Embedded newform 287.3.k.a.124.18

• Label: 287.3.k.a.124.18
• Level: $287$
• Weight: $3$
• Character: 287.124
• Analytic conductor: $7.820$
• Analytic rank: $0$
• Dimension: $108$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.k (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.82018358714\)
Analytic rank:	\(0\)
Dimension:	\(108\)
Relative dimension:	\(54\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			124.18
Character	\(\chi\)	\(=\)	287.124
Dual form			287.3.k.a.206.18

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.790461 + 1.36912i) q^{2} +(-2.95293 + 1.70487i) q^{3} +(0.750343 + 1.29963i) q^{4} +(3.10718 + 1.79393i) q^{5} -5.39054i q^{6} +(-0.932911 - 6.93756i) q^{7} -8.69615 q^{8} +(1.31318 - 2.27450i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 2 q^{2} - 6 q^{3} - 106 q^{4} - 6 q^{5} - 4 q^{7} - 4 q^{8} + 164 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).

\(n\)	\(206\)	\(211\)
\(\chi(n)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.790461	+	1.36912i	−0.395230	+	0.684559i	−0.993131	−	0.117011i	\(-0.962669\pi\)
							0.597900	+	0.801571i	\(0.296002\pi\)
\(3\)	−2.95293	+	1.70487i	−0.984309	+	0.568291i	−0.903568	−	0.428444i	\(-0.859062\pi\)
							−0.0807405	+	0.996735i	\(0.525729\pi\)
\(5\)	3.10718	+	1.79393i	0.621437	+	0.358787i	0.777428	−	0.628972i	\(-0.216524\pi\)
							−0.155991	+	0.987758i	\(0.549857\pi\)
\(7\)	−0.932911	−	6.93756i	−0.133273	−	0.991079i
							\(11\)	−8.90138	−	15.4176i	−0.809217	−	1.40160i	−0.913407	−	0.407047i	\(-0.866558\pi\)
0.104190	−	0.994557i	\(-0.466775\pi\)
\(13\)			6.35606i			0.488928i	0.969658	+	0.244464i	\(0.0786120\pi\)
							−0.969658	+	0.244464i	\(0.921388\pi\)
\(17\)	9.78119	−	5.64717i	0.575364	−	0.332186i	−0.183925	−	0.982940i	\(-0.558880\pi\)
							0.759289	+	0.650754i	\(0.225547\pi\)
\(19\)	−26.8410	−	15.4967i	−1.41269	−	0.815614i	−0.417045	−	0.908886i	\(-0.636934\pi\)
							−0.995641	+	0.0932713i	\(0.970268\pi\)
\(23\)	−17.0463	+	29.5250i	−0.741143	+	1.28370i	0.210832	+	0.977522i	\(0.432383\pi\)
							−0.951975	+	0.306175i	\(0.900951\pi\)
\(29\)	27.0760			0.933656			0.466828	−	0.884348i	\(-0.345397\pi\)
							0.466828	+	0.884348i	\(0.345397\pi\)
\(31\)	22.4342	−	12.9524i	0.723684	−	0.417819i	−0.0924234	−	0.995720i	\(-0.529461\pi\)
							0.816107	+	0.577901i	\(0.196128\pi\)
\(37\)	4.81155	−	8.33385i	0.130042	−	0.225239i	−0.793651	−	0.608374i	\(-0.791822\pi\)
							0.923692	+	0.383135i	\(0.125155\pi\)
\(41\)		−	6.40312i		−	0.156174i
							\(43\)	65.9369			1.53342			0.766708	−	0.641996i	\(-0.221893\pi\)
0.766708	+	0.641996i	\(0.221893\pi\)
\(47\)	−42.3790	−	24.4675i	−0.901681	−	0.520586i	−0.0239356	−	0.999714i	\(-0.507620\pi\)
							−0.877745	+	0.479128i	\(0.840953\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.k.a.124.18	✓	108
7.3	odd	6	inner	287.3.k.a.206.18	yes	108

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.k.a.124.18	✓	108	1.1	even	1	trivial
287.3.k.a.206.18	yes	108	7.3	odd	6	inner