Embedded newform 287.3.v.a.44.20

• Label: 287.3.v.a.44.20
• 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			44.20
Character	\(\chi\)	\(=\)	287.44
Dual form			287.3.v.a.137.20

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.345775 - 1.29045i) q^{2} +(0.635300 - 0.0836388i) q^{3} +(1.91841 - 1.10759i) q^{4} +(7.27076 - 1.94819i) q^{5} +(-0.327602 - 0.790901i) q^{6} +(-5.53537 - 4.28481i) q^{7} +(-5.87132 - 5.87132i) q^{8} +(-8.29672 + 2.22310i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 48 q^{8} - 36 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.345775	−	1.29045i	−0.172887	−	0.645224i	−0.996902	−	0.0786555i	\(-0.974937\pi\)
							0.824015	−	0.566569i	\(-0.191729\pi\)
\(3\)	0.635300	−	0.0836388i	0.211767	−	0.0278796i	−0.0238964	−	0.999714i	\(-0.507607\pi\)
							0.235663	+	0.971835i	\(0.424274\pi\)
\(5\)	7.27076	−	1.94819i	1.45415	−	0.389639i	0.556686	−	0.830723i	\(-0.312073\pi\)
							0.897466	+	0.441084i	\(0.145406\pi\)
\(7\)	−5.53537	−	4.28481i	−0.790768	−	0.612116i
							\(11\)	−2.35407	−	17.8809i	−0.214006	−	1.62554i	−0.674778	−	0.738020i	\(-0.735761\pi\)
0.460772	−	0.887518i	\(-0.347573\pi\)
\(13\)	−6.03265	+	14.5641i	−0.464050	+	1.12032i	0.502670	+	0.864478i	\(0.332351\pi\)
							−0.966720	+	0.255837i	\(0.917649\pi\)
\(17\)	3.32217	−	4.32953i	0.195422	−	0.254678i	−0.685356	−	0.728208i	\(-0.740354\pi\)
							0.880778	+	0.473529i	\(0.157020\pi\)
\(19\)	30.3097	+	3.99035i	1.59525	+	0.210018i	0.875149	−	0.483854i	\(-0.160763\pi\)
							0.720098	+	0.693872i	\(0.244097\pi\)
\(23\)	−0.0989475	−	0.0571274i	−0.00430207	−	0.00248380i	0.497847	−	0.867265i	\(-0.334124\pi\)
							−0.502149	+	0.864781i	\(0.667457\pi\)
\(29\)	−2.79136	+	6.73895i	−0.0962539	+	0.232378i	−0.964671	−	0.263456i	\(-0.915138\pi\)
							0.868417	+	0.495834i	\(0.165138\pi\)
\(31\)	−2.79443	+	1.61336i	−0.0901428	+	0.0520440i	−0.544394	−	0.838830i	\(-0.683240\pi\)
							0.454251	+	0.890874i	\(0.349907\pi\)
\(37\)	−9.89220	+	17.1338i	−0.267357	+	0.463075i	−0.968178	−	0.250261i	\(-0.919484\pi\)
							0.700822	+	0.713336i	\(0.252817\pi\)
\(41\)	39.9095	+	9.39336i	0.973401	+	0.229106i
							\(43\)	55.7239	−	55.7239i	1.29590	−	1.29590i	0.364830	−	0.931074i	\(-0.381127\pi\)
0.931074	−	0.364830i	\(-0.118873\pi\)
\(47\)	32.5468	+	4.28487i	0.692486	+	0.0911675i	0.468551	−	0.883437i	\(-0.344776\pi\)
							0.223935	+	0.974604i	\(0.428110\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.v.a.44.20	✓	432
7.4	even	3	inner	287.3.v.a.249.35	yes	432
41.14	odd	8	inner	287.3.v.a.219.35	yes	432
287.137	odd	24	inner	287.3.v.a.137.20	yes	432

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.v.a.44.20	✓	432	1.1	even	1	trivial
287.3.v.a.137.20	yes	432	287.137	odd	24	inner
287.3.v.a.219.35	yes	432	41.14	odd	8	inner
287.3.v.a.249.35	yes	432	7.4	even	3	inner