Embedded newform 143.4.n.a.25.19

• Label: 143.4.n.a.25.19
• 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			25.19
Character	\(\chi\)	\(=\)	143.25
Dual form			143.4.n.a.103.19

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.313996 - 0.432179i) q^{2} +(1.17154 + 3.60564i) q^{3} +(2.38395 - 7.33705i) q^{4} +(-4.60303 + 6.33553i) q^{5} +(1.19042 - 1.63847i) q^{6} +(4.31855 + 1.40318i) q^{7} +(-7.98392 + 2.59413i) q^{8} +(10.2153 - 7.42187i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 6 q^{3} + 146 q^{4} - 426 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.313996	−	0.432179i	−0.111014	−	0.152798i	0.749894	−	0.661558i	\(-0.230104\pi\)
							−0.860909	+	0.508759i	\(0.830104\pi\)
\(3\)	1.17154	+	3.60564i	0.225464	+	0.693906i	0.998244	+	0.0592326i	\(0.0188654\pi\)
							−0.772780	+	0.634673i	\(0.781135\pi\)
\(5\)	−4.60303	+	6.33553i	−0.411708	+	0.566667i	−0.963634	−	0.267226i	\(-0.913893\pi\)
							0.551926	+	0.833893i	\(0.313893\pi\)
\(7\)	4.31855	+	1.40318i	0.233180	+	0.0757648i	0.423276	−	0.906001i	\(-0.360880\pi\)
							−0.190096	+	0.981765i	\(0.560880\pi\)
\(11\)	31.7782	+	17.9206i	0.871044	+	0.491205i
							\(13\)	43.0942	+	18.4360i	0.919399	+	0.393326i
\(17\)	29.9308	+	21.7460i	0.427017	+	0.310246i								0.780455	−	0.625212i	\(-0.214987\pi\)
							−0.353438	+	0.935458i	\(0.614987\pi\)
\(19\)	−28.8727	+	9.38130i	−0.348623	+	0.113275i	−0.478094	−	0.878309i	\(-0.658672\pi\)
							0.129471	+	0.991583i	\(0.458672\pi\)
\(23\)	161.198			1.46139			0.730697	−	0.682702i	\(-0.239195\pi\)
							0.730697	+	0.682702i	\(0.239195\pi\)
\(29\)	16.7175	−	51.4511i	0.107047	−	0.329456i	−0.883159	−	0.469075i	\(-0.844588\pi\)
							0.990205	+	0.139618i	\(0.0445876\pi\)
\(31\)	−13.6975	−	18.8530i	−0.0793594	−	0.109229i	0.767492	−	0.641059i	\(-0.221505\pi\)
							−0.846851	+	0.531830i	\(0.821505\pi\)
\(37\)	−142.546	−	46.3161i	−0.633364	−	0.205792i	−0.0252991	−	0.999680i	\(-0.508054\pi\)
							−0.608065	+	0.793888i	\(0.708054\pi\)
\(41\)	405.801	−	131.853i	1.54574	−	0.502243i	0.592790	−	0.805357i	\(-0.298026\pi\)
							0.952954	+	0.303114i	\(0.0980263\pi\)
\(43\)	−147.389			−0.522713			−0.261356	−	0.965242i	\(-0.584170\pi\)
							−0.261356	+	0.965242i	\(0.584170\pi\)
\(47\)	−48.5854	+	15.7864i	−0.150785	+	0.0489931i	−0.383437	−	0.923567i	\(-0.625260\pi\)
							0.232652	+	0.972560i	\(0.425260\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.n.a.25.19	✓	160
11.4	even	5	inner	143.4.n.a.103.22	yes	160
13.12	even	2	inner	143.4.n.a.25.22	yes	160
143.103	even	10	inner	143.4.n.a.103.19	yes	160

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.n.a.25.19	✓	160	1.1	even	1	trivial
143.4.n.a.25.22	yes	160	13.12	even	2	inner
143.4.n.a.103.19	yes	160	143.103	even	10	inner
143.4.n.a.103.22	yes	160	11.4	even	5	inner