Embedded newform 23.5.d.a.5.3

• Label: 23.5.d.a.5.3
• Level: $23$
• Weight: $5$
• Character: 23.5
• 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			5.3
Character	\(\chi\)	\(=\)	23.5
Dual form			23.5.d.a.14.3

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.880608 - 0.258570i) q^{2} +(-5.57964 + 6.43925i) q^{3} +(-12.7514 - 8.19486i) q^{4} +(-17.0417 - 2.45023i) q^{5} +(6.57847 - 4.22773i) q^{6} +(-31.0622 + 14.1856i) q^{7} +(18.7264 + 21.6114i) q^{8} +(1.19597 + 8.31815i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q - 3 q^{2} + q^{3} - 35 q^{4} - 11 q^{5} - 110 q^{6} - 11 q^{7} + 146 q^{8} - 182 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(5\)
\(\chi(n)\)	\(e\left(\frac{1}{22}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.880608	−	0.258570i	−0.220152	−	0.0646424i	0.169796	−	0.985479i	\(-0.445689\pi\)
							−0.389948	+	0.920837i	\(0.627507\pi\)
\(3\)	−5.57964	+	6.43925i	−0.619960	+	0.715472i	−0.975699	−	0.219113i	\(-0.929684\pi\)
							0.355739	+	0.934585i	\(0.384229\pi\)
\(5\)	−17.0417	−	2.45023i	−0.681670	−	0.0980093i	−0.207223	−	0.978294i	\(-0.566443\pi\)
							−0.474447	+	0.880284i	\(0.657352\pi\)
\(7\)	−31.0622	+	14.1856i	−0.633923	+	0.289503i	−0.706341	−	0.707871i	\(-0.749656\pi\)
							0.0724184	+	0.997374i	\(0.476928\pi\)
\(11\)	−4.93571	−	16.8095i	−0.0407910	−	0.138921i	0.936580	−	0.350454i	\(-0.113973\pi\)
							−0.977371	+	0.211533i	\(0.932155\pi\)
\(13\)	36.7819	−	80.5412i	0.217645	−	0.476575i	−0.769044	−	0.639196i	\(-0.779267\pi\)
							0.986689	+	0.162620i	\(0.0519946\pi\)
\(17\)	−93.0499	−	144.788i	−0.321972	−	0.500998i	0.642107	−	0.766615i	\(-0.278061\pi\)
							−0.964079	+	0.265617i	\(0.914424\pi\)
\(19\)	−247.644	+	385.342i	−0.685996	+	1.06743i	0.307276	+	0.951620i	\(0.400583\pi\)
							−0.993271	+	0.115809i	\(0.963054\pi\)
\(23\)	−506.246	−	153.478i	−0.956988	−	0.290129i
							\(29\)	−213.791	+	137.395i	−0.254211	+	0.163372i	−0.661540	−	0.749910i	\(-0.730097\pi\)
0.407329	+	0.913282i	\(0.366460\pi\)
\(31\)	1010.81	+	1166.53i	1.05183	+	1.21387i	0.976230	+	0.216735i	\(0.0695409\pi\)
							0.0755973	+	0.997138i	\(0.475914\pi\)
\(37\)	53.4882	−	7.69045i	0.0390710	−	0.00561756i	−0.122752	−	0.992437i	\(-0.539172\pi\)
							0.161823	+	0.986820i	\(0.448263\pi\)
\(41\)	391.398	−	2722.24i	0.232837	−	1.61941i	−0.452898	−	0.891562i	\(-0.649610\pi\)
							0.685734	−	0.727852i	\(-0.259481\pi\)
\(43\)	1916.75	+	1660.88i	1.03664	+	0.898256i	0.994899	−	0.100872i	\(-0.0321632\pi\)
							0.0417438	+	0.999128i	\(0.486709\pi\)
\(47\)	−1493.34			−0.676026			−0.338013	−	0.941141i	\(-0.609755\pi\)
							−0.338013	+	0.941141i	\(0.609755\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.5.d.a.5.3	✓	70
23.14	odd	22	inner	23.5.d.a.14.3	yes	70

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.5.d.a.5.3	✓	70	1.1	even	1	trivial
23.5.d.a.14.3	yes	70	23.14	odd	22	inner