Embedded newform 287.3.o.a.139.13

• Label: 287.3.o.a.139.13
• 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			139.13
Character	\(\chi\)	\(=\)	287.139
Dual form			287.3.o.a.223.14

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.695933 + 2.14186i) q^{2} -1.83433i q^{3} +(-0.867179 - 0.630043i) q^{4} +(-0.161169 + 0.221830i) q^{5} +(3.92888 + 1.27657i) q^{6} +(-1.23898 - 6.88948i) q^{7} +(-5.33494 + 3.87606i) q^{8} +5.63523 q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 6 q^{2} - 110 q^{4} - 3 q^{7} - 2 q^{8} - 648 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.695933	+	2.14186i	−0.347966	+	1.07093i	0.612010	+	0.790850i	\(0.290361\pi\)
							−0.959976	+	0.280081i	\(0.909639\pi\)
\(3\)		−	1.83433i		−	0.611444i	−0.952121	−	0.305722i	\(-0.901102\pi\)
							0.952121	−	0.305722i	\(-0.0988977\pi\)
\(5\)	−0.161169	+	0.221830i	−0.0322338	+	0.0443660i	−0.824830	−	0.565381i	\(-0.808729\pi\)
							0.792596	+	0.609747i	\(0.208729\pi\)
\(7\)	−1.23898	−	6.88948i	−0.176998	−	0.984211i
							\(11\)	−9.05298	+	6.57738i	−0.822998	+	0.597943i	−0.917570	−	0.397575i	\(-0.869852\pi\)
0.0945714	+	0.995518i	\(0.469852\pi\)
\(13\)	21.6306	+	7.02820i	1.66389	+	0.540631i	0.981682	−	0.190526i	\(-0.0610195\pi\)
							0.682209	+	0.731157i	\(0.261019\pi\)
\(17\)	5.87135	+	8.08122i	0.345374	+	0.475366i	0.946001	−	0.324163i	\(-0.105083\pi\)
							−0.600628	+	0.799529i	\(0.705083\pi\)
\(19\)	31.3733	−	10.1938i	1.65123	−	0.536516i	0.672222	−	0.740350i	\(-0.265340\pi\)
							0.979005	+	0.203834i	\(0.0653402\pi\)
\(23\)	4.03326	−	12.4131i	0.175359	−	0.539700i	−0.824290	−	0.566167i	\(-0.808426\pi\)
							0.999650	+	0.0264668i	\(0.00842563\pi\)
\(29\)	18.6526	+	13.5519i	0.643192	+	0.467306i	0.860945	−	0.508698i	\(-0.169873\pi\)
							−0.217753	+	0.976004i	\(0.569873\pi\)
\(31\)	11.0237	+	15.1728i	0.355603	+	0.489446i	0.948917	−	0.315526i	\(-0.102181\pi\)
							−0.593314	+	0.804971i	\(0.702181\pi\)
\(37\)	24.0408	+	17.4667i	0.649752	+	0.472073i	0.863187	−	0.504885i	\(-0.168465\pi\)
							−0.213435	+	0.976957i	\(0.568465\pi\)
\(41\)	−40.9623	+	1.75867i	−0.999080	+	0.0428944i
							\(43\)	−1.67366	+	5.15100i	−0.0389224	+	0.119791i	−0.968630	−	0.248508i	\(-0.920060\pi\)
0.929707	+	0.368299i	\(0.120060\pi\)
\(47\)	37.9254	+	12.3227i	0.806924	+	0.262185i	0.683294	−	0.730143i	\(-0.260547\pi\)
							0.123629	+	0.992328i	\(0.460547\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.o.a.139.13	✓	216
7.6	odd	2	inner	287.3.o.a.139.14	yes	216
41.18	even	5	inner	287.3.o.a.223.13	yes	216
287.223	odd	10	inner	287.3.o.a.223.14	yes	216

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.o.a.139.13	✓	216	1.1	even	1	trivial
287.3.o.a.139.14	yes	216	7.6	odd	2	inner
287.3.o.a.223.13	yes	216	41.18	even	5	inner
287.3.o.a.223.14	yes	216	287.223	odd	10	inner