Embedded newform 483.2.n.a.47.18

• Label: 483.2.n.a.47.18
• Level: $483$
• Weight: $2$
• Character: 483.47
• Analytic conductor: $3.857$
• Analytic rank: $0$
• Dimension: $116$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.n (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.85677441763\)
Analytic rank:	\(0\)
Dimension:	\(116\)
Relative dimension:	\(58\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.18
Character	\(\chi\)	\(=\)	483.47
Dual form			483.2.n.a.185.18

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.07338 - 0.619715i) q^{2} +(-0.722709 - 1.57407i) q^{3} +(-0.231907 - 0.401675i) q^{4} +(-0.273772 + 0.474187i) q^{5} +(-0.199734 + 2.13744i) q^{6} +(2.55123 - 0.700882i) q^{7} +3.05372i q^{8} +(-1.95538 + 2.27519i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q + 56 q^{4} - 10 q^{7} - 4 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\)	\(323\)	\(346\)	\(442\)
\(\chi(n)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.07338	−	0.619715i	−0.758993	−	0.438205i	0.0699413	−	0.997551i	\(-0.477719\pi\)
							−0.828934	+	0.559347i	\(0.811052\pi\)
\(3\)	−0.722709	−	1.57407i	−0.417256	−	0.908789i
							\(5\)	−0.273772	+	0.474187i	−0.122434	+	0.212063i	−0.920727	−	0.390207i	\(-0.872403\pi\)
0.798293	+	0.602270i	\(0.205737\pi\)
\(7\)	2.55123	−	0.700882i	0.964274	−	0.264909i
							\(11\)	−3.30069	+	1.90565i	−0.995196	+	0.574576i	−0.906823	−	0.421511i	\(-0.861500\pi\)
−0.0883723	+	0.996088i	\(0.528167\pi\)
\(13\)			6.33716i			1.75761i	0.477178	+	0.878807i	\(0.341660\pi\)
							−0.477178	+	0.878807i	\(0.658340\pi\)
\(17\)	0.532689	+	0.922645i	0.129196	+	0.223774i	0.923365	−	0.383922i	\(-0.125427\pi\)
							−0.794169	+	0.607697i	\(0.792094\pi\)
\(19\)	−3.98747	−	2.30217i	−0.914789	−	0.528154i	−0.0328199	−	0.999461i	\(-0.510449\pi\)
							−0.881969	+	0.471308i	\(0.843782\pi\)
\(23\)	−0.866025	−	0.500000i	−0.180579	−	0.104257i
							\(29\)			4.33342i			0.804696i	0.915487	+	0.402348i	\(0.131806\pi\)
−0.915487	+	0.402348i	\(0.868194\pi\)
\(31\)	−2.78836	+	1.60986i	−0.500804	+	0.289140i	−0.729046	−	0.684465i	\(-0.760036\pi\)
							0.228241	+	0.973605i	\(0.426703\pi\)
\(37\)	1.00493	−	1.74058i	0.165209	−	0.286150i	−0.771521	−	0.636204i	\(-0.780504\pi\)
							0.936729	+	0.350054i	\(0.113837\pi\)
\(41\)	7.04500			1.10024			0.550122	−	0.835084i	\(-0.314581\pi\)
							0.550122	+	0.835084i	\(0.314581\pi\)
\(43\)	−7.94253			−1.21122			−0.605612	−	0.795760i	\(-0.707072\pi\)
							−0.605612	+	0.795760i	\(0.707072\pi\)
\(47\)	−1.88739	+	3.26905i	−0.275304	+	0.476840i	−0.970212	−	0.242259i	\(-0.922112\pi\)
							0.694908	+	0.719099i	\(0.255445\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.n.a.47.18	✓	116
3.2	odd	2	inner	483.2.n.a.47.41	yes	116
7.3	odd	6	inner	483.2.n.a.185.41	yes	116
21.17	even	6	inner	483.2.n.a.185.18	yes	116

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.n.a.47.18	✓	116	1.1	even	1	trivial
483.2.n.a.47.41	yes	116	3.2	odd	2	inner
483.2.n.a.185.18	yes	116	21.17	even	6	inner
483.2.n.a.185.41	yes	116	7.3	odd	6	inner