Embedded newform 143.4.h.b.14.5

• Label: 143.4.h.b.14.5
• 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			14.5
Character	\(\chi\)	\(=\)	143.14
Dual form			143.4.h.b.92.5

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-2.72658 + 1.98097i) q^{2} +(0.202439 + 0.623042i) q^{3} +(1.03782 - 3.19409i) q^{4} +(-5.78677 - 4.20434i) q^{5} +(-1.78619 - 1.29775i) q^{6} +(-10.4846 + 32.2682i) q^{7} +(-4.83397 - 14.8774i) q^{8} +(21.4963 - 15.6179i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{2} - 12 q^{3} - 148 q^{4} - 16 q^{5} + 77 q^{6} + 56 q^{7} - 34 q^{8} - 241 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−2.72658	+	1.98097i	−0.963990	+	0.700380i	−0.954074	−	0.299571i	\(-0.903156\pi\)
							−0.00991600	+	0.999951i	\(0.503156\pi\)
\(3\)	0.202439	+	0.623042i	0.0389594	+	0.119905i	0.968645	−	0.248450i	\(-0.0799212\pi\)
							−0.929685	+	0.368355i	\(0.879921\pi\)
\(5\)	−5.78677	−	4.20434i	−0.517585	−	0.376047i	0.298108	−	0.954532i	\(-0.403644\pi\)
							−0.815693	+	0.578485i	\(0.803644\pi\)
\(7\)	−10.4846	+	32.2682i	−0.566114	+	1.74232i	0.0985038	+	0.995137i	\(0.468594\pi\)
							−0.664618	+	0.747183i	\(0.731406\pi\)
\(11\)	−35.5348	+	8.26313i	−0.974013	+	0.226494i
							\(13\)	10.5172	−	7.64121i	0.224381	−	0.163022i
\(17\)	−94.7897	−	68.8688i	−1.35235	−	0.982537i								−0.998891	−	0.0470858i	\(-0.985007\pi\)
							−0.353456	−	0.935451i	\(-0.614993\pi\)
\(19\)	−8.53199	−	26.2588i	−0.103020	−	0.317062i	0.886241	−	0.463225i	\(-0.153308\pi\)
							−0.989261	+	0.146163i	\(0.953308\pi\)
\(23\)	209.861			1.90257			0.951286	−	0.308311i	\(-0.0997638\pi\)
							0.951286	+	0.308311i	\(0.0997638\pi\)
\(29\)	61.8625	−	190.393i	0.396123	−	1.21914i	−0.531960	−	0.846769i	\(-0.678544\pi\)
							0.928083	−	0.372372i	\(-0.121456\pi\)
\(31\)	66.4440	−	48.2744i	0.384958	−	0.279688i	−0.378428	−	0.925631i	\(-0.623535\pi\)
							0.763386	+	0.645942i	\(0.223535\pi\)
\(37\)	22.3871	−	68.9005i	0.0994709	−	0.306140i	−0.888922	−	0.458058i	\(-0.848545\pi\)
							0.988393	+	0.151918i	\(0.0485451\pi\)
\(41\)	−32.5777	−	100.264i	−0.124092	−	0.381916i	0.869642	−	0.493682i	\(-0.164349\pi\)
							−0.993735	+	0.111766i	\(0.964349\pi\)
\(43\)	−220.207			−0.780959			−0.390480	−	0.920612i	\(-0.627691\pi\)
							−0.390480	+	0.920612i	\(0.627691\pi\)
\(47\)	22.6511	+	69.7129i	0.0702980	+	0.216355i	0.980033	−	0.198834i	\(-0.0637155\pi\)
							−0.909735	+	0.415189i	\(0.863715\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.h.b.14.5	✓	76
11.2	odd	10		1573.4.a.r.1.11		38
11.4	even	5	inner	143.4.h.b.92.5	yes	76
11.9	even	5		1573.4.a.q.1.28		38

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.b.14.5	✓	76	1.1	even	1	trivial
143.4.h.b.92.5	yes	76	11.4	even	5	inner
1573.4.a.q.1.28		38	11.9	even	5
1573.4.a.r.1.11		38	11.2	odd	10