Embedded newform 143.4.n.a.25.16

• Label: 143.4.n.a.25.16
• Level: $143$
• Weight: $4$
• Character: 143.25
• Analytic conductor: $8.437$
• Analytic rank: $0$
• Dimension: $160$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.n (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.43727313082\)
Analytic rank:	\(0\)
Dimension:	\(160\)
Relative dimension:	\(40\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			25.16
Character	\(\chi\)	\(=\)	143.25
Dual form			143.4.n.a.103.16

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.959626 - 1.32081i) q^{2} +(-0.156611 - 0.482000i) q^{3} +(1.64847 - 5.07348i) q^{4} +(11.1106 - 15.2925i) q^{5} +(-0.486343 + 0.669394i) q^{6} +(30.6277 + 9.95155i) q^{7} +(-20.7047 + 6.72736i) q^{8} +(21.6357 - 15.7192i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 6 q^{3} + 146 q^{4} - 426 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).

\(n\)	\(67\)	\(79\)
\(\chi(n)\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.959626	−	1.32081i	−0.339279	−	0.466978i	0.604952	−	0.796262i	\(-0.293192\pi\)
							−0.944231	+	0.329285i	\(0.893192\pi\)
\(3\)	−0.156611	−	0.482000i	−0.0301399	−	0.0927610i	0.934855	−	0.355030i	\(-0.115529\pi\)
							−0.964995	+	0.262269i	\(0.915529\pi\)
\(5\)	11.1106	−	15.2925i	0.993767	−	1.36780i	0.0646940	−	0.997905i	\(-0.479393\pi\)
							0.929073	−	0.369897i	\(-0.120607\pi\)
\(7\)	30.6277	+	9.95155i	1.65374	+	0.537333i	0.979546	−	0.201219i	\(-0.0644904\pi\)
							0.674196	+	0.738553i	\(0.264490\pi\)
\(11\)	−19.2618	+	30.9836i	−0.527969	+	0.849263i
							\(13\)	31.0180	+	35.1410i	0.661756	+	0.749719i
\(17\)	−59.5670	−	43.2779i	−0.849830	−	0.617438i								0.0752690	−	0.997163i	\(-0.476018\pi\)
							−0.925099	+	0.379725i	\(0.876018\pi\)
\(19\)	94.5268	−	30.7136i	1.14137	−	0.370852i	0.323481	−	0.946235i	\(-0.395147\pi\)
							0.817884	+	0.575383i	\(0.195147\pi\)
\(23\)	−0.288655			−0.00261690			−0.00130845	−	0.999999i	\(-0.500416\pi\)
							−0.00130845	+	0.999999i	\(0.500416\pi\)
\(29\)	−76.1849	+	234.473i	−0.487834	+	1.50140i	0.340000	+	0.940426i	\(0.389573\pi\)
							−0.827834	+	0.560973i	\(0.810427\pi\)
\(31\)	22.6156	+	31.1277i	0.131028	+	0.180345i	0.869490	−	0.493950i	\(-0.164447\pi\)
							−0.738462	+	0.674295i	\(0.764447\pi\)
\(37\)	−288.016	−	93.5820i	−1.27972	−	0.415805i	−0.411236	−	0.911529i	\(-0.634903\pi\)
							−0.868480	+	0.495724i	\(0.834903\pi\)
\(41\)	−363.850	+	118.222i	−1.38595	+	0.450321i	−0.904620	−	0.426220i	\(-0.859845\pi\)
							−0.481327	+	0.876541i	\(0.659845\pi\)
\(43\)	−325.577			−1.15465			−0.577327	−	0.816513i	\(-0.695904\pi\)
							−0.577327	+	0.816513i	\(0.695904\pi\)
\(47\)	8.53895	−	2.77447i	0.0265007	−	0.00861061i	−0.295737	−	0.955270i	\(-0.595565\pi\)
							0.322237	+	0.946659i	\(0.395565\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.n.a.25.16	✓	160
11.4	even	5	inner	143.4.n.a.103.25	yes	160
13.12	even	2	inner	143.4.n.a.25.25	yes	160
143.103	even	10	inner	143.4.n.a.103.16	yes	160

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.n.a.25.16	✓	160	1.1	even	1	trivial
143.4.n.a.25.25	yes	160	13.12	even	2	inner
143.4.n.a.103.16	yes	160	143.103	even	10	inner
143.4.n.a.103.25	yes	160	11.4	even	5	inner