Embedded newform 483.2.y.a.466.15

• Label: 483.2.y.a.466.15
• Level: $483$
• Weight: $2$
• Character: 483.466
• Analytic conductor: $3.857$
• Analytic rank: $0$
• Dimension: $320$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.y (of order \(33\), degree \(20\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.85677441763\)
Analytic rank:	\(0\)
Dimension:	\(320\)
Relative dimension:	\(16\) over \(\Q(\zeta_{33})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			466.15
Character	\(\chi\)	\(=\)	483.466
Dual form			483.2.y.a.142.15

$q$-expansion

\(f(q)\)	\(=\)	\(q+(2.45107 - 0.234049i) q^{2} +(-0.723734 + 0.690079i) q^{3} +(3.98911 - 0.768838i) q^{4} +(-1.26807 - 0.653735i) q^{5} +(-1.61241 + 1.86082i) q^{6} +(1.32343 - 2.29097i) q^{7} +(4.87268 - 1.43075i) q^{8} +(0.0475819 - 0.998867i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 2 q^{2} - 16 q^{3} + 18 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(323\)	\(346\)	\(442\)
\(\chi(n)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{9}{11}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	2.45107	−	0.234049i	1.73317	−	0.165498i	0.819805	−	0.572643i	\(-0.194082\pi\)
							0.913363	+	0.407145i	\(0.133476\pi\)
\(3\)	−0.723734	+	0.690079i	−0.417848	+	0.398417i
							\(5\)	−1.26807	−	0.653735i	−0.567098	−	0.292359i	0.150736	−	0.988574i	\(-0.451836\pi\)
−0.717833	+	0.696215i	\(0.754866\pi\)
\(7\)	1.32343	−	2.29097i	0.500208	−	0.865905i
							\(11\)	5.56437	+	0.531333i	1.67772	+	0.160203i	0.890041	−	0.455881i	\(-0.150676\pi\)
0.787680	+	0.616084i	\(0.211282\pi\)
\(13\)	0.300255	+	2.08832i	0.0832758	+	0.579196i	0.988147	+	0.153511i	\(0.0490579\pi\)
							−0.904871	+	0.425685i	\(0.860033\pi\)
\(17\)	−0.249309	−	0.720332i	−0.0604664	−	0.174706i	0.910722	−	0.413021i	\(-0.135526\pi\)
							−0.971188	+	0.238315i	\(0.923405\pi\)
\(19\)	−0.923243	+	2.66753i	−0.211806	+	0.611974i	−0.999994	−	0.00346069i	\(-0.998898\pi\)
							0.788188	+	0.615435i	\(0.211020\pi\)
\(23\)	−4.60916	+	1.32499i	−0.961077	+	0.276280i
							\(29\)	−2.84225	+	3.28013i	−0.527793	+	0.609105i	−0.955565	−	0.294781i	\(-0.904753\pi\)
0.427772	+	0.903887i	\(0.359299\pi\)
\(31\)	1.19670	−	4.93285i	0.214933	−	0.885966i	−0.757510	−	0.652824i	\(-0.773584\pi\)
							0.972443	−	0.233142i	\(-0.0749007\pi\)
\(37\)	−0.126900	+	2.66396i	−0.0208622	+	0.437952i	0.964138	+	0.265400i	\(0.0855041\pi\)
							−0.985001	+	0.172551i	\(0.944799\pi\)
\(41\)	−6.50294	+	4.17918i	−1.01559	+	0.652679i	−0.938834	−	0.344371i	\(-0.888092\pi\)
							−0.0767547	+	0.997050i	\(0.524456\pi\)
\(43\)	−0.404503	−	0.118773i	−0.0616861	−	0.0181127i	0.250744	−	0.968053i	\(-0.419325\pi\)
							−0.312430	+	0.949941i	\(0.601143\pi\)
\(47\)	0.625055	+	1.08263i	0.0911736	+	0.157917i	0.908005	−	0.418959i	\(-0.137605\pi\)
							−0.816832	+	0.576876i	\(0.804272\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.y.a.466.15	yes	320
7.2	even	3	inner	483.2.y.a.121.2	yes	320
23.4	even	11	inner	483.2.y.a.4.2	✓	320
161.142	even	33	inner	483.2.y.a.142.15	yes	320

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.y.a.4.2	✓	320	23.4	even	11	inner
483.2.y.a.121.2	yes	320	7.2	even	3	inner
483.2.y.a.142.15	yes	320	161.142	even	33	inner
483.2.y.a.466.15	yes	320	1.1	even	1	trivial