Embedded newform 23.5.d.a.7.7

• Label: 23.5.d.a.7.7
• 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			7.7
Character	\(\chi\)	\(=\)	23.7
Dual form			23.5.d.a.10.7

$q$-expansion

\(f(q)\)	\(=\)	\(q+(4.33983 - 5.00844i) q^{2} +(-1.84102 + 1.18315i) q^{3} +(-3.97323 - 27.6344i) q^{4} +(8.83387 - 4.03429i) q^{5} +(-2.06398 + 14.3553i) q^{6} +(6.57566 + 22.3946i) q^{7} +(-66.4470 - 42.7029i) q^{8} +(-31.6591 + 69.3238i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q - 3 q^{2} + q^{3} - 35 q^{4} - 11 q^{5} - 110 q^{6} - 11 q^{7} + 146 q^{8} - 182 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	4.33983	−	5.00844i	1.08496	−	1.25211i	0.119143	−	0.992877i	\(-0.461985\pi\)
							0.965815	−	0.259232i	\(-0.0834693\pi\)
\(3\)	−1.84102	+	1.18315i	−0.204558	+	0.131461i	−0.638909	−	0.769282i	\(-0.720614\pi\)
							0.434351	+	0.900744i	\(0.356978\pi\)
\(5\)	8.83387	−	4.03429i	0.353355	−	0.161372i	−0.230827	−	0.972995i	\(-0.574143\pi\)
							0.584181	+	0.811623i	\(0.301416\pi\)
\(7\)	6.57566	+	22.3946i	0.134197	+	0.457034i	0.998982	−	0.0451089i	\(-0.0143635\pi\)
							−0.864785	+	0.502142i	\(0.832545\pi\)
\(11\)	19.4181	−	16.8258i	0.160480	−	0.139057i	−0.570919	−	0.821006i	\(-0.693413\pi\)
							0.731399	+	0.681950i	\(0.238868\pi\)
\(13\)	204.758	+	60.1224i	1.21159	+	0.355754i	0.824272	−	0.566193i	\(-0.191584\pi\)
							0.387315	+	0.921947i	\(0.373403\pi\)
\(17\)	−533.474	−	76.7019i	−1.84593	−	0.265405i	−0.871549	−	0.490309i	\(-0.836884\pi\)
							−0.974381	+	0.224904i	\(0.927793\pi\)
\(19\)	−310.874	+	44.6970i	−0.861147	+	0.123814i	−0.558718	−	0.829358i	\(-0.688707\pi\)
							−0.302429	+	0.953172i	\(0.597798\pi\)
\(23\)	292.823	−	440.563i	0.553540	−	0.832822i
							\(29\)	11.6435	−	80.9821i	0.0138448	−	0.0962926i	−0.981727	−	0.190293i	\(-0.939056\pi\)
0.995572	+	0.0940001i	\(0.0299654\pi\)
\(31\)	−1028.90	−	661.236i	−1.07066	−	0.688071i	−0.118278	−	0.992981i	\(-0.537737\pi\)
							−0.952381	+	0.304910i	\(0.901374\pi\)
\(37\)	1161.29	+	530.344i	0.848277	+	0.387395i	0.791631	−	0.610999i	\(-0.209232\pi\)
							0.0566456	+	0.998394i	\(0.481959\pi\)
\(41\)	94.3217	+	206.536i	0.0561105	+	0.122865i	0.935610	−	0.353034i	\(-0.114850\pi\)
							−0.879500	+	0.475899i	\(0.842123\pi\)
\(43\)	227.251	+	353.610i	0.122905	+	0.191244i	0.897254	−	0.441515i	\(-0.145559\pi\)
							−0.774349	+	0.632759i	\(0.781922\pi\)
\(47\)	1620.42			0.733555			0.366777	−	0.930309i	\(-0.380461\pi\)
							0.366777	+	0.930309i	\(0.380461\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.5.d.a.7.7	✓	70
23.10	odd	22	inner	23.5.d.a.10.7	yes	70

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.5.d.a.7.7	✓	70	1.1	even	1	trivial
23.5.d.a.10.7	yes	70	23.10	odd	22	inner