Embedded newform 287.3.o.a.139.5

• Label: 287.3.o.a.139.5
• 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			139.5
Character	\(\chi\)	\(=\)	287.139
Dual form			287.3.o.a.223.6

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.08527 + 3.34011i) q^{2} -1.54191i q^{3} +(-6.74248 - 4.89870i) q^{4} +(-3.83280 + 5.27539i) q^{5} +(5.15016 + 1.67339i) q^{6} +(-0.829150 + 6.95072i) q^{7} +(12.3145 - 8.94703i) q^{8} +6.62251 q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 6 q^{2} - 110 q^{4} - 3 q^{7} - 2 q^{8} - 648 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.08527	+	3.34011i	−0.542634	+	1.67006i	0.183915	+	0.982942i	\(0.441123\pi\)
							−0.726549	+	0.687115i	\(0.758877\pi\)
\(3\)		−	1.54191i		−	0.513971i	−0.966415	−	0.256985i	\(-0.917271\pi\)
							0.966415	−	0.256985i	\(-0.0827292\pi\)
\(5\)	−3.83280	+	5.27539i	−0.766559	+	1.05508i	0.230081	+	0.973172i	\(0.426101\pi\)
							−0.996640	+	0.0819067i	\(0.973899\pi\)
\(7\)	−0.829150	+	6.95072i	−0.118450	+	0.992960i
							\(11\)	−11.6861	+	8.49046i	−1.06237	+	0.771860i	−0.974526	−	0.224274i	\(-0.927999\pi\)
−0.0878480	+	0.996134i	\(0.527999\pi\)
\(13\)	−7.14291	−	2.32087i	−0.549455	−	0.178529i	0.0211162	−	0.999777i	\(-0.493278\pi\)
							−0.570571	+	0.821248i	\(0.693278\pi\)
\(17\)	−10.8233	−	14.8970i	−0.636665	−	0.876294i	0.361767	−	0.932268i	\(-0.382173\pi\)
							−0.998432	+	0.0559745i	\(0.982173\pi\)
\(19\)	18.7080	−	6.07860i	0.984633	−	0.319927i	0.227924	−	0.973679i	\(-0.426806\pi\)
							0.756709	+	0.653752i	\(0.226806\pi\)
\(23\)	1.46864	−	4.52002i	0.0638541	−	0.196523i	−0.914040	−	0.405625i	\(-0.867054\pi\)
							0.977894	+	0.209102i	\(0.0670540\pi\)
\(29\)	13.3379	+	9.69054i	0.459927	+	0.334156i	0.793503	−	0.608567i	\(-0.208255\pi\)
							−0.333576	+	0.942723i	\(0.608255\pi\)
\(31\)	−31.3005	−	43.0814i	−1.00969	−	1.38972i	−0.919185	−	0.393826i	\(-0.871151\pi\)
							−0.0905073	−	0.995896i	\(-0.528849\pi\)
\(37\)	−25.7283	−	18.6927i	−0.695360	−	0.505208i	0.183058	−	0.983102i	\(-0.441400\pi\)
							−0.878418	+	0.477894i	\(0.841400\pi\)
\(41\)	−10.1800	+	39.7161i	−0.248292	+	0.968685i
							\(43\)	1.98519	−	6.10977i	0.0461671	−	0.142088i	−0.925316	−	0.379197i	\(-0.876200\pi\)
0.971483	+	0.237110i	\(0.0762001\pi\)
\(47\)	25.0240	+	8.13080i	0.532426	+	0.172996i	0.562877	−	0.826540i	\(-0.309694\pi\)
							−0.0304510	+	0.999536i	\(0.509694\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.o.a.139.5	✓	216
7.6	odd	2	inner	287.3.o.a.139.6	yes	216
41.18	even	5	inner	287.3.o.a.223.5	yes	216
287.223	odd	10	inner	287.3.o.a.223.6	yes	216

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.o.a.139.5	✓	216	1.1	even	1	trivial
287.3.o.a.139.6	yes	216	7.6	odd	2	inner
287.3.o.a.223.5	yes	216	41.18	even	5	inner
287.3.o.a.223.6	yes	216	287.223	odd	10	inner