Embedded newform 143.4.h.b.14.19

• Label: 143.4.h.b.14.19
• Level: $143$
• Weight: $4$
• Character: 143.14
• Analytic conductor: $8.437$
• Analytic rank: $0$
• Dimension: $76$
• 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:	\(76\)
Relative dimension:	\(19\) over \(\Q(\zeta_{5})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			14.19
Character	\(\chi\)	\(=\)	143.14
Dual form			143.4.h.b.92.19

$q$-expansion

\(f(q)\)	\(=\)	\(q+(4.28158 - 3.11075i) q^{2} +(0.388610 + 1.19602i) q^{3} +(6.18303 - 19.0294i) q^{4} +(-9.86077 - 7.16427i) q^{5} +(5.38439 + 3.91199i) q^{6} +(-3.63304 + 11.1813i) q^{7} +(-19.6393 - 60.4435i) q^{8} +(20.5640 - 14.9406i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{2} - 12 q^{3} - 148 q^{4} - 16 q^{5} + 77 q^{6} + 56 q^{7} - 34 q^{8} - 241 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	4.28158	−	3.11075i	1.51377	−	1.09982i	0.549297	−	0.835627i	\(-0.314896\pi\)
							0.964471	−	0.264189i	\(-0.0851044\pi\)
\(3\)	0.388610	+	1.19602i	0.0747881	+	0.230174i	0.981462	−	0.191659i	\(-0.0613868\pi\)
							−0.906673	+	0.421833i	\(0.861387\pi\)
\(5\)	−9.86077	−	7.16427i	−0.881974	−	0.640792i	0.0517990	−	0.998658i	\(-0.483504\pi\)
							−0.933773	+	0.357866i	\(0.883504\pi\)
\(7\)	−3.63304	+	11.1813i	−0.196166	+	0.603736i	0.803795	+	0.594906i	\(0.202811\pi\)
							−0.999961	+	0.00883007i	\(0.997189\pi\)
\(11\)	−18.3682	−	31.5216i	−0.503474	−	0.864010i
							\(13\)	10.5172	−	7.64121i	0.224381	−	0.163022i
\(17\)	75.3958	+	54.7783i	1.07566	+	0.781511i								0.976921	−	0.213603i	\(-0.0685198\pi\)
							0.0987369	+	0.995114i	\(0.468520\pi\)
\(19\)	18.2413	+	56.1411i	0.220255	+	0.677876i	0.998739	+	0.0502108i	\(0.0159893\pi\)
							−0.778483	+	0.627665i	\(0.784011\pi\)
\(23\)	50.6322			0.459024			0.229512	−	0.973306i	\(-0.426287\pi\)
							0.229512	+	0.973306i	\(0.426287\pi\)
\(29\)	−78.2743	+	240.904i	−0.501213	+	1.54257i	0.305833	+	0.952085i	\(0.401065\pi\)
							−0.807046	+	0.590489i	\(0.798935\pi\)
\(31\)	255.810	−	185.857i	1.48209	−	1.07680i	0.505216	−	0.862993i	\(-0.331413\pi\)
							0.976875	−	0.213809i	\(-0.0685870\pi\)
\(37\)	45.0022	−	138.502i	0.199954	−	0.615396i	−0.799929	−	0.600095i	\(-0.795129\pi\)
							0.999883	−	0.0153009i	\(-0.00487063\pi\)
\(41\)	65.4070	+	201.302i	0.249143	+	0.766783i	0.994927	+	0.100596i	\(0.0320748\pi\)
							−0.745785	+	0.666187i	\(0.767925\pi\)
\(43\)	−330.395			−1.17174			−0.585869	−	0.810405i	\(-0.699247\pi\)
							−0.585869	+	0.810405i	\(0.699247\pi\)
\(47\)	31.6895	+	97.5303i	0.0983487	+	0.302686i	0.988112	−	0.153736i	\(-0.0491306\pi\)
							−0.889763	+	0.456422i	\(0.849131\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.h.b.14.19	✓	76
11.2	odd	10		1573.4.a.r.1.36		38
11.4	even	5	inner	143.4.h.b.92.19	yes	76
11.9	even	5		1573.4.a.q.1.3		38

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.b.14.19	✓	76	1.1	even	1	trivial
143.4.h.b.92.19	yes	76	11.4	even	5	inner
1573.4.a.q.1.3		38	11.9	even	5
1573.4.a.r.1.36		38	11.2	odd	10