Embedded newform 483.2.n.a.47.11

• Label: 483.2.n.a.47.11
• 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			47.11
Character	\(\chi\)	\(=\)	483.47
Dual form			483.2.n.a.185.11

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.75262 - 1.01188i) q^{2} +(1.45057 - 0.946485i) q^{3} +(1.04778 + 1.81482i) q^{4} +(1.57777 - 2.73277i) q^{5} +(-3.50003 + 0.191028i) q^{6} +(1.90338 + 1.83770i) q^{7} -0.193410i q^{8} +(1.20833 - 2.74589i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q + 56 q^{4} - 10 q^{7} - 4 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.75262	−	1.01188i	−1.23929	−	0.715504i	−0.270341	−	0.962765i	\(-0.587136\pi\)
							−0.968949	+	0.247261i	\(0.920470\pi\)
\(3\)	1.45057	−	0.946485i	0.837489	−	0.546453i
							\(5\)	1.57777	−	2.73277i	0.705599	−	1.22213i	−0.260877	−	0.965372i	\(-0.584012\pi\)
0.966475	−	0.256760i	\(-0.0826551\pi\)
\(7\)	1.90338	+	1.83770i	0.719411	+	0.694584i
							\(11\)	2.49899	−	1.44279i	0.753474	−	0.435019i	−0.0734735	−	0.997297i	\(-0.523408\pi\)
0.826948	+	0.562279i	\(0.190075\pi\)
\(13\)		−	0.189639i		−	0.0525964i	−0.999654	−	0.0262982i	\(-0.991628\pi\)
							0.999654	−	0.0262982i	\(-0.00837194\pi\)
\(17\)	1.96620	+	3.40556i	0.476873	+	0.825969i	0.999649	−	0.0265015i	\(-0.00843668\pi\)
							−0.522775	+	0.852470i	\(0.675103\pi\)
\(19\)	2.47167	+	1.42702i	0.567039	+	0.327380i	0.755966	−	0.654611i	\(-0.227168\pi\)
							−0.188927	+	0.981991i	\(0.560501\pi\)
\(23\)	−0.866025	−	0.500000i	−0.180579	−	0.104257i
							\(29\)			6.49450i			1.20600i	0.797742	+	0.602999i	\(0.206028\pi\)
−0.797742	+	0.602999i	\(0.793972\pi\)
\(31\)	−4.20878	+	2.42994i	−0.755919	+	0.436430i	−0.827829	−	0.560981i	\(-0.810424\pi\)
							0.0719095	+	0.997411i	\(0.477091\pi\)
\(37\)	1.90992	−	3.30808i	0.313989	−	0.543844i	−0.665233	−	0.746636i	\(-0.731668\pi\)
							0.979222	+	0.202791i	\(0.0650013\pi\)
\(41\)	−1.50725			−0.235394			−0.117697	−	0.993050i	\(-0.537551\pi\)
							−0.117697	+	0.993050i	\(0.537551\pi\)
\(43\)	−6.21375			−0.947589			−0.473794	−	0.880636i	\(-0.657116\pi\)
							−0.473794	+	0.880636i	\(0.657116\pi\)
\(47\)	−1.25429	+	2.17249i	−0.182957	+	0.316891i	−0.942886	−	0.333115i	\(-0.891900\pi\)
							0.759929	+	0.650006i	\(0.225234\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.n.a.47.11	✓	116
3.2	odd	2	inner	483.2.n.a.47.48	yes	116
7.3	odd	6	inner	483.2.n.a.185.48	yes	116
21.17	even	6	inner	483.2.n.a.185.11	yes	116

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.n.a.47.11	✓	116	1.1	even	1	trivial
483.2.n.a.47.48	yes	116	3.2	odd	2	inner
483.2.n.a.185.11	yes	116	21.17	even	6	inner
483.2.n.a.185.48	yes	116	7.3	odd	6	inner