Embedded newform 23.5.d.a.7.4

• Label: 23.5.d.a.7.4
• Level: $23$
• Weight: $5$
• Character: 23.7
• Analytic conductor: $2.378$
• Analytic rank: $0$
• Dimension: $70$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	23.d (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.37750915093\)
Analytic rank:	\(0\)
Dimension:	\(70\)
Relative dimension:	\(7\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			7.4
Character	\(\chi\)	\(=\)	23.7
Dual form			23.5.d.a.10.4

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.246852 - 0.284882i) q^{2} +(2.49375 - 1.60264i) q^{3} +(2.25682 + 15.6965i) q^{4} +(37.9584 - 17.3350i) q^{5} +(0.159024 - 1.10604i) q^{6} +(-7.04577 - 23.9957i) q^{7} +(10.1026 + 6.49253i) q^{8} +(-29.9983 + 65.6870i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q - 3 q^{2} + q^{3} - 35 q^{4} - 11 q^{5} - 110 q^{6} - 11 q^{7} + 146 q^{8} - 182 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.246852	−	0.284882i	0.0617130	−	0.0712206i	−0.724054	−	0.689744i	\(-0.757723\pi\)
							0.785767	+	0.618523i	\(0.212269\pi\)
\(3\)	2.49375	−	1.60264i	0.277083	−	0.178071i	−0.394717	−	0.918803i	\(-0.629158\pi\)
							0.671801	+	0.740732i	\(0.265521\pi\)
\(5\)	37.9584	−	17.3350i	1.51834	−	0.693401i	0.530327	−	0.847793i	\(-0.322069\pi\)
							0.988010	+	0.154391i	\(0.0493417\pi\)
\(7\)	−7.04577	−	23.9957i	−0.143791	−	0.489708i	0.855829	−	0.517259i	\(-0.173047\pi\)
							−0.999620	+	0.0275505i	\(0.991229\pi\)
\(11\)	8.74019	−	7.57342i	0.0722330	−	0.0625903i	−0.617996	−	0.786181i	\(-0.712055\pi\)
							0.690229	+	0.723591i	\(0.257510\pi\)
\(13\)	−263.788	−	77.4553i	−1.56088	−	0.458315i	−0.616549	−	0.787317i	\(-0.711470\pi\)
							−0.944329	+	0.329001i	\(0.893288\pi\)
\(17\)	−197.937	−	28.4590i	−0.684902	−	0.0984741i	−0.208925	−	0.977932i	\(-0.566996\pi\)
							−0.475977	+	0.879458i	\(0.657906\pi\)
\(19\)	519.413	−	74.6803i	1.43882	−	0.206871i	0.621661	−	0.783287i	\(-0.286458\pi\)
							0.817156	+	0.576416i	\(0.195549\pi\)
\(23\)	−414.764	−	328.347i	−0.784053	−	0.620694i
							\(29\)	−107.141	+	745.185i	−0.127398	+	0.886070i	0.821438	+	0.570298i	\(0.193172\pi\)
−0.948835	+	0.315771i	\(0.897737\pi\)
\(31\)	624.622	+	401.420i	0.649971	+	0.417711i	0.823655	−	0.567091i	\(-0.191931\pi\)
							−0.173685	+	0.984801i	\(0.555567\pi\)
\(37\)	−1185.36	−	541.337i	−0.865860	−	0.395425i	−0.0675817	−	0.997714i	\(-0.521528\pi\)
							−0.798278	+	0.602289i	\(0.794256\pi\)
\(41\)	−12.7180	−	27.8486i	−0.00756575	−	0.0165667i	0.905811	−	0.423681i	\(-0.139262\pi\)
							−0.913377	+	0.407114i	\(0.866535\pi\)
\(43\)	−622.546	−	968.700i	−0.336693	−	0.523905i	0.631083	−	0.775715i	\(-0.282611\pi\)
							−0.967777	+	0.251810i	\(0.918974\pi\)
\(47\)	1085.28			0.491299			0.245650	−	0.969359i	\(-0.420999\pi\)
							0.245650	+	0.969359i	\(0.420999\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.5.d.a.7.4	✓	70
23.10	odd	22	inner	23.5.d.a.10.4	yes	70

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.5.d.a.7.4	✓	70	1.1	even	1	trivial
23.5.d.a.10.4	yes	70	23.10	odd	22	inner