Embedded newform 143.4.e.b.100.6

• Label: 143.4.e.b.100.6
• 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			100.6
Character	\(\chi\)	\(=\)	143.100
Dual form			143.4.e.b.133.6

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.944521 + 1.63596i) q^{2} +(-0.783201 + 1.35654i) q^{3} +(2.21576 + 3.83781i) q^{4} +2.20557 q^{5} +(-1.47950 - 2.56257i) q^{6} +(0.902360 + 1.56293i) q^{7} -23.4837 q^{8} +(12.2732 + 21.2578i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.944521	+	1.63596i	−0.333938	+	0.578398i	−0.983280	−	0.182098i	\(-0.941711\pi\)
							0.649342	+	0.760497i	\(0.275044\pi\)
\(3\)	−0.783201	+	1.35654i	−0.150727	+	0.261067i	−0.931495	−	0.363754i	\(-0.881495\pi\)
							0.780768	+	0.624821i	\(0.214828\pi\)
\(5\)	2.20557			0.197272			0.0986359	−	0.995124i	\(-0.468552\pi\)
							0.0986359	+	0.995124i	\(0.468552\pi\)
\(7\)	0.902360	+	1.56293i	0.0487229	+	0.0843905i	0.889358	−	0.457211i	\(-0.151152\pi\)
							−0.840635	+	0.541601i	\(0.817818\pi\)
\(11\)	−5.50000	+	9.52628i	−0.150756	+	0.261116i
							\(13\)	22.7888	+	40.9594i	0.486190	+	0.873853i
\(17\)	−49.5741	−	85.8649i	−0.707264	−	1.22502i								−0.965868	−	0.259034i	\(-0.916596\pi\)
							0.258604	−	0.965983i	\(-0.416737\pi\)
\(19\)	−8.59144	−	14.8808i	−0.103737	−	0.179678i	0.809484	−	0.587142i	\(-0.199747\pi\)
							−0.913222	+	0.407463i	\(0.866413\pi\)
\(23\)	−78.0771	+	135.234i	−0.707835	+	1.22601i	0.257824	+	0.966192i	\(0.416995\pi\)
							−0.965659	+	0.259814i	\(0.916339\pi\)
\(29\)	−25.3935	+	43.9828i	−0.162602	+	0.281635i	−0.935801	−	0.352529i	\(-0.885322\pi\)
							0.773199	+	0.634163i	\(0.218655\pi\)
\(31\)	35.0502			0.203071			0.101535	−	0.994832i	\(-0.467624\pi\)
							0.101535	+	0.994832i	\(0.467624\pi\)
\(37\)	−93.9055	+	162.649i	−0.417242	+	0.722685i	−0.995661	−	0.0930550i	\(-0.970337\pi\)
							0.578418	+	0.815740i	\(0.303670\pi\)
\(41\)	140.100	−	242.661i	0.533659	−	0.924324i	−0.465568	−	0.885012i	\(-0.654150\pi\)
							0.999227	−	0.0393118i	\(-0.0125166\pi\)
\(43\)	152.418	+	263.995i	0.540546	+	0.936254i	0.998873	+	0.0474696i	\(0.0151157\pi\)
							−0.458326	+	0.888784i	\(0.651551\pi\)
\(47\)	314.310			0.975465			0.487732	−	0.872993i	\(-0.337824\pi\)
							0.487732	+	0.872993i	\(0.337824\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.e.b.100.6	✓	34
13.3	even	3	inner	143.4.e.b.133.6	yes	34
13.4	even	6		1859.4.a.h.1.6		17
13.9	even	3		1859.4.a.g.1.12		17

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.b.100.6	✓	34	1.1	even	1	trivial
143.4.e.b.133.6	yes	34	13.3	even	3	inner
1859.4.a.g.1.12		17	13.9	even	3
1859.4.a.h.1.6		17	13.4	even	6