Embedded newform 143.2.n.a.25.5

• Label: 143.2.n.a.25.5
• Level: $143$
• Weight: $2$
• Character: 143.25
• Analytic conductor: $1.142$
• Analytic rank: $0$
• Dimension: $48$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.n (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.14186074890\)
Analytic rank:	\(0\)
Dimension:	\(48\)
Relative dimension:	\(12\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			25.5
Character	\(\chi\)	\(=\)	143.25
Dual form			143.2.n.a.103.5

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.510840 - 0.703111i) q^{2} +(-0.187568 - 0.577275i) q^{3} +(0.384627 - 1.18376i) q^{4} +(0.238211 - 0.327869i) q^{5} +(-0.310071 + 0.426776i) q^{6} +(-0.926647 - 0.301086i) q^{7} +(-2.68191 + 0.871405i) q^{8} +(2.12899 - 1.54680i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{3} + 4 q^{4} - 2 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.510840	−	0.703111i	−0.361218	−	0.497174i	0.589269	−	0.807937i	\(-0.299416\pi\)
							−0.950488	+	0.310762i	\(0.899416\pi\)
\(3\)	−0.187568	−	0.577275i	−0.108292	−	0.333290i	0.882197	−	0.470881i	\(-0.156064\pi\)
							−0.990489	+	0.137591i	\(0.956064\pi\)
\(5\)	0.238211	−	0.327869i	0.106531	−	0.146628i	−0.752423	−	0.658681i	\(-0.771115\pi\)
							0.858954	+	0.512053i	\(0.171115\pi\)
\(7\)	−0.926647	−	0.301086i	−0.350240	−	0.113800i	0.128613	−	0.991695i	\(-0.458947\pi\)
							−0.478853	+	0.877895i	\(0.658947\pi\)
\(11\)	−0.972371	−	3.17088i	−0.293181	−	0.956057i
							\(13\)	−1.07872	+	3.44040i	−0.299184	+	0.954195i
\(17\)	−2.49227	−	1.81074i	−0.604464	−	0.439168i								0.242997	−	0.970027i	\(-0.421870\pi\)
							−0.847460	+	0.530859i	\(0.821870\pi\)
\(19\)	6.89120	−	2.23909i	1.58095	−	0.513682i	0.618648	−	0.785668i	\(-0.287681\pi\)
							0.962301	+	0.271986i	\(0.0876806\pi\)
\(23\)	5.11524			1.06660			0.533301	−	0.845926i	\(-0.320951\pi\)
							0.533301	+	0.845926i	\(0.320951\pi\)
\(29\)	−2.31544	+	7.12619i	−0.429966	+	1.32330i	0.468192	+	0.883627i	\(0.344906\pi\)
							−0.898158	+	0.439673i	\(0.855094\pi\)
\(31\)	0.431936	+	0.594509i	0.0775780	+	0.106777i	0.846042	−	0.533116i	\(-0.178979\pi\)
							−0.768464	+	0.639892i	\(0.778979\pi\)
\(37\)	10.3634	+	3.36728i	1.70374	+	0.553578i	0.989271	−	0.146091i	\(-0.0466691\pi\)
							0.714467	+	0.699669i	\(0.246669\pi\)
\(41\)	3.44194	−	1.11835i	0.537540	−	0.174657i	−0.0276505	−	0.999618i	\(-0.508803\pi\)
							0.565191	+	0.824960i	\(0.308803\pi\)
\(43\)	9.28471			1.41590			0.707952	−	0.706260i	\(-0.249619\pi\)
							0.707952	+	0.706260i	\(0.249619\pi\)
\(47\)	−8.10146	+	2.63232i	−1.18172	+	0.383964i	−0.833005	−	0.553265i	\(-0.813382\pi\)
							−0.348714	+	0.937229i	\(0.613382\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.2.n.a.25.5	✓	48
11.4	even	5	inner	143.2.n.a.103.8	yes	48
13.12	even	2	inner	143.2.n.a.25.8	yes	48
143.103	even	10	inner	143.2.n.a.103.5	yes	48

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.n.a.25.5	✓	48	1.1	even	1	trivial
143.2.n.a.25.8	yes	48	13.12	even	2	inner
143.2.n.a.103.5	yes	48	143.103	even	10	inner
143.2.n.a.103.8	yes	48	11.4	even	5	inner