Embedded newform 143.4.h.a.14.15

• Label: 143.4.h.a.14.15
• 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			14.15
Character	\(\chi\)	\(=\)	143.14
Dual form			143.4.h.a.92.15

$q$-expansion

\(f(q)\)	\(=\)	\(q+(3.57791 - 2.59950i) q^{2} +(0.693568 + 2.13458i) q^{3} +(3.57187 - 10.9931i) q^{4} +(11.6383 + 8.45575i) q^{5} +(8.03038 + 5.83441i) q^{6} +(-10.3864 + 31.9661i) q^{7} +(-4.86361 - 14.9687i) q^{8} +(17.7680 - 12.9092i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{2} + 12 q^{3} - 16 q^{4} + 24 q^{5} + 7 q^{6} + 8 q^{7} - 34 q^{8} - 55 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	3.57791	−	2.59950i	1.26498	−	0.919062i	0.265990	−	0.963976i	\(-0.414301\pi\)
							0.998991	+	0.0449135i	\(0.0143012\pi\)
\(3\)	0.693568	+	2.13458i	0.133477	+	0.410801i	0.995350	−	0.0963237i	\(-0.0307084\pi\)
							−0.861873	+	0.507125i	\(0.830708\pi\)
\(5\)	11.6383	+	8.45575i	1.04097	+	0.756306i	0.970474	−	0.241207i	\(-0.0775432\pi\)
							0.0704917	+	0.997512i	\(0.477543\pi\)
\(7\)	−10.3864	+	31.9661i	−0.560814	+	1.72601i	0.119257	+	0.992863i	\(0.461949\pi\)
							−0.680072	+	0.733146i	\(0.738051\pi\)
\(11\)	18.7756	−	31.2806i	0.514642	−	0.857405i
							\(13\)	−10.5172	+	7.64121i	−0.224381	+	0.163022i
\(17\)	−91.5776	−	66.5350i	−1.30652	−	0.949242i								−0.306523	−	0.951863i	\(-0.599166\pi\)
							−0.999997	+	0.00262082i	\(0.999166\pi\)
\(19\)	−23.5170	−	72.3780i	−0.283957	−	0.873929i	−0.986709	−	0.162495i	\(-0.948046\pi\)
							0.702753	−	0.711434i	\(-0.251954\pi\)
\(23\)	−81.6655			−0.740366			−0.370183	−	0.928959i	\(-0.620705\pi\)
							−0.370183	+	0.928959i	\(0.620705\pi\)
\(29\)	25.1610	−	77.4375i	0.161113	−	0.495855i	−0.837616	−	0.546260i	\(-0.816051\pi\)
							0.998729	+	0.0504050i	\(0.0160512\pi\)
\(31\)	74.0756	−	53.8191i	0.429173	−	0.311813i	−0.352145	−	0.935946i	\(-0.614548\pi\)
							0.781318	+	0.624133i	\(0.214548\pi\)
\(37\)	9.41658	−	28.9813i	0.0418399	−	0.128770i	−0.927955	−	0.372693i	\(-0.878434\pi\)
							0.969795	+	0.243923i	\(0.0784344\pi\)
\(41\)	−29.3150	−	90.2224i	−0.111664	−	0.343668i	0.879572	−	0.475765i	\(-0.157829\pi\)
							−0.991237	+	0.132097i	\(0.957829\pi\)
\(43\)	304.797			1.08096			0.540478	−	0.841358i	\(-0.318243\pi\)
							0.540478	+	0.841358i	\(0.318243\pi\)
\(47\)	55.4818	+	170.755i	0.172188	+	0.529941i	0.999494	−	0.0318109i	\(-0.0101274\pi\)
							−0.827306	+	0.561752i	\(0.810127\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.h.a.14.15	✓	68
11.2	odd	10		1573.4.a.p.1.30		34
11.4	even	5	inner	143.4.h.a.92.15	yes	68
11.9	even	5		1573.4.a.o.1.5		34

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.14.15	✓	68	1.1	even	1	trivial
143.4.h.a.92.15	yes	68	11.4	even	5	inner
1573.4.a.o.1.5		34	11.9	even	5
1573.4.a.p.1.30		34	11.2	odd	10