Embedded newform 143.4.n.a.25.20

• Label: 143.4.n.a.25.20
• 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			25.20
Character	\(\chi\)	\(=\)	143.25
Dual form			143.4.n.a.103.20

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.249988 - 0.344080i) q^{2} +(-1.06869 - 3.28909i) q^{3} +(2.41624 - 7.43642i) q^{4} +(-0.222452 + 0.306179i) q^{5} +(-0.864547 + 1.18995i) q^{6} +(24.1058 + 7.83243i) q^{7} +(-6.39867 + 2.07905i) q^{8} +(12.1675 - 8.84018i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 6 q^{3} + 146 q^{4} - 426 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.249988	−	0.344080i	−0.0883843	−	0.121651i	0.762535	−	0.646947i	\(-0.223954\pi\)
							−0.850919	+	0.525296i	\(0.823954\pi\)
\(3\)	−1.06869	−	3.28909i	−0.205669	−	0.632985i	−0.999685	−	0.0250880i	\(-0.992013\pi\)
							0.794016	−	0.607897i	\(-0.207987\pi\)
\(5\)	−0.222452	+	0.306179i	−0.0198967	+	0.0273855i	−0.818849	−	0.574008i	\(-0.805388\pi\)
							0.798953	+	0.601394i	\(0.205388\pi\)
\(7\)	24.1058	+	7.83243i	1.30159	+	0.422912i	0.876134	−	0.482068i	\(-0.160114\pi\)
							0.425455	+	0.904980i	\(0.360114\pi\)
\(11\)	32.5526	−	16.4720i	0.892272	−	0.451499i
							\(13\)	−42.1107	−	20.5836i	−0.898417	−	0.439144i
\(17\)	−34.6330	−	25.1623i	−0.494102	−	0.358986i								0.312658	−	0.949866i	\(-0.398781\pi\)
							−0.806760	+	0.590880i	\(0.798781\pi\)
\(19\)	−19.5242	+	6.34379i	−0.235745	+	0.0765982i	−0.424507	−	0.905425i	\(-0.639553\pi\)
							0.188762	+	0.982023i	\(0.439553\pi\)
\(23\)	−107.754			−0.976884			−0.488442	−	0.872596i	\(-0.662435\pi\)
							−0.488442	+	0.872596i	\(0.662435\pi\)
\(29\)	94.2020	−	289.924i	0.603202	−	1.85647i	0.0944964	−	0.995525i	\(-0.469876\pi\)
							0.508706	−	0.860940i	\(-0.330124\pi\)
\(31\)	121.536	+	167.281i	0.704148	+	0.969177i	0.999903	+	0.0139131i	\(0.00442881\pi\)
							−0.295755	+	0.955264i	\(0.595571\pi\)
\(37\)	85.3852	+	27.7433i	0.379385	+	0.123270i	0.492500	−	0.870312i	\(-0.336083\pi\)
							−0.113115	+	0.993582i	\(0.536083\pi\)
\(41\)	−12.3402	+	4.00957i	−0.0470052	+	0.0152729i	−0.332425	−	0.943130i	\(-0.607867\pi\)
							0.285420	+	0.958403i	\(0.407867\pi\)
\(43\)	255.885			0.907490			0.453745	−	0.891132i	\(-0.350088\pi\)
							0.453745	+	0.891132i	\(0.350088\pi\)
\(47\)	−310.331	+	100.833i	−0.963115	+	0.312935i	−0.748034	−	0.663661i	\(-0.769002\pi\)
							−0.215082	+	0.976596i	\(0.569002\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.n.a.25.20	✓	160
11.4	even	5	inner	143.4.n.a.103.21	yes	160
13.12	even	2	inner	143.4.n.a.25.21	yes	160
143.103	even	10	inner	143.4.n.a.103.20	yes	160

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.n.a.25.20	✓	160	1.1	even	1	trivial
143.4.n.a.25.21	yes	160	13.12	even	2	inner
143.4.n.a.103.20	yes	160	143.103	even	10	inner
143.4.n.a.103.21	yes	160	11.4	even	5	inner