Embedded newform 143.4.h.b.14.6

• Label: 143.4.h.b.14.6
• 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			14.6
Character	\(\chi\)	\(=\)	143.14
Dual form			143.4.h.b.92.6

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.83784 + 1.33527i) q^{2} +(3.01069 + 9.26595i) q^{3} +(-0.877420 + 2.70042i) q^{4} +(-5.97680 - 4.34240i) q^{5} +(-17.9057 - 13.0093i) q^{6} +(4.55364 - 14.0147i) q^{7} +(-7.60918 - 23.4186i) q^{8} +(-54.9500 + 39.9235i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{2} - 12 q^{3} - 148 q^{4} - 16 q^{5} + 77 q^{6} + 56 q^{7} - 34 q^{8} - 241 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.83784	+	1.33527i	−0.649775	+	0.472089i	−0.863195	−	0.504871i	\(-0.831540\pi\)
							0.213419	+	0.976961i	\(0.431540\pi\)
\(3\)	3.01069	+	9.26595i	0.579407	+	1.78323i	0.620656	+	0.784083i	\(0.286866\pi\)
							−0.0412485	+	0.999149i	\(0.513134\pi\)
\(5\)	−5.97680	−	4.34240i	−0.534581	−	0.388396i	0.287487	−	0.957784i	\(-0.407180\pi\)
							−0.822069	+	0.569388i	\(0.807180\pi\)
\(7\)	4.55364	−	14.0147i	0.245874	−	0.756721i	−0.749618	−	0.661871i	\(-0.769763\pi\)
							0.995492	−	0.0948504i	\(-0.0302373\pi\)
\(11\)	−33.2010	−	15.1226i	−0.910044	−	0.414512i
							\(13\)	10.5172	−	7.64121i	0.224381	−	0.163022i
\(17\)	−22.7098	−	16.4996i	−0.323996	−	0.235397i								0.413883	−	0.910330i	\(-0.364172\pi\)
							−0.737878	+	0.674934i	\(0.764172\pi\)
\(19\)	48.9446	+	150.636i	0.590982	+	1.81886i	0.573790	+	0.819003i	\(0.305473\pi\)
							0.0171923	+	0.999852i	\(0.494527\pi\)
\(23\)	−36.9879			−0.335326			−0.167663	−	0.985844i	\(-0.553622\pi\)
							−0.167663	+	0.985844i	\(0.553622\pi\)
\(29\)	−43.5548	+	134.048i	−0.278894	+	0.858347i	0.709269	+	0.704938i	\(0.249025\pi\)
							−0.988163	+	0.153409i	\(0.950975\pi\)
\(31\)	−214.399	+	155.770i	−1.24217	+	0.902490i	−0.997741	−	0.0671774i	\(-0.978601\pi\)
							−0.244429	+	0.969667i	\(0.578601\pi\)
\(37\)	59.3040	−	182.519i	0.263500	−	0.810970i	−0.728535	−	0.685009i	\(-0.759798\pi\)
							0.992035	−	0.125962i	\(-0.0402016\pi\)
\(41\)	−116.301	−	357.938i	−0.443005	−	1.36343i	−0.884657	−	0.466243i	\(-0.845607\pi\)
							0.441652	−	0.897186i	\(-0.354393\pi\)
\(43\)	−358.448			−1.27123			−0.635614	−	0.772007i	\(-0.719253\pi\)
							−0.635614	+	0.772007i	\(0.719253\pi\)
\(47\)	102.754	+	316.245i	0.318899	+	0.981469i	0.974120	+	0.226032i	\(0.0725754\pi\)
							−0.655221	+	0.755437i	\(0.727425\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.h.b.14.6	✓	76
11.2	odd	10		1573.4.a.r.1.13		38
11.4	even	5	inner	143.4.h.b.92.6	yes	76
11.9	even	5		1573.4.a.q.1.26		38

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.b.14.6	✓	76	1.1	even	1	trivial
143.4.h.b.92.6	yes	76	11.4	even	5	inner
1573.4.a.q.1.26		38	11.9	even	5
1573.4.a.r.1.13		38	11.2	odd	10