Embedded newform 287.3.o.a.139.9

• Label: 287.3.o.a.139.9
• 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			139.9
Character	\(\chi\)	\(=\)	287.139
Dual form			287.3.o.a.223.10

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.875068 + 2.69318i) q^{2} -3.79026i q^{3} +(-3.25142 - 2.36230i) q^{4} +(2.82818 - 3.89266i) q^{5} +(10.2079 + 3.31674i) q^{6} +(6.36840 - 2.90576i) q^{7} +(0.0434828 - 0.0315921i) q^{8} -5.36606 q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 6 q^{2} - 110 q^{4} - 3 q^{7} - 2 q^{8} - 648 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.875068	+	2.69318i	−0.437534	+	1.34659i	0.452933	+	0.891544i	\(0.350378\pi\)
							−0.890467	+	0.455047i	\(0.849622\pi\)
\(3\)		−	3.79026i		−	1.26342i	−0.775205	−	0.631710i	\(-0.782353\pi\)
							0.775205	−	0.631710i	\(-0.217647\pi\)
\(5\)	2.82818	−	3.89266i	0.565637	−	0.778532i	−0.426393	−	0.904538i	\(-0.640216\pi\)
							0.992029	+	0.126006i	\(0.0402158\pi\)
\(7\)	6.36840	−	2.90576i	0.909772	−	0.415109i
							\(11\)	0.157909	−	0.114728i	0.0143554	−	0.0104298i	−0.580584	−	0.814200i	\(-0.697176\pi\)
0.594940	+	0.803770i	\(0.297176\pi\)
\(13\)	−21.1667	−	6.87748i	−1.62821	−	0.529037i	−0.654349	−	0.756192i	\(-0.727057\pi\)
							−0.973859	+	0.227155i	\(0.927057\pi\)
\(17\)	−5.76370	−	7.93305i	−0.339041	−	0.466650i	0.605120	−	0.796134i	\(-0.293125\pi\)
							−0.944161	+	0.329484i	\(0.893125\pi\)
\(19\)	11.4824	−	3.73085i	0.604336	−	0.196361i	0.00916258	−	0.999958i	\(-0.497083\pi\)
							0.595173	+	0.803597i	\(0.297083\pi\)
\(23\)	2.10176	−	6.46854i	0.0913807	−	0.281241i	−0.894913	−	0.446241i	\(-0.852762\pi\)
							0.986294	+	0.165000i	\(0.0527625\pi\)
\(29\)	9.56014	+	6.94585i	0.329660	+	0.239512i	0.740286	−	0.672292i	\(-0.234690\pi\)
							−0.410626	+	0.911804i	\(0.634690\pi\)
\(31\)	5.71623	+	7.86772i	0.184395	+	0.253797i	0.891200	−	0.453611i	\(-0.149864\pi\)
							−0.706805	+	0.707408i	\(0.749864\pi\)
\(37\)	−46.4563	−	33.7525i	−1.25558	−	0.912230i	−0.257045	−	0.966399i	\(-0.582749\pi\)
							−0.998532	+	0.0541695i	\(0.982749\pi\)
\(41\)	−32.6193	−	24.8392i	−0.795592	−	0.605833i
							\(43\)	9.06984	−	27.9141i	0.210927	−	0.649165i	−0.788491	−	0.615046i	\(-0.789137\pi\)
0.999418	−	0.0341192i	\(-0.0108626\pi\)
\(47\)	−4.47097	−	1.45271i	−0.0951270	−	0.0309086i	0.261067	−	0.965321i	\(-0.415926\pi\)
							−0.356194	+	0.934412i	\(0.615926\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.o.a.139.9	✓	216
7.6	odd	2	inner	287.3.o.a.139.10	yes	216
41.18	even	5	inner	287.3.o.a.223.9	yes	216
287.223	odd	10	inner	287.3.o.a.223.10	yes	216

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.o.a.139.9	✓	216	1.1	even	1	trivial
287.3.o.a.139.10	yes	216	7.6	odd	2	inner
287.3.o.a.223.9	yes	216	41.18	even	5	inner
287.3.o.a.223.10	yes	216	287.223	odd	10	inner