Embedded newform 287.3.q.a.73.14

• Label: 287.3.q.a.73.14
• Level: $287$
• Weight: $3$
• Character: 287.73
• 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.q (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.82018358714\)
Analytic rank:	\(0\)
Dimension:	\(216\)
Relative dimension:	\(54\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.14
Character	\(\chi\)	\(=\)	287.73
Dual form			287.3.q.a.173.14

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-2.04653 + 1.18156i) q^{2} +(-2.47138 + 0.662204i) q^{3} +(0.792187 - 1.37211i) q^{4} +(3.06597 + 5.31041i) q^{5} +(4.27531 - 4.27531i) q^{6} +(-1.68831 + 6.79335i) q^{7} -5.70843i q^{8} +(-2.12504 + 1.22689i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 6 q^{3} + 204 q^{4} - 4 q^{7}+O(q^{10}) \)

Character values

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

\(n\)	\(206\)	\(211\)
\(\chi(n)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{4}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−2.04653	+	1.18156i	−1.02326	+	0.590782i	−0.915048	−	0.403345i	\(-0.867847\pi\)
							−0.108217	+	0.994127i	\(0.534514\pi\)
\(3\)	−2.47138	+	0.662204i	−0.823792	+	0.220735i	−0.646004	−	0.763334i	\(-0.723561\pi\)
							−0.177789	+	0.984069i	\(0.556894\pi\)
\(5\)	3.06597	+	5.31041i	0.613194	+	1.06208i	0.990699	+	0.136075i	\(0.0434489\pi\)
							−0.377505	+	0.926008i	\(0.623218\pi\)
\(7\)	−1.68831	+	6.79335i	−0.241188	+	0.970479i
							\(11\)	3.46578	+	12.9345i	0.315071	+	1.17586i	0.923923	+	0.382578i	\(0.124964\pi\)
−0.608852	+	0.793284i	\(0.708370\pi\)
\(13\)	9.28370	+	9.28370i	0.714131	+	0.714131i	0.967397	−	0.253266i	\(-0.0815047\pi\)
							−0.253266	+	0.967397i	\(0.581505\pi\)
\(17\)	7.73132	+	28.8537i	0.454784	+	1.69728i	0.688723	+	0.725024i	\(0.258171\pi\)
							−0.233940	+	0.972251i	\(0.575162\pi\)
\(19\)	15.4865	+	4.14959i	0.815078	+	0.218399i	0.642193	−	0.766543i	\(-0.278025\pi\)
							0.172884	+	0.984942i	\(0.444691\pi\)
\(23\)	−11.6597	−	20.1952i	−0.506943	−	0.878051i	−0.999968	−	0.00803596i	\(-0.997442\pi\)
							0.493025	−	0.870015i	\(-0.335891\pi\)
\(29\)	−14.3002	+	14.3002i	−0.493109	+	0.493109i	−0.909284	−	0.416176i	\(-0.863370\pi\)
							0.416176	+	0.909284i	\(0.363370\pi\)
\(31\)	−45.7225	−	26.3979i	−1.47492	−	0.851546i	−0.475320	−	0.879813i	\(-0.657668\pi\)
							−0.999600	+	0.0282673i	\(0.991001\pi\)
\(37\)	7.86937	+	13.6302i	0.212686	+	0.368382i	0.952554	−	0.304369i	\(-0.0984456\pi\)
							−0.739868	+	0.672752i	\(0.765112\pi\)
\(41\)	−0.623840	−	40.9953i	−0.0152156	−	0.999884i
							\(43\)		−	22.9582i		−	0.533912i	−0.963709	−	0.266956i	\(-0.913982\pi\)
0.963709	−	0.266956i	\(-0.0860178\pi\)
\(47\)	48.0570	+	12.8768i	1.02249	+	0.273975i	0.730839	−	0.682550i	\(-0.239129\pi\)
							0.291650	+	0.956525i	\(0.405796\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.q.a.73.14	✓	216
7.5	odd	6	inner	287.3.q.a.278.41	yes	216
41.9	even	4	inner	287.3.q.a.255.41	yes	216
287.173	odd	12	inner	287.3.q.a.173.14	yes	216

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.q.a.73.14	✓	216	1.1	even	1	trivial
287.3.q.a.173.14	yes	216	287.173	odd	12	inner
287.3.q.a.255.41	yes	216	41.9	even	4	inner
287.3.q.a.278.41	yes	216	7.5	odd	6	inner