Embedded newform 287.3.v.a.44.18

• Label: 287.3.v.a.44.18
• 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			44.18
Character	\(\chi\)	\(=\)	287.44
Dual form			287.3.v.a.137.18

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.432281 - 1.61329i) q^{2} +(-1.08853 + 0.143308i) q^{3} +(1.04825 - 0.605209i) q^{4} +(-2.34666 + 0.628787i) q^{5} +(0.701750 + 1.69417i) q^{6} +(5.57803 - 4.22914i) q^{7} +(-6.15357 - 6.15357i) q^{8} +(-7.52897 + 2.01738i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 48 q^{8} - 36 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.432281	−	1.61329i	−0.216140	−	0.806647i	−0.985762	−	0.168147i	\(-0.946222\pi\)
							0.769622	−	0.638500i	\(-0.220445\pi\)
\(3\)	−1.08853	+	0.143308i	−0.362844	+	0.0477694i	−0.309744	−	0.950820i	\(-0.600244\pi\)
							−0.0530999	+	0.998589i	\(0.516910\pi\)
\(5\)	−2.34666	+	0.628787i	−0.469333	+	0.125757i	−0.485731	−	0.874108i	\(-0.661447\pi\)
							0.0163984	+	0.999866i	\(0.494780\pi\)
\(7\)	5.57803	−	4.22914i	0.796861	−	0.604162i
							\(11\)	−0.392217	−	2.97919i	−0.0356561	−	0.270835i	−0.999981	−	0.00611461i	\(-0.998054\pi\)
0.964325	−	0.264720i	\(-0.0852797\pi\)
\(13\)	−3.35001	+	8.08763i	−0.257693	+	0.622126i	−0.998785	−	0.0492776i	\(-0.984308\pi\)
							0.741092	+	0.671403i	\(0.234308\pi\)
\(17\)	18.4992	−	24.1086i	1.08819	−	1.41815i	0.188256	−	0.982120i	\(-0.439716\pi\)
							0.899931	−	0.436033i	\(-0.143617\pi\)
\(19\)	−22.1890	−	2.92124i	−1.16784	−	0.153750i	−0.478436	−	0.878122i	\(-0.658796\pi\)
							−0.689408	+	0.724373i	\(0.742129\pi\)
\(23\)	−27.1839	−	15.6946i	−1.18191	−	0.682374i	−0.225452	−	0.974254i	\(-0.572386\pi\)
							−0.956455	+	0.291880i	\(0.905719\pi\)
\(29\)	1.66744	−	4.02556i	0.0574979	−	0.138812i	−0.892520	−	0.451008i	\(-0.851065\pi\)
							0.950018	+	0.312196i	\(0.101065\pi\)
\(31\)	−36.6304	+	21.1486i	−1.18163	+	0.682212i	−0.956390	−	0.292093i	\(-0.905648\pi\)
							−0.225235	+	0.974304i	\(0.572315\pi\)
\(37\)	−16.8497	+	29.1845i	−0.455396	+	0.788769i	−0.998711	−	0.0507598i	\(-0.983836\pi\)
							0.543315	+	0.839529i	\(0.317169\pi\)
\(41\)	37.3310	−	16.9527i	0.910513	−	0.413481i
							\(43\)	−32.4811	+	32.4811i	−0.755374	+	0.755374i	−0.975477	−	0.220102i	\(-0.929361\pi\)
0.220102	+	0.975477i	\(0.429361\pi\)
\(47\)	52.3110	+	6.88687i	1.11300	+	0.146529i	0.664525	−	0.747266i	\(-0.268634\pi\)
							0.448475	+	0.893796i	\(0.351967\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.v.a.44.18	✓	432
7.4	even	3	inner	287.3.v.a.249.37	yes	432
41.14	odd	8	inner	287.3.v.a.219.37	yes	432
287.137	odd	24	inner	287.3.v.a.137.18	yes	432

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.v.a.44.18	✓	432	1.1	even	1	trivial
287.3.v.a.137.18	yes	432	287.137	odd	24	inner
287.3.v.a.219.37	yes	432	41.14	odd	8	inner
287.3.v.a.249.37	yes	432	7.4	even	3	inner