Embedded newform 143.4.j.a.23.14

• Label: 143.4.j.a.23.14
• 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			23.14
Character	\(\chi\)	\(=\)	143.23
Dual form			143.4.j.a.56.14

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.943417 + 0.544682i) q^{2} +(-1.41111 - 2.44412i) q^{3} +(-3.40664 + 5.90048i) q^{4} +21.6301i q^{5} +(2.66254 + 1.53722i) q^{6} +(-24.7951 - 14.3155i) q^{7} -16.1371i q^{8} +(9.51752 - 16.4848i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 12 q^{3} + 152 q^{4} + 90 q^{6} - 36 q^{7} - 360 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.943417	+	0.544682i	−0.333548	+	0.192574i	−0.657415	−	0.753528i	\(-0.728350\pi\)
							0.323867	+	0.946103i	\(0.395017\pi\)
\(3\)	−1.41111	−	2.44412i	−0.271569	−	0.470371i	0.697695	−	0.716395i	\(-0.254209\pi\)
							−0.969264	+	0.246024i	\(0.920876\pi\)
\(5\)			21.6301i			1.93465i	0.253532	+	0.967327i	\(0.418408\pi\)
							−0.253532	+	0.967327i	\(0.581592\pi\)
\(7\)	−24.7951	−	14.3155i	−1.33881	−	0.772963i	−0.352181	−	0.935932i	\(-0.614560\pi\)
							−0.986631	+	0.162969i	\(0.947893\pi\)
\(11\)	−9.52628	+	5.50000i	−0.261116	+	0.150756i
							\(13\)	31.2843	+	34.9040i	0.667439	+	0.744665i
\(17\)	61.7383	−	106.934i	0.880807	−	1.52560i								0.0303625	−	0.999539i	\(-0.490334\pi\)
							0.850445	−	0.526064i	\(-0.176333\pi\)
\(19\)	−30.8476	−	17.8099i	−0.372469	−	0.215045i	0.302067	−	0.953287i	\(-0.402323\pi\)
							−0.674537	+	0.738241i	\(0.735657\pi\)
\(23\)	−30.0586	−	52.0630i	−0.272507	−	0.471995i	0.696996	−	0.717075i	\(-0.254519\pi\)
							−0.969503	+	0.245079i	\(0.921186\pi\)
\(29\)	−8.37934	−	14.5134i	−0.0536553	−	0.0929337i	0.837950	−	0.545747i	\(-0.183754\pi\)
							−0.891606	+	0.452813i	\(0.850421\pi\)
\(31\)		−	99.4093i		−	0.575949i	−0.957638	−	0.287975i	\(-0.907018\pi\)
							0.957638	−	0.287975i	\(-0.0929819\pi\)
\(37\)	−166.147	+	95.9248i	−0.738225	+	0.426214i	−0.821424	−	0.570319i	\(-0.806820\pi\)
							0.0831986	+	0.996533i	\(0.473486\pi\)
\(41\)	−206.555	+	119.254i	−0.786791	+	0.454254i	−0.838831	−	0.544391i	\(-0.816761\pi\)
							0.0520409	+	0.998645i	\(0.483427\pi\)
\(43\)	−38.0977	+	65.9871i	−0.135113	+	0.234022i	−0.925640	−	0.378404i	\(-0.876473\pi\)
							0.790528	+	0.612426i	\(0.209806\pi\)
\(47\)			74.6060i			0.231540i	0.993276	+	0.115770i	\(0.0369336\pi\)
							−0.993276	+	0.115770i	\(0.963066\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.j.a.23.14	✓	72
13.2	odd	12		1859.4.a.m.1.14		36
13.4	even	6	inner	143.4.j.a.56.14	yes	72
13.11	odd	12		1859.4.a.l.1.23		36

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.j.a.23.14	✓	72	1.1	even	1	trivial
143.4.j.a.56.14	yes	72	13.4	even	6	inner
1859.4.a.l.1.23		36	13.11	odd	12
1859.4.a.m.1.14		36	13.2	odd	12