Embedded newform 143.4.h.a.14.3

• Label: 143.4.h.a.14.3
• 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			14.3
Character	\(\chi\)	\(=\)	143.14
Dual form			143.4.h.a.92.3

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-3.01508 + 2.19058i) q^{2} +(2.64240 + 8.13246i) q^{3} +(1.81991 - 5.60111i) q^{4} +(9.33768 + 6.78422i) q^{5} +(-25.7819 - 18.7316i) q^{6} +(-3.65701 + 11.2551i) q^{7} +(-2.43074 - 7.48105i) q^{8} +(-37.3112 + 27.1082i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{2} + 12 q^{3} - 16 q^{4} + 24 q^{5} + 7 q^{6} + 8 q^{7} - 34 q^{8} - 55 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−3.01508	+	2.19058i	−1.06599	+	0.774488i	−0.975187	−	0.221381i	\(-0.928944\pi\)
							−0.0908039	+	0.995869i	\(0.528944\pi\)
\(3\)	2.64240	+	8.13246i	0.508530	+	1.56509i	0.794755	+	0.606931i	\(0.207600\pi\)
							−0.286225	+	0.958162i	\(0.592400\pi\)
\(5\)	9.33768	+	6.78422i	0.835187	+	0.606799i	0.921022	−	0.389510i	\(-0.127356\pi\)
							−0.0858349	+	0.996309i	\(0.527356\pi\)
\(7\)	−3.65701	+	11.2551i	−0.197460	+	0.607719i	0.802479	+	0.596680i	\(0.203514\pi\)
							−0.999939	+	0.0110390i	\(0.996486\pi\)
\(11\)	13.3344	+	33.9587i	0.365499	+	0.930812i
							\(13\)	−10.5172	+	7.64121i	−0.224381	+	0.163022i
\(17\)	18.9147	+	13.7424i	0.269853	+	0.196060i								0.714479	−	0.699656i	\(-0.246664\pi\)
							−0.444627	+	0.895716i	\(0.646664\pi\)
\(19\)	−11.9266	−	36.7063i	−0.144008	−	0.443210i	0.852874	−	0.522116i	\(-0.174857\pi\)
							−0.996882	+	0.0789061i	\(0.974857\pi\)
\(23\)	22.1550			0.200854			0.100427	−	0.994944i	\(-0.467979\pi\)
							0.100427	+	0.994944i	\(0.467979\pi\)
\(29\)	56.5213	−	173.955i	0.361922	−	1.11388i	−0.589964	−	0.807429i	\(-0.700858\pi\)
							0.951886	−	0.306452i	\(-0.0991418\pi\)
\(31\)	162.109	−	117.779i	0.939216	−	0.682380i	−0.00901599	−	0.999959i	\(-0.502870\pi\)
							0.948232	+	0.317579i	\(0.102870\pi\)
\(37\)	−99.2730	+	305.531i	−0.441091	+	1.35754i	0.445623	+	0.895221i	\(0.352982\pi\)
							−0.886714	+	0.462318i	\(0.847018\pi\)
\(41\)	−149.149	−	459.032i	−0.568125	−	1.74851i	−0.658480	−	0.752598i	\(-0.728800\pi\)
							0.0903551	−	0.995910i	\(-0.471200\pi\)
\(43\)	288.716			1.02393			0.511963	−	0.859008i	\(-0.328919\pi\)
							0.511963	+	0.859008i	\(0.328919\pi\)
\(47\)	4.34059	+	13.3590i	0.0134711	+	0.0414597i	0.957566	−	0.288214i	\(-0.0930614\pi\)
							−0.944095	+	0.329673i	\(0.893061\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.h.a.14.3	✓	68
11.2	odd	10		1573.4.a.p.1.6		34
11.4	even	5	inner	143.4.h.a.92.3	yes	68
11.9	even	5		1573.4.a.o.1.29		34

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.14.3	✓	68	1.1	even	1	trivial
143.4.h.a.92.3	yes	68	11.4	even	5	inner
1573.4.a.o.1.29		34	11.9	even	5
1573.4.a.p.1.6		34	11.2	odd	10