Embedded newform 143.4.n.a.25.11

• Label: 143.4.n.a.25.11
• 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			25.11
Character	\(\chi\)	\(=\)	143.25
Dual form			143.4.n.a.103.11

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.84899 - 2.54492i) q^{2} +(2.52460 + 7.76993i) q^{3} +(-0.585700 + 1.80260i) q^{4} +(2.53463 - 3.48862i) q^{5} +(15.1059 - 20.7914i) q^{6} +(31.9374 + 10.3771i) q^{7} +(-18.2634 + 5.93414i) q^{8} +(-32.1547 + 23.3618i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 6 q^{3} + 146 q^{4} - 426 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.84899	−	2.54492i	−0.653717	−	0.899764i	0.345536	−	0.938405i	\(-0.387697\pi\)
							−0.999253	+	0.0386414i	\(0.987697\pi\)
\(3\)	2.52460	+	7.76993i	0.485860	+	1.49532i	0.830731	+	0.556674i	\(0.187923\pi\)
							−0.344871	+	0.938650i	\(0.612077\pi\)
\(5\)	2.53463	−	3.48862i	0.226704	−	0.312031i	−0.680479	−	0.732768i	\(-0.738228\pi\)
							0.907183	+	0.420736i	\(0.138228\pi\)
\(7\)	31.9374	+	10.3771i	1.72446	+	0.560311i	0.992631	−	0.121177i	\(-0.0386669\pi\)
							0.731829	+	0.681488i	\(0.238667\pi\)
\(11\)	2.96872	−	36.3619i	0.0813729	−	0.996684i
							\(13\)	−33.6942	+	32.5837i	−0.718853	+	0.695162i
\(17\)	76.1135	+	55.2997i	1.08590	+	0.788949i								0.978701	−	0.205289i	\(-0.0658134\pi\)
							0.107194	+	0.994238i	\(0.465813\pi\)
\(19\)	−29.7843	+	9.67750i	−0.359631	+	0.116851i	−0.483259	−	0.875478i	\(-0.660547\pi\)
							0.123628	+	0.992329i	\(0.460547\pi\)
\(23\)	132.214			1.19863			0.599317	−	0.800512i	\(-0.295439\pi\)
							0.599317	+	0.800512i	\(0.295439\pi\)
\(29\)	30.2133	−	92.9869i	0.193464	−	0.595422i	−0.806527	−	0.591198i	\(-0.798655\pi\)
							0.999991	−	0.00422441i	\(-0.00134468\pi\)
\(31\)	24.2103	+	33.3226i	0.140268	+	0.193062i	0.873371	−	0.487055i	\(-0.161929\pi\)
							−0.733104	+	0.680117i	\(0.761929\pi\)
\(37\)	67.7799	+	22.0230i	0.301161	+	0.0978531i	0.455700	−	0.890134i	\(-0.349389\pi\)
							−0.154539	+	0.987987i	\(0.549389\pi\)
\(41\)	−175.142	+	56.9072i	−0.667138	+	0.216766i	−0.622956	−	0.782257i	\(-0.714068\pi\)
							−0.0441824	+	0.999023i	\(0.514068\pi\)
\(43\)	−139.856			−0.495996			−0.247998	−	0.968761i	\(-0.579773\pi\)
							−0.247998	+	0.968761i	\(0.579773\pi\)
\(47\)	168.289	−	54.6805i	0.522288	−	0.169702i	−0.0359956	−	0.999352i	\(-0.511460\pi\)
							0.558283	+	0.829650i	\(0.311460\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.n.a.25.11	✓	160
11.4	even	5	inner	143.4.n.a.103.30	yes	160
13.12	even	2	inner	143.4.n.a.25.30	yes	160
143.103	even	10	inner	143.4.n.a.103.11	yes	160

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.n.a.25.11	✓	160	1.1	even	1	trivial
143.4.n.a.25.30	yes	160	13.12	even	2	inner
143.4.n.a.103.11	yes	160	143.103	even	10	inner
143.4.n.a.103.30	yes	160	11.4	even	5	inner