Embedded newform 23.11.d.a.5.19

• Label: 23.11.d.a.5.19
• 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			5.19
Character	\(\chi\)	\(=\)	23.5
Dual form			23.11.d.a.14.19

$q$-expansion

\(f(q)\)	\(=\)	\(q+(58.0720 + 17.0515i) q^{2} +(-299.179 + 345.271i) q^{3} +(2220.16 + 1426.81i) q^{4} +(3804.62 + 547.022i) q^{5} +(-23261.3 + 14949.1i) q^{6} +(-11603.6 + 5299.20i) q^{7} +(64014.2 + 73876.3i) q^{8} +(-21300.4 - 148148. i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 190 q + 13 q^{2} - 71 q^{3} - 11699 q^{4} - 11 q^{5} + 3346 q^{6} - 11 q^{7} - 50582 q^{8} - 394850 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	58.0720	+	17.0515i	1.81475	+	0.532859i	0.998965	−	0.0454955i	\(-0.0144867\pi\)
							0.815786	+	0.578354i	\(0.196305\pi\)
\(3\)	−299.179	+	345.271i	−1.23119	+	1.42087i	−0.357833	+	0.933785i	\(0.616484\pi\)
							−0.873356	+	0.487083i	\(0.838061\pi\)
\(5\)	3804.62	+	547.022i	1.21748	+	0.175047i	0.720959	−	0.692978i	\(-0.243702\pi\)
							0.496521	+	0.868025i	\(0.334611\pi\)
\(7\)	−11603.6	+	5299.20i	−0.690405	+	0.315297i	−0.729542	−	0.683936i	\(-0.760267\pi\)
							0.0391366	+	0.999234i	\(0.487539\pi\)
\(11\)	162.476	+	553.342i	0.00100885	+	0.00343582i	0.959996	−	0.280014i	\(-0.0903392\pi\)
							−0.958987	+	0.283450i	\(0.908521\pi\)
\(13\)	77435.9	−	169561.i	0.208557	−	0.456677i	−0.776228	−	0.630452i	\(-0.782869\pi\)
							0.984785	+	0.173775i	\(0.0555967\pi\)
\(17\)	−379366.	−	590306.i	−0.267186	−	0.415750i	0.681573	−	0.731750i	\(-0.261296\pi\)
							−0.948759	+	0.316000i	\(0.897660\pi\)
\(19\)	−775679.	+	1.20698e6i	−0.313267	+	0.487452i	−0.961807	−	0.273728i	\(-0.911743\pi\)
							0.648541	+	0.761180i	\(0.275380\pi\)
\(23\)	4.61439e6	+	4.48708e6i	0.716928	+	0.697147i
							\(29\)	2.37765e7	−	1.52802e7i	1.15920	−	0.744971i	0.187748	−	0.982217i	\(-0.439881\pi\)
0.971450	+	0.237246i	\(0.0762449\pi\)
\(31\)	4.12065e6	+	4.75548e6i	0.143932	+	0.166106i	0.823138	−	0.567841i	\(-0.192221\pi\)
							−0.679206	+	0.733948i	\(0.737676\pi\)
\(37\)	1.06335e8	−	1.52886e7i	1.53344	−	0.220476i	0.676714	−	0.736246i	\(-0.263403\pi\)
							0.856727	+	0.515770i	\(0.172494\pi\)
\(41\)	−1.19923e7	+	8.34085e7i	−0.103510	+	0.719931i	0.870292	+	0.492536i	\(0.163930\pi\)
							−0.973803	+	0.227395i	\(0.926979\pi\)
\(43\)	−9.91863e7	−	8.59454e7i	−0.674698	−	0.584629i	0.248650	−	0.968593i	\(-0.420013\pi\)
							−0.923348	+	0.383964i	\(0.874559\pi\)
\(47\)	6.00903e7			0.262008			0.131004	−	0.991382i	\(-0.458180\pi\)
							0.131004	+	0.991382i	\(0.458180\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.11.d.a.5.19	✓	190
23.14	odd	22	inner	23.11.d.a.14.19	yes	190

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.11.d.a.5.19	✓	190	1.1	even	1	trivial
23.11.d.a.14.19	yes	190	23.14	odd	22	inner