Embedded newform 143.4.h.b.14.1

• Label: 143.4.h.b.14.1
• 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			14.1
Character	\(\chi\)	\(=\)	143.14
Dual form			143.4.h.b.92.1

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-3.97940 + 2.89120i) q^{2} +(1.95471 + 6.01598i) q^{3} +(5.00442 - 15.4020i) q^{4} +(-11.7650 - 8.54779i) q^{5} +(-25.1720 - 18.2885i) q^{6} +(3.34037 - 10.2806i) q^{7} +(12.4558 + 38.3350i) q^{8} +(-10.5277 + 7.64881i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{2} - 12 q^{3} - 148 q^{4} - 16 q^{5} + 77 q^{6} + 56 q^{7} - 34 q^{8} - 241 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−3.97940	+	2.89120i	−1.40693	+	1.02219i	−0.413169	+	0.910654i	\(0.635578\pi\)
							−0.993760	+	0.111539i	\(0.964422\pi\)
\(3\)	1.95471	+	6.01598i	0.376184	+	1.15778i	0.942676	+	0.333709i	\(0.108300\pi\)
							−0.566492	+	0.824067i	\(0.691700\pi\)
\(5\)	−11.7650	−	8.54779i	−1.05230	−	0.764538i	−0.0796480	−	0.996823i	\(-0.525380\pi\)
							−0.972648	+	0.232286i	\(0.925380\pi\)
\(7\)	3.34037	−	10.2806i	0.180363	−	0.555100i	−0.819475	−	0.573115i	\(-0.805735\pi\)
							0.999838	+	0.0180151i	\(0.00573471\pi\)
\(11\)	29.0381	+	22.0859i	0.795939	+	0.605377i
							\(13\)	10.5172	−	7.64121i	0.224381	−	0.163022i
\(17\)	−1.65231	−	1.20048i	−0.0235732	−	0.0171269i								0.575936	−	0.817495i	\(-0.304638\pi\)
							−0.599509	+	0.800368i	\(0.704638\pi\)
\(19\)	−22.8101	−	70.2021i	−0.275420	−	0.847657i	−0.989108	−	0.147192i	\(-0.952976\pi\)
							0.713688	−	0.700464i	\(-0.247024\pi\)
\(23\)	145.961			1.32326			0.661630	−	0.749830i	\(-0.269865\pi\)
							0.661630	+	0.749830i	\(0.269865\pi\)
\(29\)	−49.7223	+	153.030i	−0.318386	+	0.979892i	0.655952	+	0.754803i	\(0.272267\pi\)
							−0.974338	+	0.225089i	\(0.927733\pi\)
\(31\)	5.48663	−	3.98627i	0.0317880	−	0.0230953i	−0.571778	−	0.820409i	\(-0.693746\pi\)
							0.603566	+	0.797313i	\(0.293746\pi\)
\(37\)	138.212	−	425.374i	0.614108	−	1.89003i	0.200021	−	0.979792i	\(-0.435899\pi\)
							0.414087	−	0.910237i	\(-0.364101\pi\)
\(41\)	128.754	+	396.264i	0.490439	+	1.50942i	0.823946	+	0.566668i	\(0.191768\pi\)
							−0.333507	+	0.942747i	\(0.608232\pi\)
\(43\)	84.1153			0.298313			0.149156	−	0.988814i	\(-0.452344\pi\)
							0.149156	+	0.988814i	\(0.452344\pi\)
\(47\)	−111.123	−	342.003i	−0.344873	−	1.06141i	−0.961652	−	0.274273i	\(-0.911563\pi\)
							0.616779	−	0.787136i	\(-0.288437\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.h.b.14.1	✓	76
11.2	odd	10		1573.4.a.r.1.4		38
11.4	even	5	inner	143.4.h.b.92.1	yes	76
11.9	even	5		1573.4.a.q.1.35		38

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.b.14.1	✓	76	1.1	even	1	trivial
143.4.h.b.92.1	yes	76	11.4	even	5	inner
1573.4.a.q.1.35		38	11.9	even	5
1573.4.a.r.1.4		38	11.2	odd	10