Embedded newform 143.4.j.a.23.4

• Label: 143.4.j.a.23.4
• Level: $143$
• Weight: $4$
• Character: 143.23
• Analytic conductor: $8.437$
• Analytic rank: $0$
• Dimension: $72$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.j (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.43727313082\)
Analytic rank:	\(0\)
Dimension:	\(72\)
Relative dimension:	\(36\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.4
Character	\(\chi\)	\(=\)	143.23
Dual form			143.4.j.a.56.4

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-4.25281 + 2.45536i) q^{2} +(-2.48451 - 4.30330i) q^{3} +(8.05759 - 13.9562i) q^{4} -14.5097i q^{5} +(21.1323 + 12.2007i) q^{6} +(21.5060 + 12.4165i) q^{7} +39.8514i q^{8} +(1.15443 - 1.99953i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 12 q^{3} + 152 q^{4} + 90 q^{6} - 36 q^{7} - 360 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(67\)	\(79\)
\(\chi(n)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−4.25281	+	2.45536i	−1.50360	+	0.868101i	−0.503604	+	0.863935i	\(0.667993\pi\)
							−0.999991	+	0.00416637i	\(0.998674\pi\)
\(3\)	−2.48451	−	4.30330i	−0.478144	−	0.828170i	0.521542	−	0.853226i	\(-0.325357\pi\)
							−0.999686	+	0.0250559i	\(0.992024\pi\)
\(5\)		−	14.5097i		−	1.29779i	−0.760879	−	0.648893i	\(-0.775232\pi\)
							0.760879	−	0.648893i	\(-0.224768\pi\)
\(7\)	21.5060	+	12.4165i	1.16122	+	0.670429i	0.951595	−	0.307354i	\(-0.0994436\pi\)
							0.209621	+	0.977783i	\(0.432777\pi\)
\(11\)	9.52628	−	5.50000i	0.261116	−	0.150756i
							\(13\)	−37.1603	−	28.5677i	−0.792801	−	0.609481i
\(17\)	43.3129	−	75.0201i	0.617937	−	1.07030i								−0.371925	−	0.928263i	\(-0.621302\pi\)
							0.989862	−	0.142035i	\(-0.0453645\pi\)
\(19\)	106.498	+	61.4864i	1.28591	+	0.742419i	0.977922	−	0.208972i	\(-0.0670118\pi\)
							0.307985	+	0.951391i	\(0.400345\pi\)
\(23\)	53.3882	+	92.4710i	0.484009	+	0.838328i	0.999831	−	0.0183677i	\(-0.00584696\pi\)
							−0.515823	+	0.856695i	\(0.672514\pi\)
\(29\)	−117.589	−	203.669i	−0.752953	−	1.30415i	−0.946385	−	0.323040i	\(-0.895295\pi\)
							0.193432	−	0.981114i	\(-0.438038\pi\)
\(31\)		−	236.429i		−	1.36980i	−0.728637	−	0.684900i	\(-0.759846\pi\)
							0.728637	−	0.684900i	\(-0.240154\pi\)
\(37\)	−24.8385	+	14.3405i	−0.110363	+	0.0637179i	−0.554165	−	0.832407i	\(-0.686962\pi\)
							0.443803	+	0.896125i	\(0.353629\pi\)
\(41\)	110.811	−	63.9767i	0.422092	−	0.243695i	−0.273880	−	0.961764i	\(-0.588307\pi\)
							0.695972	+	0.718069i	\(0.254974\pi\)
\(43\)	−179.432	+	310.785i	−0.636350	+	1.10219i	0.349877	+	0.936796i	\(0.386223\pi\)
							−0.986227	+	0.165395i	\(0.947110\pi\)
\(47\)		−	335.949i		−	1.04262i	−0.853367	−	0.521310i	\(-0.825443\pi\)
							0.853367	−	0.521310i	\(-0.174557\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.j.a.23.4	✓	72
13.2	odd	12		1859.4.a.l.1.4		36
13.4	even	6	inner	143.4.j.a.56.4	yes	72
13.11	odd	12		1859.4.a.m.1.33		36

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.j.a.23.4	✓	72	1.1	even	1	trivial
143.4.j.a.56.4	yes	72	13.4	even	6	inner
1859.4.a.l.1.4		36	13.2	odd	12
1859.4.a.m.1.33		36	13.11	odd	12