Embedded newform 287.3.p.a.146.17

• Label: 287.3.p.a.146.17
• Level: $287$
• Weight: $3$
• Character: 287.146
• 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.p (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			146.17
Character	\(\chi\)	\(=\)	287.146
Dual form			287.3.p.a.230.17

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.517693 - 1.59330i) q^{2} -2.17790 q^{3} +(0.965480 - 0.701463i) q^{4} +(-3.00150 - 4.13121i) q^{5} +(1.12748 + 3.47003i) q^{6} +(6.85258 + 1.42904i) q^{7} +(-7.03882 - 5.11400i) q^{8} -4.25677 q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 6 q^{2} - 110 q^{4} - 5 q^{7} + 22 q^{8} + 552 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(206\)	\(211\)
\(\chi(n)\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.517693	−	1.59330i	−0.258847	−	0.796648i	−0.993047	−	0.117716i	\(-0.962443\pi\)
							0.734201	−	0.678933i	\(-0.237557\pi\)
\(3\)	−2.17790			−0.725965			−0.362983	−	0.931796i	\(-0.618242\pi\)
							−0.362983	+	0.931796i	\(0.618242\pi\)
\(5\)	−3.00150	−	4.13121i	−0.600300	−	0.826242i	0.395436	−	0.918494i	\(-0.370594\pi\)
							−0.995736	+	0.0922514i	\(0.970594\pi\)
\(7\)	6.85258	+	1.42904i	0.978940	+	0.204149i
							\(11\)	6.57137	−	9.04472i	0.597398	−	0.822247i	−0.398069	−	0.917355i	\(-0.630320\pi\)
0.995467	+	0.0951081i	\(0.0303197\pi\)
\(13\)	−0.862601	−	2.65481i	−0.0663539	−	0.204216i	0.912382	−	0.409339i	\(-0.134241\pi\)
							−0.978736	+	0.205123i	\(0.934241\pi\)
\(17\)	−19.8135	−	14.3953i	−1.16550	−	0.846784i	−0.175035	−	0.984562i	\(-0.556004\pi\)
							−0.990463	+	0.137778i	\(0.956004\pi\)
\(19\)	−4.55391	+	14.0155i	−0.239680	+	0.737658i	0.756787	+	0.653662i	\(0.226768\pi\)
							−0.996466	+	0.0839958i	\(0.973232\pi\)
\(23\)	9.07213	+	27.9211i	0.394440	+	1.21396i	0.929397	+	0.369083i	\(0.120328\pi\)
							−0.534956	+	0.844880i	\(0.679672\pi\)
\(29\)	−9.46924	−	13.0333i	−0.326526	−	0.449424i	0.613920	−	0.789368i	\(-0.289592\pi\)
							−0.940446	+	0.339944i	\(0.889592\pi\)
\(31\)	−29.8759	+	41.1206i	−0.963737	+	1.32647i	−0.0185896	+	0.999827i	\(0.505918\pi\)
							−0.945148	+	0.326643i	\(0.894082\pi\)
\(37\)	−50.2774	+	36.5287i	−1.35885	+	0.987262i	−0.360333	+	0.932824i	\(0.617337\pi\)
							−0.998517	+	0.0544384i	\(0.982663\pi\)
\(41\)	−22.6204	−	34.1953i	−0.551717	−	0.834031i
							\(43\)	−14.7258	−	45.3213i	−0.342460	−	1.05398i	−0.962930	−	0.269753i	\(-0.913058\pi\)
0.620470	−	0.784230i	\(-0.286942\pi\)
\(47\)	11.2156	+	34.5182i	0.238631	+	0.734430i	0.996619	+	0.0821616i	\(0.0261824\pi\)
							−0.757988	+	0.652268i	\(0.773818\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.p.a.146.17	✓	216
7.6	odd	2	inner	287.3.p.a.146.18	yes	216
41.25	even	10	inner	287.3.p.a.230.18	yes	216
287.230	odd	10	inner	287.3.p.a.230.17	yes	216

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.p.a.146.17	✓	216	1.1	even	1	trivial
287.3.p.a.146.18	yes	216	7.6	odd	2	inner
287.3.p.a.230.17	yes	216	287.230	odd	10	inner
287.3.p.a.230.18	yes	216	41.25	even	10	inner