Embedded newform 143.4.h.b.14.10

• Label: 143.4.h.b.14.10
• Level: $143$
• Weight: $4$
• Character: 143.14
• Analytic conductor: $8.437$
• Analytic rank: $0$
• Dimension: $76$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.43727313082\)
Analytic rank:	\(0\)
Dimension:	\(76\)
Relative dimension:	\(19\) over \(\Q(\zeta_{5})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			14.10
Character	\(\chi\)	\(=\)	143.14
Dual form			143.4.h.b.92.10

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.367022 + 0.266657i) q^{2} +(2.05644 + 6.32908i) q^{3} +(-2.40854 + 7.41271i) q^{4} +(4.33326 + 3.14829i) q^{5} +(-2.44245 - 1.77455i) q^{6} +(-8.57944 + 26.4048i) q^{7} +(-2.21419 - 6.81457i) q^{8} +(-13.9848 + 10.1606i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{2} - 12 q^{3} - 148 q^{4} - 16 q^{5} + 77 q^{6} + 56 q^{7} - 34 q^{8} - 241 q^{9}+O(q^{10}) \)

Character values

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

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

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.367022	+	0.266657i	−0.129762	+	0.0942776i	−0.650773	−	0.759272i	\(-0.725555\pi\)
							0.521011	+	0.853550i	\(0.325555\pi\)
\(3\)	2.05644	+	6.32908i	0.395762	+	1.21803i	0.928366	+	0.371667i	\(0.121214\pi\)
							−0.532604	+	0.846365i	\(0.678786\pi\)
\(5\)	4.33326	+	3.14829i	0.387578	+	0.281592i	0.764462	−	0.644668i	\(-0.223005\pi\)
							−0.376884	+	0.926260i	\(0.623005\pi\)
\(7\)	−8.57944	+	26.4048i	−0.463246	+	1.42572i	0.397929	+	0.917416i	\(0.369729\pi\)
							−0.861175	+	0.508308i	\(0.830271\pi\)
\(11\)	18.7532	−	31.2940i	0.514028	−	0.857774i
							\(13\)	10.5172	−	7.64121i	0.224381	−	0.163022i
\(17\)	63.5370	+	46.1623i	0.906469	+	0.658588i								0.940119	−	0.340845i	\(-0.110713\pi\)
							−0.0336502	+	0.999434i	\(0.510713\pi\)
\(19\)	−22.6595	−	69.7389i	−0.273603	−	0.842063i	−0.989586	−	0.143945i	\(-0.954021\pi\)
							0.715983	−	0.698118i	\(-0.245979\pi\)
\(23\)	47.4408			0.430091			0.215045	−	0.976604i	\(-0.431010\pi\)
							0.215045	+	0.976604i	\(0.431010\pi\)
\(29\)	−21.5072	+	66.1924i	−0.137717	+	0.423849i	−0.996003	−	0.0893229i	\(-0.971530\pi\)
							0.858286	+	0.513172i	\(0.171530\pi\)
\(31\)	−221.117	+	160.651i	−1.28109	+	0.930768i	−0.999585	−	0.0287912i	\(-0.990834\pi\)
							−0.281507	+	0.959559i	\(0.590834\pi\)
\(37\)	−72.5359	+	223.243i	−0.322293	+	0.991915i	0.650355	+	0.759630i	\(0.274620\pi\)
							−0.972648	+	0.232285i	\(0.925380\pi\)
\(41\)	95.6379	+	294.343i	0.364296	+	1.12119i	0.950421	+	0.310967i	\(0.100653\pi\)
							−0.586125	+	0.810221i	\(0.699347\pi\)
\(43\)	375.060			1.33014			0.665070	−	0.746781i	\(-0.268402\pi\)
							0.665070	+	0.746781i	\(0.268402\pi\)
\(47\)	−155.349	−	478.115i	−0.482127	−	1.48383i	−0.836099	−	0.548579i	\(-0.815169\pi\)
							0.353972	−	0.935256i	\(-0.384831\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.h.b.14.10	✓	76
11.2	odd	10		1573.4.a.r.1.19		38
11.4	even	5	inner	143.4.h.b.92.10	yes	76
11.9	even	5		1573.4.a.q.1.20		38

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.b.14.10	✓	76	1.1	even	1	trivial
143.4.h.b.92.10	yes	76	11.4	even	5	inner
1573.4.a.q.1.20		38	11.9	even	5
1573.4.a.r.1.19		38	11.2	odd	10