Embedded newform 287.3.q.a.73.18

• Label: 287.3.q.a.73.18
• Level: $287$
• Weight: $3$
• Character: 287.73
• 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.q (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.82018358714\)
Analytic rank:	\(0\)
Dimension:	\(216\)
Relative dimension:	\(54\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.18
Character	\(\chi\)	\(=\)	287.73
Dual form			287.3.q.a.173.18

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.21135 + 0.699374i) q^{2} +(-5.22513 + 1.40007i) q^{3} +(-1.02175 + 1.76973i) q^{4} +(-1.85825 - 3.21859i) q^{5} +(5.35029 - 5.35029i) q^{6} +(6.57733 + 2.39557i) q^{7} -8.45334i q^{8} +(17.5475 - 10.1311i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 6 q^{3} + 204 q^{4} - 4 q^{7}+O(q^{10}) \)

Character values

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

\(n\)	\(206\)	\(211\)
\(\chi(n)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{4}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.21135	+	0.699374i	−0.605675	+	0.349687i	−0.771271	−	0.636507i	\(-0.780379\pi\)
							0.165596	+	0.986194i	\(0.447045\pi\)
\(3\)	−5.22513	+	1.40007i	−1.74171	+	0.466689i	−0.982825	−	0.184537i	\(-0.940921\pi\)
							−0.758883	+	0.651227i	\(0.774255\pi\)
\(5\)	−1.85825	−	3.21859i	−0.371651	−	0.643718i	0.618169	−	0.786045i	\(-0.287875\pi\)
							−0.989820	+	0.142327i	\(0.954541\pi\)
\(7\)	6.57733	+	2.39557i	0.939618	+	0.342224i
							\(11\)	−0.815015	−	3.04168i	−0.0740923	−	0.276516i	0.918934	−	0.394412i	\(-0.129052\pi\)
−0.993026	+	0.117896i	\(0.962385\pi\)
\(13\)	15.9606	+	15.9606i	1.22774	+	1.22774i	0.964816	+	0.262926i	\(0.0846876\pi\)
							0.262926	+	0.964816i	\(0.415312\pi\)
\(17\)	0.543657	+	2.02895i	0.0319798	+	0.119350i	0.980071	−	0.198650i	\(-0.0636555\pi\)
							−0.948091	+	0.318000i	\(0.896989\pi\)
\(19\)	−16.4485	−	4.40736i	−0.865711	−	0.231967i	−0.201479	−	0.979493i	\(-0.564575\pi\)
							−0.664232	+	0.747526i	\(0.731241\pi\)
\(23\)	−19.9480	−	34.5509i	−0.867304	−	1.50222i	−0.864741	−	0.502218i	\(-0.832517\pi\)
							−0.00256354	−	0.999997i	\(-0.500816\pi\)
\(29\)	−26.9002	+	26.9002i	−0.927594	+	0.927594i	−0.997550	−	0.0699564i	\(-0.977714\pi\)
							0.0699564	+	0.997550i	\(0.477714\pi\)
\(31\)	43.9267	+	25.3611i	1.41699	+	0.818099i	0.996033	−	0.0889821i	\(-0.0283614\pi\)
							0.420956	+	0.907081i	\(0.361695\pi\)
\(37\)	18.9196	+	32.7698i	0.511342	+	0.885670i	0.999914	+	0.0131463i	\(0.00418470\pi\)
							−0.488572	+	0.872524i	\(0.662482\pi\)
\(41\)	1.89179	+	40.9563i	0.0461411	+	0.998935i
							\(43\)		−	30.8145i		−	0.716616i	−0.933603	−	0.358308i	\(-0.883354\pi\)
0.933603	−	0.358308i	\(-0.116646\pi\)
\(47\)	−1.65229	−	0.442731i	−0.0351552	−	0.00941981i	0.241199	−	0.970476i	\(-0.422459\pi\)
							−0.276354	+	0.961056i	\(0.589126\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.q.a.73.18	✓	216
7.5	odd	6	inner	287.3.q.a.278.37	yes	216
41.9	even	4	inner	287.3.q.a.255.37	yes	216
287.173	odd	12	inner	287.3.q.a.173.18	yes	216

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.q.a.73.18	✓	216	1.1	even	1	trivial
287.3.q.a.173.18	yes	216	287.173	odd	12	inner
287.3.q.a.255.37	yes	216	41.9	even	4	inner
287.3.q.a.278.37	yes	216	7.5	odd	6	inner