Embedded newform 287.3.v.a.44.19

• Label: 287.3.v.a.44.19
• Level: $287$
• Weight: $3$
• Character: 287.44
• Analytic conductor: $7.820$
• Analytic rank: $0$
• Dimension: $432$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.v (of order \(24\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.82018358714\)
Analytic rank:	\(0\)
Dimension:	\(432\)
Relative dimension:	\(54\) over \(\Q(\zeta_{24})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			44.19
Character	\(\chi\)	\(=\)	287.44
Dual form			287.3.v.a.137.19

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.358555 - 1.33815i) q^{2} +(2.81232 - 0.370250i) q^{3} +(1.80203 - 1.04040i) q^{4} +(-9.33412 + 2.50107i) q^{5} +(-1.50382 - 3.63054i) q^{6} +(-3.19103 + 6.23036i) q^{7} +(-5.95670 - 5.95670i) q^{8} +(-0.921246 + 0.246847i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 48 q^{8} - 36 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(206\)	\(211\)
\(\chi(n)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{8}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.358555	−	1.33815i	−0.179277	−	0.669073i	−0.995783	−	0.0917356i	\(-0.970759\pi\)
							0.816506	−	0.577337i	\(-0.195908\pi\)
\(3\)	2.81232	−	0.370250i	0.937442	−	0.123417i	0.353703	−	0.935358i	\(-0.384922\pi\)
							0.583739	+	0.811941i	\(0.301589\pi\)
\(5\)	−9.33412	+	2.50107i	−1.86682	+	0.500214i	−0.866824	+	0.498614i	\(0.833843\pi\)
							−0.999999	+	0.00159998i	\(0.999491\pi\)
\(7\)	−3.19103	+	6.23036i	−0.455861	+	0.890051i
							\(11\)	−1.06210	−	8.06742i	−0.0965542	−	0.733402i	−0.969414	−	0.245431i	\(-0.921071\pi\)
0.872860	−	0.487971i	\(-0.162263\pi\)
\(13\)	−7.58582	+	18.3138i	−0.583525	+	1.40875i	0.306073	+	0.952008i	\(0.400985\pi\)
							−0.889597	+	0.456745i	\(0.849015\pi\)
\(17\)	−7.60723	+	9.91393i	−0.447484	+	0.583172i	−0.961568	−	0.274568i	\(-0.911465\pi\)
							0.514084	+	0.857740i	\(0.328132\pi\)
\(19\)	−7.96366	−	1.04844i	−0.419140	−	0.0551808i	−0.0819931	−	0.996633i	\(-0.526129\pi\)
							−0.337147	+	0.941452i	\(0.609462\pi\)
\(23\)	−5.26389	−	3.03911i	−0.228865	−	0.132135i	0.381183	−	0.924499i	\(-0.375517\pi\)
							−0.610048	+	0.792364i	\(0.708850\pi\)
\(29\)	17.0026	−	41.0480i	0.586297	−	1.41545i	−0.300721	−	0.953712i	\(-0.597227\pi\)
							0.887018	−	0.461735i	\(-0.152773\pi\)
\(31\)	12.0537	−	6.95918i	0.388828	−	0.224490i	−0.292824	−	0.956166i	\(-0.594595\pi\)
							0.681652	+	0.731676i	\(0.261262\pi\)
\(37\)	−25.6075	+	44.3535i	−0.692094	+	1.19874i	0.279056	+	0.960275i	\(0.409978\pi\)
							−0.971150	+	0.238467i	\(0.923355\pi\)
\(41\)	−27.0863	−	30.7787i	−0.660643	−	0.750701i
							\(43\)	−7.30561	+	7.30561i	−0.169898	+	0.169898i	−0.786935	−	0.617037i	\(-0.788333\pi\)
0.617037	+	0.786935i	\(0.288333\pi\)
\(47\)	22.7939	+	3.00088i	0.484977	+	0.0638484i	0.369050	−	0.929409i	\(-0.379683\pi\)
							0.115926	+	0.993258i	\(0.463016\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.v.a.44.19	✓	432
7.4	even	3	inner	287.3.v.a.249.36	yes	432
41.14	odd	8	inner	287.3.v.a.219.36	yes	432
287.137	odd	24	inner	287.3.v.a.137.19	yes	432

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.v.a.44.19	✓	432	1.1	even	1	trivial
287.3.v.a.137.19	yes	432	287.137	odd	24	inner
287.3.v.a.219.36	yes	432	41.14	odd	8	inner
287.3.v.a.249.36	yes	432	7.4	even	3	inner