Embedded newform 143.4.j.a.23.16

• Label: 143.4.j.a.23.16
• 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			23.16
Character	\(\chi\)	\(=\)	143.23
Dual form			143.4.j.a.56.16

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.737315 + 0.425689i) q^{2} +(-2.76813 - 4.79455i) q^{3} +(-3.63758 + 6.30047i) q^{4} +7.50257i q^{5} +(4.08197 + 2.35673i) q^{6} +(7.20298 + 4.15864i) q^{7} -13.0049i q^{8} +(-1.82513 + 3.16122i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 12 q^{3} + 152 q^{4} + 90 q^{6} - 36 q^{7} - 360 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.737315	+	0.425689i	−0.260680	+	0.150504i	−0.624645	−	0.780909i	\(-0.714756\pi\)
							0.363965	+	0.931413i	\(0.381423\pi\)
\(3\)	−2.76813	−	4.79455i	−0.532728	−	0.922711i	−0.999270	−	0.0382123i	\(-0.987834\pi\)
							0.466542	−	0.884499i	\(-0.345500\pi\)
\(5\)			7.50257i			0.671050i	0.942031	+	0.335525i	\(0.108914\pi\)
							−0.942031	+	0.335525i	\(0.891086\pi\)
\(7\)	7.20298	+	4.15864i	0.388924	+	0.224546i	0.681694	−	0.731637i	\(-0.261244\pi\)
							−0.292770	+	0.956183i	\(0.594577\pi\)
\(11\)	9.52628	−	5.50000i	0.261116	−	0.150756i
							\(13\)	−31.5662	−	34.6493i	−0.673453	−	0.739230i
\(17\)	−0.356986	+	0.618317i	−0.00509304	+	0.00882141i								−0.868561	−	0.495583i	\(-0.834955\pi\)
							0.863468	+	0.504404i	\(0.168288\pi\)
\(19\)	−68.0640	−	39.2967i	−0.821839	−	0.474489i	0.0292111	−	0.999573i	\(-0.490700\pi\)
							−0.851050	+	0.525084i	\(0.824034\pi\)
\(23\)	−88.1174	−	152.624i	−0.798859	−	1.38366i	−0.920360	−	0.391072i	\(-0.872104\pi\)
							0.121501	−	0.992591i	\(-0.461229\pi\)
\(29\)	−29.5580	−	51.1959i	−0.189268	−	0.327822i	0.755738	−	0.654874i	\(-0.227278\pi\)
							−0.945006	+	0.327052i	\(0.893945\pi\)
\(31\)		−	36.1060i		−	0.209188i	−0.994515	−	0.104594i	\(-0.966646\pi\)
							0.994515	−	0.104594i	\(-0.0333543\pi\)
\(37\)	301.864	−	174.281i	1.34125	−	0.774369i	0.354256	−	0.935148i	\(-0.384734\pi\)
							0.986990	+	0.160780i	\(0.0514008\pi\)
\(41\)	139.817	−	80.7235i	0.532580	−	0.307485i	−0.209487	−	0.977812i	\(-0.567179\pi\)
							0.742066	+	0.670326i	\(0.233846\pi\)
\(43\)	163.297	−	282.839i	0.579131	−	1.00308i	−0.416449	−	0.909159i	\(-0.636725\pi\)
							0.995579	−	0.0939246i	\(-0.0299413\pi\)
\(47\)			147.099i			0.456523i	0.973600	+	0.228261i	\(0.0733041\pi\)
							−0.973600	+	0.228261i	\(0.926696\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.j.a.23.16	✓	72
13.2	odd	12		1859.4.a.l.1.16		36
13.4	even	6	inner	143.4.j.a.56.16	yes	72
13.11	odd	12		1859.4.a.m.1.21		36

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.j.a.23.16	✓	72	1.1	even	1	trivial
143.4.j.a.56.16	yes	72	13.4	even	6	inner
1859.4.a.l.1.16		36	13.2	odd	12
1859.4.a.m.1.21		36	13.11	odd	12