Embedded newform 143.4.n.a.25.7

• Label: 143.4.n.a.25.7
• Level: $143$
• Weight: $4$
• Character: 143.25
• Analytic conductor: $8.437$
• Analytic rank: $0$
• Dimension: $160$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.n (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.43727313082\)
Analytic rank:	\(0\)
Dimension:	\(160\)
Relative dimension:	\(40\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			25.7
Character	\(\chi\)	\(=\)	143.25
Dual form			143.4.n.a.103.7

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-2.35953 - 3.24761i) q^{2} +(-3.09622 - 9.52919i) q^{3} +(-2.50747 + 7.71720i) q^{4} +(8.33529 - 11.4725i) q^{5} +(-23.6415 + 32.5397i) q^{6} +(7.59080 + 2.46640i) q^{7} +(0.436537 - 0.141839i) q^{8} +(-59.3754 + 43.1388i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 6 q^{3} + 146 q^{4} - 426 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−2.35953	−	3.24761i	−0.834219	−	1.14820i	−0.987123	−	0.159963i	\(-0.948863\pi\)
							0.152904	−	0.988241i	\(-0.451137\pi\)
\(3\)	−3.09622	−	9.52919i	−0.595868	−	1.83389i	−0.550357	−	0.834929i	\(-0.685508\pi\)
							−0.0455111	−	0.998964i	\(-0.514492\pi\)
\(5\)	8.33529	−	11.4725i	0.745531	−	1.02614i	−0.252751	−	0.967531i	\(-0.581335\pi\)
							0.998281	−	0.0586036i	\(-0.0186648\pi\)
\(7\)	7.59080	+	2.46640i	0.409865	+	0.133173i	0.506690	−	0.862128i	\(-0.330869\pi\)
							−0.0968253	+	0.995301i	\(0.530869\pi\)
\(11\)	−7.02242	−	35.8006i	−0.192485	−	0.981300i
							\(13\)	−16.8002	+	43.7579i	−0.358426	+	0.933558i
\(17\)	−26.4753	−	19.2355i	−0.377719	−	0.274429i								0.382686	−	0.923879i	\(-0.374999\pi\)
							−0.760404	+	0.649450i	\(0.774999\pi\)
\(19\)	111.363	−	36.1841i	1.34466	−	0.436905i	0.453765	−	0.891121i	\(-0.350081\pi\)
							0.890892	+	0.454216i	\(0.150081\pi\)
\(23\)	−125.111			−1.13424			−0.567121	−	0.823635i	\(-0.691943\pi\)
							−0.567121	+	0.823635i	\(0.691943\pi\)
\(29\)	89.6679	−	275.970i	0.574170	−	1.76711i	−0.0648203	−	0.997897i	\(-0.520647\pi\)
							0.638990	−	0.769215i	\(-0.279353\pi\)
\(31\)	−9.91588	−	13.6480i	−0.0574498	−	0.0790729i	0.779325	−	0.626619i	\(-0.215562\pi\)
							−0.836775	+	0.547546i	\(0.815562\pi\)
\(37\)	−132.836	−	43.1609i	−0.590218	−	0.191773i	−0.00134488	−	0.999999i	\(-0.500428\pi\)
							−0.588873	+	0.808226i	\(0.700428\pi\)
\(41\)	−47.1994	+	15.3360i	−0.179788	+	0.0584167i	−0.397528	−	0.917590i	\(-0.630132\pi\)
							0.217739	+	0.976007i	\(0.430132\pi\)
\(43\)	151.610			0.537681			0.268840	−	0.963185i	\(-0.413360\pi\)
							0.268840	+	0.963185i	\(0.413360\pi\)
\(47\)	−247.287	+	80.3483i	−0.767456	+	0.249362i	−0.666476	−	0.745527i	\(-0.732198\pi\)
							−0.100981	+	0.994888i	\(0.532198\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.n.a.25.7	✓	160
11.4	even	5	inner	143.4.n.a.103.34	yes	160
13.12	even	2	inner	143.4.n.a.25.34	yes	160
143.103	even	10	inner	143.4.n.a.103.7	yes	160

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.n.a.25.7	✓	160	1.1	even	1	trivial
143.4.n.a.25.34	yes	160	13.12	even	2	inner
143.4.n.a.103.7	yes	160	143.103	even	10	inner
143.4.n.a.103.34	yes	160	11.4	even	5	inner