Embedded newform 143.4.e.b.100.14

• Label: 143.4.e.b.100.14
• 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			100.14
Character	\(\chi\)	\(=\)	143.100
Dual form			143.4.e.b.133.14

$q$-expansion

\(f(q)\)	\(=\)	\(q+(1.58752 - 2.74967i) q^{2} +(0.300230 - 0.520013i) q^{3} +(-1.04047 - 1.80214i) q^{4} +12.4679 q^{5} +(-0.953244 - 1.65107i) q^{6} +(-5.31270 - 9.20186i) q^{7} +18.7933 q^{8} +(13.3197 + 23.0704i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	1.58752	−	2.74967i	0.561275	−	0.972156i	−0.436111	−	0.899893i	\(-0.643644\pi\)
							0.997386	−	0.0722633i	\(-0.0230222\pi\)
\(3\)	0.300230	−	0.520013i	0.0577792	−	0.100077i	−0.835689	−	0.549203i	\(-0.814931\pi\)
							0.893468	+	0.449126i	\(0.148265\pi\)
\(5\)	12.4679			1.11516			0.557582	−	0.830122i	\(-0.311729\pi\)
							0.557582	+	0.830122i	\(0.311729\pi\)
\(7\)	−5.31270	−	9.20186i	−0.286859	−	0.496854i	0.686200	−	0.727413i	\(-0.259278\pi\)
							−0.973058	+	0.230560i	\(0.925944\pi\)
\(11\)	−5.50000	+	9.52628i	−0.150756	+	0.261116i
							\(13\)	19.1701	−	42.7727i	0.408987	−	0.912540i
\(17\)	31.4971	+	54.5545i	0.449363	+	0.778319i								0.998345	−	0.0575153i	\(-0.0183178\pi\)
							−0.548982	+	0.835834i	\(0.684984\pi\)
\(19\)	−70.2277	−	121.638i	−0.847966	−	1.46872i	−0.883021	−	0.469334i	\(-0.844494\pi\)
							0.0350548	−	0.999385i	\(-0.488839\pi\)
\(23\)	−34.6465	+	60.0095i	−0.314100	+	0.544037i	−0.979246	−	0.202676i	\(-0.935036\pi\)
							0.665146	+	0.746714i	\(0.268369\pi\)
\(29\)	69.1320	−	119.740i	0.442672	−	0.766731i	−0.555215	−	0.831707i	\(-0.687364\pi\)
							0.997887	+	0.0649765i	\(0.0206972\pi\)
\(31\)	−168.325			−0.975229			−0.487614	−	0.873059i	\(-0.662133\pi\)
							−0.487614	+	0.873059i	\(0.662133\pi\)
\(37\)	−118.309	+	204.917i	−0.525672	+	0.910490i	0.473881	+	0.880589i	\(0.342853\pi\)
							−0.999553	+	0.0299015i	\(0.990481\pi\)
\(41\)	−103.798	+	179.784i	−0.395379	+	0.684817i	−0.993149	−	0.116851i	\(-0.962720\pi\)
							0.597770	+	0.801667i	\(0.296053\pi\)
\(43\)	150.904	+	261.373i	0.535177	+	0.926954i	0.999155	+	0.0411072i	\(0.0130885\pi\)
							−0.463977	+	0.885847i	\(0.653578\pi\)
\(47\)	−343.732			−1.06677			−0.533387	−	0.845871i	\(-0.679081\pi\)
							−0.533387	+	0.845871i	\(0.679081\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.e.b.100.14	✓	34
13.3	even	3	inner	143.4.e.b.133.14	yes	34
13.4	even	6		1859.4.a.h.1.14		17
13.9	even	3		1859.4.a.g.1.4		17

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.b.100.14	✓	34	1.1	even	1	trivial
143.4.e.b.133.14	yes	34	13.3	even	3	inner
1859.4.a.g.1.4		17	13.9	even	3
1859.4.a.h.1.14		17	13.4	even	6