Embedded newform 287.3.v.a.44.14

• Label: 287.3.v.a.44.14
• 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			44.14
Character	\(\chi\)	\(=\)	287.44
Dual form			287.3.v.a.137.14

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.585405 - 2.18476i) q^{2} +(2.68487 - 0.353470i) q^{3} +(-0.966375 + 0.557937i) q^{4} +(7.59297 - 2.03453i) q^{5} +(-2.34399 - 5.65888i) q^{6} +(2.78312 - 6.42295i) q^{7} +(-4.61274 - 4.61274i) q^{8} +(-1.60972 + 0.431323i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 48 q^{8} - 36 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.585405	−	2.18476i	−0.292702	−	1.09238i	−0.943025	−	0.332722i	\(-0.892033\pi\)
							0.650323	−	0.759658i	\(-0.274634\pi\)
\(3\)	2.68487	−	0.353470i	0.894958	−	0.117823i	0.331004	−	0.943629i	\(-0.392613\pi\)
							0.563954	+	0.825806i	\(0.309279\pi\)
\(5\)	7.59297	−	2.03453i	1.51859	−	0.406906i	0.599315	−	0.800513i	\(-0.295440\pi\)
							0.919279	+	0.393607i	\(0.128773\pi\)
\(7\)	2.78312	−	6.42295i	0.397588	−	0.917564i
							\(11\)	2.44037	+	18.5365i	0.221852	+	1.68513i	0.633463	+	0.773773i	\(0.281633\pi\)
−0.411611	+	0.911359i	\(0.635034\pi\)
\(13\)	5.60988	−	13.5435i	0.431530	−	1.04180i	−0.547265	−	0.836959i	\(-0.684331\pi\)
							0.978794	−	0.204845i	\(-0.0656690\pi\)
\(17\)	−9.41018	+	12.2636i	−0.553540	+	0.721388i	−0.983388	−	0.181513i	\(-0.941900\pi\)
							0.429848	+	0.902901i	\(0.358567\pi\)
\(19\)	4.85630	+	0.639344i	0.255595	+	0.0336497i	0.257235	−	0.966349i	\(-0.417189\pi\)
							−0.00164001	+	0.999999i	\(0.500522\pi\)
\(23\)	19.0819	+	11.0169i	0.829646	+	0.478996i	0.853731	−	0.520714i	\(-0.174334\pi\)
							−0.0240854	+	0.999710i	\(0.507667\pi\)
\(29\)	5.18761	−	12.5240i	0.178883	−	0.431862i	−0.808850	−	0.588015i	\(-0.799909\pi\)
							0.987733	+	0.156154i	\(0.0499095\pi\)
\(31\)	−27.2042	+	15.7064i	−0.877556	+	0.506657i	−0.869852	−	0.493313i	\(-0.835786\pi\)
							−0.00770439	+	0.999970i	\(0.502452\pi\)
\(37\)	−14.9281	+	25.8562i	−0.403461	+	0.698816i	−0.994141	−	0.108091i	\(-0.965526\pi\)
							0.590680	+	0.806906i	\(0.298860\pi\)
\(41\)	12.3159	−	39.1065i	0.300387	−	0.953817i
							\(43\)	−40.9167	+	40.9167i	−0.951551	+	0.951551i	−0.998879	−	0.0473282i	\(-0.984929\pi\)
0.0473282	+	0.998879i	\(0.484929\pi\)
\(47\)	7.37634	+	0.971114i	0.156943	+	0.0206620i	0.208588	−	0.978004i	\(-0.433113\pi\)
							−0.0516450	+	0.998666i	\(0.516446\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.v.a.44.14	✓	432
7.4	even	3	inner	287.3.v.a.249.41	yes	432
41.14	odd	8	inner	287.3.v.a.219.41	yes	432
287.137	odd	24	inner	287.3.v.a.137.14	yes	432

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.v.a.44.14	✓	432	1.1	even	1	trivial
287.3.v.a.137.14	yes	432	287.137	odd	24	inner
287.3.v.a.219.41	yes	432	41.14	odd	8	inner
287.3.v.a.249.41	yes	432	7.4	even	3	inner