Embedded newform 143.4.h.a.14.2

• Label: 143.4.h.a.14.2
• Level: $143$
• Weight: $4$
• Character: 143.14
• Analytic conductor: $8.437$
• Analytic rank: $0$
• Dimension: $68$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.43727313082\)
Analytic rank:	\(0\)
Dimension:	\(68\)
Relative dimension:	\(17\) over \(\Q(\zeta_{5})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			14.2
Character	\(\chi\)	\(=\)	143.14
Dual form			143.4.h.a.92.2

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-3.47986 + 2.52827i) q^{2} +(-0.669520 - 2.06057i) q^{3} +(3.24516 - 9.98758i) q^{4} +(-8.81271 - 6.40281i) q^{5} +(7.53951 + 5.47777i) q^{6} +(1.33129 - 4.09730i) q^{7} +(3.32506 + 10.2335i) q^{8} +(18.0458 - 13.1110i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{2} + 12 q^{3} - 16 q^{4} + 24 q^{5} + 7 q^{6} + 8 q^{7} - 34 q^{8} - 55 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−3.47986	+	2.52827i	−1.23032	+	0.893877i	−0.996914	−	0.0785027i	\(-0.974986\pi\)
							−0.233403	+	0.972380i	\(0.574986\pi\)
\(3\)	−0.669520	−	2.06057i	−0.128849	−	0.396557i	0.865734	−	0.500505i	\(-0.166852\pi\)
							−0.994583	+	0.103948i	\(0.966852\pi\)
\(5\)	−8.81271	−	6.40281i	−0.788233	−	0.572684i	0.119206	−	0.992870i	\(-0.461965\pi\)
							−0.907438	+	0.420185i	\(0.861965\pi\)
\(7\)	1.33129	−	4.09730i	0.0718831	−	0.221233i	−0.908660	−	0.417536i	\(-0.862894\pi\)
							0.980543	+	0.196303i	\(0.0628936\pi\)
\(11\)	−29.8531	+	20.9713i	−0.818276	+	0.574825i
							\(13\)	−10.5172	+	7.64121i	−0.224381	+	0.163022i
\(17\)	63.3835	+	46.0508i	0.904280	+	0.656998i								0.939562	−	0.342379i	\(-0.111233\pi\)
							−0.0352815	+	0.999377i	\(0.511233\pi\)
\(19\)	4.85074	+	14.9290i	0.0585703	+	0.180261i	0.976061	−	0.217496i	\(-0.0697888\pi\)
							−0.917491	+	0.397757i	\(0.869789\pi\)
\(23\)	−124.985			−1.13310			−0.566549	−	0.824028i	\(-0.691722\pi\)
							−0.566549	+	0.824028i	\(0.691722\pi\)
\(29\)	−84.8857	+	261.251i	−0.543547	+	1.67287i	0.180871	+	0.983507i	\(0.442108\pi\)
							−0.724419	+	0.689360i	\(0.757892\pi\)
\(31\)	−119.300	+	86.6764i	−0.691190	+	0.502179i	−0.877051	−	0.480397i	\(-0.840493\pi\)
							0.185861	+	0.982576i	\(0.440493\pi\)
\(37\)	−47.8735	+	147.339i	−0.212712	+	0.654661i	0.786596	+	0.617468i	\(0.211842\pi\)
							−0.999308	+	0.0371929i	\(0.988158\pi\)
\(41\)	−53.7377	−	165.388i	−0.204693	−	0.629981i	−0.999726	−	0.0234142i	\(-0.992546\pi\)
							0.795033	−	0.606567i	\(-0.207454\pi\)
\(43\)	474.372			1.68235			0.841175	−	0.540763i	\(-0.181864\pi\)
							0.841175	+	0.540763i	\(0.181864\pi\)
\(47\)	41.0971	+	126.484i	0.127545	+	0.392544i	0.994356	−	0.106093i	\(-0.0338342\pi\)
							−0.866811	+	0.498637i	\(0.833834\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.h.a.14.2	✓	68
11.2	odd	10		1573.4.a.p.1.3		34
11.4	even	5	inner	143.4.h.a.92.2	yes	68
11.9	even	5		1573.4.a.o.1.32		34

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.14.2	✓	68	1.1	even	1	trivial
143.4.h.a.92.2	yes	68	11.4	even	5	inner
1573.4.a.o.1.32		34	11.9	even	5
1573.4.a.p.1.3		34	11.2	odd	10