Embedded newform 143.4.h.b.14.15

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

$q$-expansion

\(f(q)\)	\(=\)	\(q+(2.81215 - 2.04314i) q^{2} +(2.92761 + 9.01025i) q^{3} +(1.26159 - 3.88278i) q^{4} +(-15.8411 - 11.5093i) q^{5} +(26.6421 + 19.3566i) q^{6} +(-7.78834 + 23.9700i) q^{7} +(4.20786 + 12.9505i) q^{8} +(-50.7703 + 36.8868i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{2} - 12 q^{3} - 148 q^{4} - 16 q^{5} + 77 q^{6} + 56 q^{7} - 34 q^{8} - 241 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	2.81215	−	2.04314i	0.994243	−	0.722360i	0.0333971	−	0.999442i	\(-0.489367\pi\)
							0.960846	+	0.277082i	\(0.0893674\pi\)
\(3\)	2.92761	+	9.01025i	0.563419	+	1.73402i	0.672604	+	0.740003i	\(0.265176\pi\)
							−0.109185	+	0.994021i	\(0.534824\pi\)
\(5\)	−15.8411	−	11.5093i	−1.41688	−	1.02942i	−0.992277	−	0.124038i	\(-0.960416\pi\)
							−0.424598	−	0.905382i	\(-0.639584\pi\)
\(7\)	−7.78834	+	23.9700i	−0.420531	+	1.29426i	0.486679	+	0.873581i	\(0.338208\pi\)
							−0.907209	+	0.420679i	\(0.861792\pi\)
\(11\)	35.9253	+	6.35377i	0.984718	+	0.174158i
							\(13\)	10.5172	−	7.64121i	0.224381	−	0.163022i
\(17\)	−53.2745	−	38.7062i	−0.760057	−	0.552214i								0.138871	−	0.990311i	\(-0.455653\pi\)
							−0.898928	+	0.438097i	\(0.855653\pi\)
\(19\)	22.7379	+	69.9799i	0.274549	+	0.844974i	0.989338	+	0.145634i	\(0.0465223\pi\)
							−0.714790	+	0.699339i	\(0.753478\pi\)
\(23\)	35.1141			0.318339			0.159170	−	0.987251i	\(-0.449118\pi\)
							0.159170	+	0.987251i	\(0.449118\pi\)
\(29\)	57.7053	−	177.599i	0.369504	−	1.13722i	−0.577608	−	0.816314i	\(-0.696014\pi\)
							0.947112	−	0.320902i	\(-0.103986\pi\)
\(31\)	123.968	−	90.0680i	0.718235	−	0.521829i	−0.167585	−	0.985858i	\(-0.553597\pi\)
							0.885820	+	0.464029i	\(0.153597\pi\)
\(37\)	−49.2553	+	151.592i	−0.218852	+	0.673557i	0.780006	+	0.625772i	\(0.215216\pi\)
							−0.998858	+	0.0477845i	\(0.984784\pi\)
\(41\)	8.27807	+	25.4773i	0.0315321	+	0.0970459i	0.965584	−	0.260092i	\(-0.0837528\pi\)
							−0.934052	+	0.357137i	\(0.883753\pi\)
\(43\)	102.075			0.362008			0.181004	−	0.983482i	\(-0.442065\pi\)
							0.181004	+	0.983482i	\(0.442065\pi\)
\(47\)	90.4599	+	278.407i	0.280743	+	0.864039i	0.987642	+	0.156724i	\(0.0500934\pi\)
							−0.706899	+	0.707314i	\(0.749907\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.h.b.14.15	✓	76
11.2	odd	10		1573.4.a.r.1.29		38
11.4	even	5	inner	143.4.h.b.92.15	yes	76
11.9	even	5		1573.4.a.q.1.10		38

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.b.14.15	✓	76	1.1	even	1	trivial
143.4.h.b.92.15	yes	76	11.4	even	5	inner
1573.4.a.q.1.10		38	11.9	even	5
1573.4.a.r.1.29		38	11.2	odd	10