Embedded newform 143.4.q.a.3.17

• Label: 143.4.q.a.3.17
• Level: $143$
• Weight: $4$
• Character: 143.3
• Analytic conductor: $8.437$
• Analytic rank: $0$
• Dimension: $320$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.q (of order \(15\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.43727313082\)
Analytic rank:	\(0\)
Dimension:	\(320\)
Relative dimension:	\(40\) over \(\Q(\zeta_{15})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			3.17
Character	\(\chi\)	\(=\)	143.3
Dual form			143.4.q.a.48.17

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.978817 - 0.435797i) q^{2} +(-5.19277 + 5.76716i) q^{3} +(-4.58488 - 5.09203i) q^{4} +(-11.4291 - 8.30375i) q^{5} +(7.59609 - 3.38200i) q^{6} +(-1.86862 - 2.07532i) q^{7} +(4.91743 + 15.1343i) q^{8} +(-3.47296 - 33.0430i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 3 q^{2} - 3 q^{3} + 149 q^{4} - 12 q^{5} - 35 q^{6} - 3 q^{7} - 44 q^{8} + 369 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(67\)	\(79\)
\(\chi(n)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{5}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.978817	−	0.435797i	−0.346064	−	0.154078i	0.226342	−	0.974048i	\(-0.427323\pi\)
							−0.572406	+	0.819970i	\(0.693990\pi\)
\(3\)	−5.19277	+	5.76716i	−0.999350	+	1.10989i	−0.00540768	+	0.999985i	\(0.501721\pi\)
							−0.993942	+	0.109905i	\(0.964945\pi\)
\(5\)	−11.4291	−	8.30375i	−1.02225	−	0.742710i	−0.0555091	−	0.998458i	\(-0.517678\pi\)
							−0.966743	+	0.255748i	\(0.917678\pi\)
\(7\)	−1.86862	−	2.07532i	−0.100896	−	0.112057i	0.690582	−	0.723254i	\(-0.257355\pi\)
							−0.791478	+	0.611198i	\(0.790688\pi\)
\(11\)	−29.6003	+	21.3266i	−0.811347	+	0.584566i
							\(13\)	7.91366	−	46.1993i	0.168835	−	0.985644i
\(17\)	−39.4527	+	17.5655i	−0.562864	+	0.250603i								−0.668387	−	0.743814i	\(-0.733015\pi\)
							0.105523	+	0.994417i	\(0.466348\pi\)
\(19\)	136.870	+	29.0925i	1.65263	+	0.351278i	0.937574	−	0.347785i	\(-0.113066\pi\)
							0.715060	+	0.699063i	\(0.246399\pi\)
\(23\)	69.1511	+	119.773i	0.626913	+	1.08585i	0.988168	+	0.153379i	\(0.0490154\pi\)
							−0.361254	+	0.932467i	\(0.617651\pi\)
\(29\)	151.501	−	32.2025i	0.970104	−	0.206202i	0.304504	−	0.952511i	\(-0.401509\pi\)
							0.665600	+	0.746309i	\(0.268176\pi\)
\(31\)	−152.919	+	111.102i	−0.885970	+	0.643695i	−0.934824	−	0.355111i	\(-0.884443\pi\)
							0.0488544	+	0.998806i	\(0.484443\pi\)
\(37\)	−34.7682	+	7.39022i	−0.154483	+	0.0328363i	−0.284504	−	0.958675i	\(-0.591829\pi\)
							0.130021	+	0.991511i	\(0.458496\pi\)
\(41\)	191.518	−	212.702i	0.729514	−	0.810207i	−0.258264	−	0.966074i	\(-0.583151\pi\)
							0.987778	+	0.155867i	\(0.0498172\pi\)
\(43\)	142.633	−	247.047i	0.505844	−	0.876148i	−0.494133	−	0.869386i	\(-0.664514\pi\)
							0.999977	−	0.00676144i	\(-0.00215225\pi\)
\(47\)	−105.378	−	324.321i	−0.327043	−	1.00653i	−0.970510	−	0.241061i	\(-0.922505\pi\)
							0.643467	−	0.765474i	\(-0.277495\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.q.a.3.17	✓	320
11.4	even	5	inner	143.4.q.a.81.24	yes	320
13.9	even	3	inner	143.4.q.a.113.24	yes	320
143.48	even	15	inner	143.4.q.a.48.17	yes	320

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.q.a.3.17	✓	320	1.1	even	1	trivial
143.4.q.a.48.17	yes	320	143.48	even	15	inner
143.4.q.a.81.24	yes	320	11.4	even	5	inner
143.4.q.a.113.24	yes	320	13.9	even	3	inner