Embedded newform 143.4.o.a.32.15

• Label: 143.4.o.a.32.15
• Level: $143$
• Weight: $4$
• Character: 143.32
• Analytic conductor: $8.437$
• Analytic rank: $0$
• Dimension: $160$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.o (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.43727313082\)
Analytic rank:	\(0\)
Dimension:	\(160\)
Relative dimension:	\(40\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			32.15
Character	\(\chi\)	\(=\)	143.32
Dual form			143.4.o.a.76.15

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.41412 + 0.378911i) q^{2} +(1.05641 - 1.82975i) q^{3} +(-5.07206 + 2.92835i) q^{4} +(4.68157 - 4.68157i) q^{5} +(-0.800569 + 2.98776i) q^{6} +(-20.9341 - 5.60929i) q^{7} +(14.3445 - 14.3445i) q^{8} +(11.2680 + 19.5168i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 4 q^{3} - 12 q^{4} - 8 q^{5} - 652 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(67\)	\(79\)
\(\chi(n)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.41412	+	0.378911i	−0.499965	+	0.133965i	−0.499984	−	0.866035i	\(-0.666661\pi\)
							1.86669e−5		1.00000i	\(0.499994\pi\)
\(3\)	1.05641	−	1.82975i	0.203306	−	0.352136i	−0.746286	−	0.665626i	\(-0.768165\pi\)
							0.949592	+	0.313490i	\(0.101498\pi\)
\(5\)	4.68157	−	4.68157i	0.418732	−	0.418732i	−0.466034	−	0.884767i	\(-0.654318\pi\)
							0.884767	+	0.466034i	\(0.154318\pi\)
\(7\)	−20.9341	−	5.60929i	−1.13034	−	0.302873i	−0.355278	−	0.934761i	\(-0.615614\pi\)
							−0.775060	+	0.631888i	\(0.782280\pi\)
\(11\)	32.9391	+	15.6849i	0.902864	+	0.429926i
							\(13\)	−30.7215	+	35.4004i	−0.655431	+	0.755255i
\(17\)	−4.52546	−	7.83832i	−0.0645638	−	0.111828i								0.831937	−	0.554871i	\(-0.187232\pi\)
							−0.896500	+	0.443043i	\(0.853899\pi\)
\(19\)	−26.4630	+	98.7614i	−0.319528	+	1.19250i	0.600171	+	0.799872i	\(0.295099\pi\)
							−0.919699	+	0.392624i	\(0.871567\pi\)
\(23\)	123.340	+	71.2105i	1.11818	+	0.645583i	0.940936	−	0.338583i	\(-0.109948\pi\)
							0.177246	+	0.984166i	\(0.443281\pi\)
\(29\)	75.7339	+	43.7250i	0.484946	+	0.279984i	0.722475	−	0.691397i	\(-0.243004\pi\)
							−0.237529	+	0.971380i	\(0.576338\pi\)
\(31\)	−222.907	+	222.907i	−1.29146	+	1.29146i	−0.357581	+	0.933882i	\(0.616398\pi\)
							−0.933882	+	0.357581i	\(0.883602\pi\)
\(37\)	5.39897	−	1.44665i	0.0239888	−	0.00642777i	−0.246805	−	0.969065i	\(-0.579381\pi\)
							0.270793	+	0.962637i	\(0.412714\pi\)
\(41\)	191.318	−	51.2635i	0.728753	−	0.195269i	0.124679	−	0.992197i	\(-0.460210\pi\)
							0.604074	+	0.796928i	\(0.293543\pi\)
\(43\)	−49.1219	−	85.0817i	−0.174210	−	0.301740i	0.765678	−	0.643224i	\(-0.222404\pi\)
							−0.939888	+	0.341484i	\(0.889070\pi\)
\(47\)	−69.9218	−	69.9218i	−0.217003	−	0.217003i	0.590231	−	0.807234i	\(-0.299037\pi\)
							−0.807234	+	0.590231i	\(0.799037\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.o.a.32.15	✓	160
11.10	odd	2	inner	143.4.o.a.32.26	yes	160
13.11	odd	12	inner	143.4.o.a.76.26	yes	160
143.76	even	12	inner	143.4.o.a.76.15	yes	160

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.o.a.32.15	✓	160	1.1	even	1	trivial
143.4.o.a.32.26	yes	160	11.10	odd	2	inner
143.4.o.a.76.15	yes	160	143.76	even	12	inner
143.4.o.a.76.26	yes	160	13.11	odd	12	inner