Embedded newform 143.4.j.a.23.12

• Label: 143.4.j.a.23.12
• 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			23.12
Character	\(\chi\)	\(=\)	143.23
Dual form			143.4.j.a.56.12

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-2.21820 + 1.28068i) q^{2} +(0.591773 + 1.02498i) q^{3} +(-0.719733 + 1.24661i) q^{4} -4.85042i q^{5} +(-2.62534 - 1.51574i) q^{6} +(5.49965 + 3.17522i) q^{7} -24.1778i q^{8} +(12.7996 - 22.1696i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 12 q^{3} + 152 q^{4} + 90 q^{6} - 36 q^{7} - 360 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−2.21820	+	1.28068i	−0.784251	+	0.452788i	−0.837935	−	0.545770i	\(-0.816237\pi\)
							0.0536835	+	0.998558i	\(0.482904\pi\)
\(3\)	0.591773	+	1.02498i	0.113887	+	0.197258i	0.917334	−	0.398118i	\(-0.130337\pi\)
							−0.803447	+	0.595376i	\(0.797003\pi\)
\(5\)		−	4.85042i		−	0.433835i	−0.976190	−	0.216918i	\(-0.930400\pi\)
							0.976190	−	0.216918i	\(-0.0696003\pi\)
\(7\)	5.49965	+	3.17522i	0.296953	+	0.171446i	0.641073	−	0.767480i	\(-0.278489\pi\)
							−0.344120	+	0.938926i	\(0.611823\pi\)
\(11\)	9.52628	−	5.50000i	0.261116	−	0.150756i
							\(13\)	3.21137	+	46.7620i	0.0685133	+	0.997650i
\(17\)	34.2308	−	59.2895i	0.488364	−	0.845871i								−0.511547	−	0.859256i	\(-0.670927\pi\)
							0.999910	+	0.0133846i	\(0.00426057\pi\)
\(19\)	19.0329	+	10.9887i	0.229813	+	0.132683i	0.610486	−	0.792027i	\(-0.290974\pi\)
							−0.380673	+	0.924710i	\(0.624308\pi\)
\(23\)	19.1270	+	33.1290i	0.173403	+	0.300342i	0.939607	−	0.342255i	\(-0.111191\pi\)
							−0.766205	+	0.642596i	\(0.777857\pi\)
\(29\)	126.223	+	218.625i	0.808243	+	1.39992i	0.914080	+	0.405535i	\(0.132915\pi\)
							−0.105836	+	0.994384i	\(0.533752\pi\)
\(31\)			98.5002i			0.570682i	0.958426	+	0.285341i	\(0.0921069\pi\)
							−0.958426	+	0.285341i	\(0.907893\pi\)
\(37\)	−8.87515	+	5.12407i	−0.0394342	+	0.0227673i	−0.519587	−	0.854417i	\(-0.673914\pi\)
							0.480153	+	0.877185i	\(0.340581\pi\)
\(41\)	272.300	−	157.212i	1.03722	−	0.598840i	0.118176	−	0.992993i	\(-0.462295\pi\)
							0.919045	+	0.394153i	\(0.128962\pi\)
\(43\)	124.889	−	216.314i	0.442917	−	0.767155i	−0.554988	−	0.831859i	\(-0.687277\pi\)
							0.997904	+	0.0647041i	\(0.0206104\pi\)
\(47\)		−	21.9504i		−	0.0681232i	−0.999420	−	0.0340616i	\(-0.989156\pi\)
							0.999420	−	0.0340616i	\(-0.0108442\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.j.a.23.12	✓	72
13.2	odd	12		1859.4.a.l.1.13		36
13.4	even	6	inner	143.4.j.a.56.12	yes	72
13.11	odd	12		1859.4.a.m.1.24		36

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.j.a.23.12	✓	72	1.1	even	1	trivial
143.4.j.a.56.12	yes	72	13.4	even	6	inner
1859.4.a.l.1.13		36	13.2	odd	12
1859.4.a.m.1.24		36	13.11	odd	12