Embedded newform 143.4.h.a.14.13

• Label: 143.4.h.a.14.13
• 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			14.13
Character	\(\chi\)	\(=\)	143.14
Dual form			143.4.h.a.92.13

$q$-expansion

\(f(q)\)	\(=\)	\(q+(2.24227 - 1.62910i) q^{2} +(2.35875 + 7.25948i) q^{3} +(-0.0983427 + 0.302668i) q^{4} +(3.65722 + 2.65713i) q^{5} +(17.1154 + 12.4351i) q^{6} +(0.863031 - 2.65614i) q^{7} +(7.12433 + 21.9264i) q^{8} +(-25.2928 + 18.3763i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{2} + 12 q^{3} - 16 q^{4} + 24 q^{5} + 7 q^{6} + 8 q^{7} - 34 q^{8} - 55 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	2.24227	−	1.62910i	0.792762	−	0.575975i	−0.116020	−	0.993247i	\(-0.537014\pi\)
							0.908782	+	0.417271i	\(0.137014\pi\)
\(3\)	2.35875	+	7.25948i	0.453941	+	1.39709i	0.872374	+	0.488839i	\(0.162579\pi\)
							−0.418433	+	0.908248i	\(0.637421\pi\)
\(5\)	3.65722	+	2.65713i	0.327112	+	0.237661i	0.739204	−	0.673481i	\(-0.235202\pi\)
							−0.412092	+	0.911142i	\(0.635202\pi\)
\(7\)	0.863031	−	2.65614i	0.0465993	−	0.143418i	−0.925050	−	0.379846i	\(-0.875977\pi\)
							0.971649	+	0.236428i	\(0.0759769\pi\)
\(11\)	−31.1505	−	18.9906i	−0.853840	−	0.520535i
							\(13\)	−10.5172	+	7.64121i	−0.224381	+	0.163022i
\(17\)	45.4517	+	33.0226i	0.648451	+	0.471127i								0.862743	−	0.505642i	\(-0.168744\pi\)
							−0.214292	+	0.976770i	\(0.568744\pi\)
\(19\)	12.6137	+	38.8209i	0.152304	+	0.468743i	0.997878	−	0.0651152i	\(-0.0207415\pi\)
							−0.845574	+	0.533859i	\(0.820741\pi\)
\(23\)	83.8545			0.760211			0.380106	−	0.924943i	\(-0.375888\pi\)
							0.380106	+	0.924943i	\(0.375888\pi\)
\(29\)	−7.09289	+	21.8297i	−0.0454178	+	0.139782i	−0.971194	−	0.238291i	\(-0.923413\pi\)
							0.925776	+	0.378072i	\(0.123413\pi\)
\(31\)	161.592	−	117.403i	0.936217	−	0.680202i	−0.0112900	−	0.999936i	\(-0.503594\pi\)
							0.947507	+	0.319735i	\(0.103594\pi\)
\(37\)	14.6837	−	45.1919i	0.0652431	−	0.200798i	−0.913121	−	0.407689i	\(-0.866335\pi\)
							0.978364	+	0.206892i	\(0.0663347\pi\)
\(41\)	−15.6342	−	48.1170i	−0.0595523	−	0.183283i	0.916855	−	0.399221i	\(-0.130719\pi\)
							−0.976407	+	0.215937i	\(0.930719\pi\)
\(43\)	330.544			1.17227			0.586134	−	0.810214i	\(-0.300649\pi\)
							0.586134	+	0.810214i	\(0.300649\pi\)
\(47\)	−119.644	−	368.227i	−0.371317	−	1.14280i	−0.945930	−	0.324372i	\(-0.894847\pi\)
							0.574612	−	0.818426i	\(-0.305153\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.h.a.14.13	✓	68
11.2	odd	10		1573.4.a.p.1.26		34
11.4	even	5	inner	143.4.h.a.92.13	yes	68
11.9	even	5		1573.4.a.o.1.9		34

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.14.13	✓	68	1.1	even	1	trivial
143.4.h.a.92.13	yes	68	11.4	even	5	inner
1573.4.a.o.1.9		34	11.9	even	5
1573.4.a.p.1.26		34	11.2	odd	10