Embedded newform 143.4.h.a.14.8

• Label: 143.4.h.a.14.8
• Level: $143$
• Weight: $4$
• Character: 143.14
• Analytic conductor: $8.437$
• Analytic rank: $0$
• Dimension: $68$
• 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:	\(68\)
Relative dimension:	\(17\) over \(\Q(\zeta_{5})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			14.8
Character	\(\chi\)	\(=\)	143.14
Dual form			143.4.h.a.92.8

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.400584 + 0.291041i) q^{2} +(0.225252 + 0.693255i) q^{3} +(-2.39637 + 7.37528i) q^{4} +(16.7143 + 12.1437i) q^{5} +(-0.291998 - 0.212149i) q^{6} +(-2.65028 + 8.15671i) q^{7} +(-2.41064 - 7.41918i) q^{8} +(21.4136 - 15.5579i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{2} + 12 q^{3} - 16 q^{4} + 24 q^{5} + 7 q^{6} + 8 q^{7} - 34 q^{8} - 55 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.400584	+	0.291041i	−0.141628	+	0.102899i	−0.656343	−	0.754463i	\(-0.727898\pi\)
							0.514715	+	0.857361i	\(0.327898\pi\)
\(3\)	0.225252	+	0.693255i	0.0433498	+	0.133417i	0.970389	−	0.241547i	\(-0.0776549\pi\)
							−0.927039	+	0.374964i	\(0.877655\pi\)
\(5\)	16.7143	+	12.1437i	1.49497	+	1.08616i	0.972330	+	0.233610i	\(0.0750539\pi\)
							0.522643	+	0.852552i	\(0.324946\pi\)
\(7\)	−2.65028	+	8.15671i	−0.143101	+	0.440421i	−0.996762	−	0.0804088i	\(-0.974377\pi\)
							0.853660	+	0.520830i	\(0.174377\pi\)
\(11\)	−36.1356	+	5.02193i	−0.990481	+	0.137652i
							\(13\)	−10.5172	+	7.64121i	−0.224381	+	0.163022i
\(17\)	2.27357	+	1.65184i	0.0324365	+	0.0235665i								0.603885	−	0.797071i	\(-0.293618\pi\)
							−0.571449	+	0.820638i	\(0.693618\pi\)
\(19\)	23.1939	+	71.3834i	0.280055	+	0.861919i	0.987838	+	0.155489i	\(0.0496954\pi\)
							−0.707783	+	0.706430i	\(0.750305\pi\)
\(23\)	63.3410			0.574239			0.287120	−	0.957895i	\(-0.407302\pi\)
							0.287120	+	0.957895i	\(0.407302\pi\)
\(29\)	34.7058	−	106.813i	0.222231	−	0.683957i	−0.776330	−	0.630327i	\(-0.782921\pi\)
							0.998561	−	0.0536299i	\(-0.0170791\pi\)
\(31\)	−162.518	+	118.076i	−0.941582	+	0.684099i	−0.948801	−	0.315875i	\(-0.897702\pi\)
							0.00721889	+	0.999974i	\(0.497702\pi\)
\(37\)	30.1092	−	92.6665i	0.133782	−	0.411737i	−0.861617	−	0.507559i	\(-0.830548\pi\)
							0.995398	+	0.0958219i	\(0.0305479\pi\)
\(41\)	−124.179	−	382.183i	−0.473012	−	1.45578i	−0.848621	−	0.529002i	\(-0.822566\pi\)
							0.375609	−	0.926778i	\(-0.377434\pi\)
\(43\)	−266.165			−0.943949			−0.471974	−	0.881612i	\(-0.656459\pi\)
							−0.471974	+	0.881612i	\(0.656459\pi\)
\(47\)	39.4244	+	121.336i	0.122354	+	0.376567i	0.993410	−	0.114617i	\(-0.0365642\pi\)
							−0.871056	+	0.491184i	\(0.836564\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.h.a.14.8	✓	68
11.2	odd	10		1573.4.a.p.1.16		34
11.4	even	5	inner	143.4.h.a.92.8	yes	68
11.9	even	5		1573.4.a.o.1.19		34

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.14.8	✓	68	1.1	even	1	trivial
143.4.h.a.92.8	yes	68	11.4	even	5	inner
1573.4.a.o.1.19		34	11.9	even	5
1573.4.a.p.1.16		34	11.2	odd	10