Embedded newform 287.3.o.a.139.19

• Label: 287.3.o.a.139.19
• Level: $287$
• Weight: $3$
• Character: 287.139
• Analytic conductor: $7.820$
• Analytic rank: $0$
• Dimension: $216$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.o (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.82018358714\)
Analytic rank:	\(0\)
Dimension:	\(216\)
Relative dimension:	\(54\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			139.19
Character	\(\chi\)	\(=\)	287.139
Dual form			287.3.o.a.223.20

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.350708 + 1.07937i) q^{2} -2.32451i q^{3} +(2.19403 + 1.59406i) q^{4} +(4.01634 - 5.52802i) q^{5} +(2.50900 + 0.815222i) q^{6} +(2.21612 + 6.63994i) q^{7} +(-6.16269 + 4.47746i) q^{8} +3.59668 q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 6 q^{2} - 110 q^{4} - 3 q^{7} - 2 q^{8} - 648 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(206\)	\(211\)
\(\chi(n)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.350708	+	1.07937i	−0.175354	+	0.539684i	−0.999649	−	0.0264760i	\(-0.991571\pi\)
							0.824296	+	0.566160i	\(0.191571\pi\)
\(3\)		−	2.32451i		−	0.774835i	−0.921904	−	0.387418i	\(-0.873367\pi\)
							0.921904	−	0.387418i	\(-0.126633\pi\)
\(5\)	4.01634	−	5.52802i	0.803269	−	1.10560i	−0.189059	−	0.981966i	\(-0.560544\pi\)
							0.992327	−	0.123639i	\(-0.0394564\pi\)
\(7\)	2.21612	+	6.63994i	0.316589	+	0.948563i
							\(11\)	4.43561	−	3.22266i	0.403238	−	0.292969i	−0.367621	−	0.929976i	\(-0.619828\pi\)
0.770858	+	0.637006i	\(0.219828\pi\)
\(13\)	−2.93678	−	0.954217i	−0.225906	−	0.0734013i	0.193877	−	0.981026i	\(-0.437894\pi\)
							−0.419783	+	0.907625i	\(0.637894\pi\)
\(17\)	6.09441	+	8.38824i	0.358495	+	0.493426i	0.949729	−	0.313074i	\(-0.101359\pi\)
							−0.591234	+	0.806500i	\(0.701359\pi\)
\(19\)	−7.71820	+	2.50780i	−0.406221	+	0.131989i	−0.504998	−	0.863120i	\(-0.668507\pi\)
							0.0987772	+	0.995110i	\(0.468507\pi\)
\(23\)	12.6326	−	38.8793i	0.549245	−	1.69040i	−0.161432	−	0.986884i	\(-0.551611\pi\)
							0.710677	−	0.703519i	\(-0.248389\pi\)
\(29\)	18.3299	+	13.3175i	0.632066	+	0.459223i	0.857115	−	0.515124i	\(-0.172254\pi\)
							−0.225049	+	0.974347i	\(0.572254\pi\)
\(31\)	−2.85200	−	3.92545i	−0.0920001	−	0.126627i	0.760536	−	0.649296i	\(-0.224936\pi\)
							−0.852536	+	0.522669i	\(0.824936\pi\)
\(37\)	15.6256	+	11.3527i	0.422314	+	0.306829i	0.778568	−	0.627560i	\(-0.215946\pi\)
							−0.356254	+	0.934389i	\(0.615946\pi\)
\(41\)	18.7667	+	36.4529i	0.457724	+	0.889094i
							\(43\)	0.815294	−	2.50922i	0.0189603	−	0.0583539i	−0.941129	−	0.338048i	\(-0.890233\pi\)
0.960089	+	0.279695i	\(0.0902332\pi\)
\(47\)	48.9483	+	15.9043i	1.04145	+	0.338389i	0.779309	−	0.626640i	\(-0.215570\pi\)
							0.262145	+	0.965029i	\(0.415570\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.o.a.139.19	✓	216
7.6	odd	2	inner	287.3.o.a.139.20	yes	216
41.18	even	5	inner	287.3.o.a.223.19	yes	216
287.223	odd	10	inner	287.3.o.a.223.20	yes	216

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.o.a.139.19	✓	216	1.1	even	1	trivial
287.3.o.a.139.20	yes	216	7.6	odd	2	inner
287.3.o.a.223.19	yes	216	41.18	even	5	inner
287.3.o.a.223.20	yes	216	287.223	odd	10	inner