.d.a.7.1	✓	190	1.1	even	1	trivial
23.11.d.a.10.1	yes	190	23.10	odd	22	inner