Embedded newform 143.4.h.b.92.10

• Label: 143.4.h.b.92.10
• Level: $143$
• Weight: $4$
• Character: 143.92
• Analytic conductor: $8.437$
• Analytic rank: $0$
• Dimension: $76$
• 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			92.10
Character	\(\chi\)	\(=\)	143.92
Dual form			143.4.h.b.14.10

$q$-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 \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).

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

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	0.521011	−	0.853550i	\(-0.325555\pi\)
							−0.650773	+	0.759272i	\(0.725555\pi\)
\(3\)	2.05644	−	6.32908i	0.395762	−	1.21803i	−0.532604	−	0.846365i	\(-0.678786\pi\)
							0.928366	−	0.371667i	\(-0.121214\pi\)
\(5\)	4.33326	−	3.14829i	0.387578	−	0.281592i	−0.376884	−	0.926260i	\(-0.623005\pi\)
							0.764462	+	0.644668i	\(0.223005\pi\)
\(7\)	−8.57944	−	26.4048i	−0.463246	−	1.42572i	−0.861175	−	0.508308i	\(-0.830271\pi\)
							0.397929	−	0.917416i	\(-0.369729\pi\)
\(11\)	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								−0.0336502	−	0.999434i	\(-0.510713\pi\)
							0.940119	+	0.340845i	\(0.110713\pi\)
\(19\)	−22.6595	+	69.7389i	−0.273603	+	0.842063i	0.715983	+	0.698118i	\(0.245979\pi\)
							−0.989586	+	0.143945i	\(0.954021\pi\)
\(23\)	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	0.858286	−	0.513172i	\(-0.171530\pi\)
							−0.996003	+	0.0893229i	\(0.971530\pi\)
\(31\)	−221.117	−	160.651i	−1.28109	−	0.930768i	−0.281507	−	0.959559i	\(-0.590834\pi\)
							−0.999585	+	0.0287912i	\(0.990834\pi\)
\(37\)	−72.5359	−	223.243i	−0.322293	−	0.991915i	−0.972648	−	0.232285i	\(-0.925380\pi\)
							0.650355	−	0.759630i	\(-0.274620\pi\)
\(41\)	95.6379	−	294.343i	0.364296	−	1.12119i	−0.586125	−	0.810221i	\(-0.699347\pi\)
							0.950421	−	0.310967i	\(-0.100653\pi\)
\(43\)	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	0.353972	+	0.935256i	\(0.384831\pi\)
							−0.836099	+	0.548579i	\(0.815169\pi\)

(See \(a_n\) instead)

Twists

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

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.b.14.10	✓	76	11.3	even	5	inner
143.4.h.b.92.10	yes	76	1.1	even	1	trivial
1573.4.a.q.1.20		38	11.5	even	5
1573.4.a.r.1.19		38	11.6	odd	10