Embedded newform 287.3.o.a.139.12

• Label: 287.3.o.a.139.12
• 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			139.12
Character	\(\chi\)	\(=\)	287.139
Dual form			287.3.o.a.223.11

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.862122 + 2.65334i) q^{2} +5.31208i q^{3} +(-3.06088 - 2.22386i) q^{4} +(1.17908 - 1.62286i) q^{5} +(-14.0948 - 4.57966i) q^{6} +(2.73659 + 6.44291i) q^{7} +(-0.488754 + 0.355101i) q^{8} -19.2182 q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 6 q^{2} - 110 q^{4} - 3 q^{7} - 2 q^{8} - 648 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.862122	+	2.65334i	−0.431061	+	1.32667i	0.466009	+	0.884780i	\(0.345691\pi\)
							−0.897070	+	0.441889i	\(0.854309\pi\)
\(3\)			5.31208i			1.77069i	0.464930	+	0.885347i	\(0.346079\pi\)
							−0.464930	+	0.885347i	\(0.653921\pi\)
\(5\)	1.17908	−	1.62286i	0.235815	−	0.324572i	−0.674665	−	0.738124i	\(-0.735712\pi\)
							0.910480	+	0.413552i	\(0.135712\pi\)
\(7\)	2.73659	+	6.44291i	0.390942	+	0.920415i
							\(11\)	6.62591	−	4.81400i	0.602355	−	0.437637i	−0.244359	−	0.969685i	\(-0.578577\pi\)
0.846714	+	0.532048i	\(0.178577\pi\)
\(13\)	−10.6390	−	3.45683i	−0.818387	−	0.265910i	−0.130241	−	0.991482i	\(-0.541575\pi\)
							−0.688146	+	0.725572i	\(0.741575\pi\)
\(17\)	−7.03729	−	9.68600i	−0.413958	−	0.569765i	0.550220	−	0.835020i	\(-0.314544\pi\)
							−0.964178	+	0.265255i	\(0.914544\pi\)
\(19\)	−4.76325	+	1.54767i	−0.250697	+	0.0814565i	−0.431670	−	0.902032i	\(-0.642075\pi\)
							0.180973	+	0.983488i	\(0.442075\pi\)
\(23\)	−7.50979	+	23.1128i	−0.326513	+	1.00490i	0.644240	+	0.764823i	\(0.277174\pi\)
							−0.970753	+	0.240080i	\(0.922826\pi\)
\(29\)	19.7069	+	14.3179i	0.679547	+	0.493720i	0.873207	−	0.487349i	\(-0.162036\pi\)
							−0.193660	+	0.981069i	\(0.562036\pi\)
\(31\)	−14.2283	−	19.5836i	−0.458979	−	0.631730i	0.515318	−	0.856999i	\(-0.327674\pi\)
							−0.974297	+	0.225269i	\(0.927674\pi\)
\(37\)	55.5481	+	40.3581i	1.50130	+	1.09076i	0.969860	+	0.243662i	\(0.0783488\pi\)
							0.531440	+	0.847096i	\(0.321651\pi\)
\(41\)	−38.0247	+	15.3337i	−0.927432	+	0.373992i
							\(43\)	2.52967	−	7.78552i	0.0588295	−	0.181058i	−0.917323	−	0.398143i	\(-0.869655\pi\)
0.976153	+	0.217085i	\(0.0696547\pi\)
\(47\)	61.0775	+	19.8453i	1.29952	+	0.422240i	0.875415	−	0.483373i	\(-0.160588\pi\)
							0.424106	+	0.905613i	\(0.360588\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.o.a.139.12	yes	216
7.6	odd	2	inner	287.3.o.a.139.11	✓	216
41.18	even	5	inner	287.3.o.a.223.12	yes	216
287.223	odd	10	inner	287.3.o.a.223.11	yes	216

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.o.a.139.11	✓	216	7.6	odd	2	inner
287.3.o.a.139.12	yes	216	1.1	even	1	trivial
287.3.o.a.223.11	yes	216	287.223	odd	10	inner
287.3.o.a.223.12	yes	216	41.18	even	5	inner