Embedded newform 143.4.e.b.100.8

• Label: 143.4.e.b.100.8
• Level: $143$
• Weight: $4$
• Character: 143.100
• Analytic conductor: $8.437$
• Analytic rank: $0$
• Dimension: $34$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.43727313082\)
Analytic rank:	\(0\)
Dimension:	\(34\)
Relative dimension:	\(17\) over \(\Q(\zeta_{3})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.8
Character	\(\chi\)	\(=\)	143.100
Dual form			143.4.e.b.133.8

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.495908 + 0.858937i) q^{2} +(2.68049 - 4.64275i) q^{3} +(3.50815 + 6.07630i) q^{4} +18.5970 q^{5} +(2.65856 + 4.60475i) q^{6} +(6.70244 + 11.6090i) q^{7} -14.8934 q^{8} +(-0.870106 - 1.50707i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(67\)	\(79\)
\(\chi(n)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.495908	+	0.858937i	−0.175330	+	0.303680i	−0.940275	−	0.340415i	\(-0.889433\pi\)
							0.764946	+	0.644095i	\(0.222766\pi\)
\(3\)	2.68049	−	4.64275i	0.515861	−	0.893498i	−0.483969	−	0.875085i	\(-0.660805\pi\)
							0.999830	−	0.0184132i	\(-0.00586142\pi\)
\(5\)	18.5970			1.66336			0.831681	−	0.555253i	\(-0.187379\pi\)
							0.831681	+	0.555253i	\(0.187379\pi\)
\(7\)	6.70244	+	11.6090i	0.361898	+	0.626825i	0.988273	−	0.152696i	\(-0.0487956\pi\)
							−0.626375	+	0.779521i	\(0.715462\pi\)
\(11\)	−5.50000	+	9.52628i	−0.150756	+	0.261116i
							\(13\)	−44.3782	−	15.0856i	−0.946792	−	0.321845i
\(17\)	−3.51179	−	6.08259i	−0.0501020	−	0.0867792i								0.839887	−	0.542762i	\(-0.182621\pi\)
							−0.889989	+	0.455982i	\(0.849288\pi\)
\(19\)	−1.46921	−	2.54475i	−0.0177400	−	0.0307266i	0.857019	−	0.515285i	\(-0.172314\pi\)
							−0.874759	+	0.484558i	\(0.838980\pi\)
\(23\)	31.3502	−	54.3002i	0.284216	−	0.492277i	−0.688203	−	0.725519i	\(-0.741600\pi\)
							0.972419	+	0.233242i	\(0.0749333\pi\)
\(29\)	55.6211	−	96.3386i	0.356158	−	0.616884i	−0.631157	−	0.775655i	\(-0.717420\pi\)
							0.987315	+	0.158771i	\(0.0507531\pi\)
\(31\)	−117.698			−0.681910			−0.340955	−	0.940080i	\(-0.610750\pi\)
							−0.340955	+	0.940080i	\(0.610750\pi\)
\(37\)	−31.4051	+	54.3952i	−0.139540	+	0.241690i	−0.927322	−	0.374263i	\(-0.877896\pi\)
							0.787783	+	0.615953i	\(0.211229\pi\)
\(41\)	−8.52428	+	14.7645i	−0.0324700	+	0.0562397i	−0.881804	−	0.471617i	\(-0.843671\pi\)
							0.849334	+	0.527856i	\(0.177004\pi\)
\(43\)	−218.064	−	377.697i	−0.773358	−	1.33950i	−0.935713	−	0.352763i	\(-0.885242\pi\)
							0.162354	−	0.986732i	\(-0.448091\pi\)
\(47\)	595.205			1.84722			0.923612	−	0.383328i	\(-0.125222\pi\)
							0.923612	+	0.383328i	\(0.125222\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.e.b.100.8	✓	34
13.3	even	3	inner	143.4.e.b.133.8	yes	34
13.4	even	6		1859.4.a.h.1.8		17
13.9	even	3		1859.4.a.g.1.10		17

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.b.100.8	✓	34	1.1	even	1	trivial
143.4.e.b.133.8	yes	34	13.3	even	3	inner
1859.4.a.g.1.10		17	13.9	even	3
1859.4.a.h.1.8		17	13.4	even	6