Embedded newform 143.4.h.a.14.4

• Label: 143.4.h.a.14.4
• 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			14.4
Character	\(\chi\)	\(=\)	143.14
Dual form			143.4.h.a.92.4

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-2.45816 + 1.78596i) q^{2} +(0.944462 + 2.90676i) q^{3} +(0.380774 - 1.17190i) q^{4} +(6.23533 + 4.53024i) q^{5} +(-7.51299 - 5.45850i) q^{6} +(9.62984 - 29.6376i) q^{7} +(-6.35451 - 19.5572i) q^{8} +(14.2862 - 10.3796i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{2} + 12 q^{3} - 16 q^{4} + 24 q^{5} + 7 q^{6} + 8 q^{7} - 34 q^{8} - 55 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−2.45816	+	1.78596i	−0.869091	+	0.631432i	−0.930343	−	0.366690i	\(-0.880491\pi\)
							0.0612516	+	0.998122i	\(0.480491\pi\)
\(3\)	0.944462	+	2.90676i	0.181762	+	0.559405i	0.999878	−	0.0156483i	\(-0.00498120\pi\)
							−0.818116	+	0.575054i	\(0.804981\pi\)
\(5\)	6.23533	+	4.53024i	0.557705	+	0.405197i	0.830618	−	0.556842i	\(-0.187987\pi\)
							−0.272913	+	0.962039i	\(0.587987\pi\)
\(7\)	9.62984	−	29.6376i	0.519962	−	1.60028i	−0.254105	−	0.967177i	\(-0.581781\pi\)
							0.774067	−	0.633103i	\(-0.218219\pi\)
\(11\)	7.61258	−	35.6798i	0.208662	−	0.977988i
							\(13\)	−10.5172	+	7.64121i	−0.224381	+	0.163022i
\(17\)	−43.1841	−	31.3751i	−0.616099	−	0.447622i								0.235458	−	0.971885i	\(-0.424341\pi\)
							−0.851557	+	0.524263i	\(0.824341\pi\)
\(19\)	−36.8388	−	113.378i	−0.444811	−	1.36899i	−0.882691	−	0.469954i	\(-0.844271\pi\)
							0.437880	−	0.899033i	\(-0.355729\pi\)
\(23\)	156.169			1.41580			0.707901	−	0.706311i	\(-0.249642\pi\)
							0.707901	+	0.706311i	\(0.249642\pi\)
\(29\)	−75.2195	+	231.502i	−0.481652	+	1.48237i	0.355119	+	0.934821i	\(0.384440\pi\)
							−0.836772	+	0.547552i	\(0.815560\pi\)
\(31\)	−15.0455	+	10.9312i	−0.0871692	+	0.0633321i	−0.630516	−	0.776176i	\(-0.717157\pi\)
							0.543347	+	0.839508i	\(0.317157\pi\)
\(37\)	−38.1556	+	117.431i	−0.169533	+	0.521770i	−0.999342	−	0.0362784i	\(-0.988450\pi\)
							0.829808	+	0.558048i	\(0.188450\pi\)
\(41\)	−66.9524	−	206.058i	−0.255030	−	0.784900i	−0.993824	−	0.110969i	\(-0.964605\pi\)
							0.738794	−	0.673931i	\(-0.235395\pi\)
\(43\)	−63.9973			−0.226965			−0.113483	−	0.993540i	\(-0.536201\pi\)
							−0.113483	+	0.993540i	\(0.536201\pi\)
\(47\)	66.9403	+	206.021i	0.207750	+	0.639388i	0.999589	+	0.0286589i	\(0.00912367\pi\)
							−0.791839	+	0.610729i	\(0.790876\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.h.a.14.4	✓	68
11.2	odd	10		1573.4.a.p.1.7		34
11.4	even	5	inner	143.4.h.a.92.4	yes	68
11.9	even	5		1573.4.a.o.1.28		34

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.14.4	✓	68	1.1	even	1	trivial
143.4.h.a.92.4	yes	68	11.4	even	5	inner
1573.4.a.o.1.28		34	11.9	even	5
1573.4.a.p.1.7		34	11.2	odd	10