Embedded newform 143.4.n.a.25.15

• Label: 143.4.n.a.25.15
• 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			25.15
Character	\(\chi\)	\(=\)	143.25
Dual form			143.4.n.a.103.15

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.00857 - 1.38817i) q^{2} +(-2.62521 - 8.07958i) q^{3} +(1.56232 - 4.80832i) q^{4} +(-2.93663 + 4.04193i) q^{5} +(-8.56815 + 11.7930i) q^{6} +(-18.0190 - 5.85473i) q^{7} +(-21.3057 + 6.92263i) q^{8} +(-36.5444 + 26.5511i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 6 q^{3} + 146 q^{4} - 426 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.00857	−	1.38817i	−0.356582	−	0.490793i	0.592610	−	0.805489i	\(-0.298097\pi\)
							−0.949193	+	0.314696i	\(0.898097\pi\)
\(3\)	−2.62521	−	8.07958i	−0.505223	−	1.55492i	−0.800396	−	0.599472i	\(-0.795377\pi\)
							0.295173	−	0.955444i	\(-0.404623\pi\)
\(5\)	−2.93663	+	4.04193i	−0.262660	+	0.361521i	−0.919895	−	0.392165i	\(-0.871726\pi\)
							0.657234	+	0.753686i	\(0.271726\pi\)
\(7\)	−18.0190	−	5.85473i	−0.972934	−	0.316126i	−0.220934	−	0.975289i	\(-0.570911\pi\)
							−0.752000	+	0.659163i	\(0.770911\pi\)
\(11\)	32.1580	+	17.2297i	0.881455	+	0.472268i
							\(13\)	30.5505	−	35.5481i	0.651784	−	0.758404i
\(17\)	−71.8476	−	52.2003i	−1.02503	−	0.744731i								−0.0577259	−	0.998332i	\(-0.518385\pi\)
							−0.967309	+	0.253601i	\(0.918385\pi\)
\(19\)	68.6924	−	22.3195i	0.829427	−	0.269497i	0.136623	−	0.990623i	\(-0.456375\pi\)
							0.692804	+	0.721126i	\(0.256375\pi\)
\(23\)	37.1472			0.336770			0.168385	−	0.985721i	\(-0.446145\pi\)
							0.168385	+	0.985721i	\(0.446145\pi\)
\(29\)	−44.0655	+	135.620i	−0.282164	+	0.868412i	0.705070	+	0.709137i	\(0.250915\pi\)
							−0.987234	+	0.159274i	\(0.949085\pi\)
\(31\)	−84.2905	−	116.016i	−0.488355	−	0.672163i	0.491728	−	0.870749i	\(-0.336365\pi\)
							−0.980084	+	0.198585i	\(0.936365\pi\)
\(37\)	−79.7643	−	25.9170i	−0.354410	−	0.115155i	0.126401	−	0.991979i	\(-0.459658\pi\)
							−0.480811	+	0.876825i	\(0.659658\pi\)
\(41\)	−379.537	+	123.319i	−1.44570	+	0.469736i	−0.923669	−	0.383191i	\(-0.874825\pi\)
							−0.522030	+	0.852927i	\(0.674825\pi\)
\(43\)	11.8543			0.0420411			0.0210206	−	0.999779i	\(-0.493308\pi\)
							0.0210206	+	0.999779i	\(0.493308\pi\)
\(47\)	−249.891	+	81.1944i	−0.775538	+	0.251988i	−0.669934	−	0.742421i	\(-0.733678\pi\)
							−0.105604	+	0.994408i	\(0.533678\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.n.a.25.15	✓	160
11.4	even	5	inner	143.4.n.a.103.26	yes	160
13.12	even	2	inner	143.4.n.a.25.26	yes	160
143.103	even	10	inner	143.4.n.a.103.15	yes	160

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.n.a.25.15	✓	160	1.1	even	1	trivial
143.4.n.a.25.26	yes	160	13.12	even	2	inner
143.4.n.a.103.15	yes	160	143.103	even	10	inner
143.4.n.a.103.26	yes	160	11.4	even	5	inner