Embedded newform 483.2.n.a.47.14

• Label: 483.2.n.a.47.14
• 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			47.14
Character	\(\chi\)	\(=\)	483.47
Dual form			483.2.n.a.185.14

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.40944 - 0.813741i) q^{2} +(1.19429 - 1.25446i) q^{3} +(0.324350 + 0.561790i) q^{4} +(-0.349118 + 0.604691i) q^{5} +(-2.70409 + 0.796242i) q^{6} +(0.554890 - 2.58691i) q^{7} +2.19922i q^{8} +(-0.147336 - 2.99638i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q + 56 q^{4} - 10 q^{7} - 4 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.40944	−	0.813741i	−0.996625	−	0.575402i	−0.0893773	−	0.995998i	\(-0.528488\pi\)
							−0.907248	+	0.420596i	\(0.861821\pi\)
\(3\)	1.19429	−	1.25446i	0.689524	−	0.724262i
							\(5\)	−0.349118	+	0.604691i	−0.156130	+	0.270426i	−0.933470	−	0.358655i	\(-0.883235\pi\)
0.777340	+	0.629081i	\(0.216569\pi\)
\(7\)	0.554890	−	2.58691i	0.209729	−	0.977760i
							\(11\)	3.81554	−	2.20290i	1.15043	−	0.664200i	0.201436	−	0.979502i	\(-0.435439\pi\)
0.948991	+	0.315302i	\(0.102106\pi\)
\(13\)			2.50071i			0.693572i	0.937944	+	0.346786i	\(0.112727\pi\)
							−0.937944	+	0.346786i	\(0.887273\pi\)
\(17\)	−2.77750	−	4.81077i	−0.673643	−	1.16678i	−0.976864	−	0.213863i	\(-0.931395\pi\)
							0.303221	−	0.952920i	\(-0.401938\pi\)
\(19\)	−3.97050	−	2.29237i	−0.910894	−	0.525905i	−0.0301754	−	0.999545i	\(-0.509607\pi\)
							−0.880719	+	0.473640i	\(0.842940\pi\)
\(23\)	0.866025	+	0.500000i	0.180579	+	0.104257i
							\(29\)		−	6.86171i		−	1.27419i	−0.770786	−	0.637094i	\(-0.780136\pi\)
0.770786	−	0.637094i	\(-0.219864\pi\)
\(31\)	−0.792026	+	0.457276i	−0.142252	+	0.0821292i	−0.569437	−	0.822035i	\(-0.692839\pi\)
							0.427185	+	0.904164i	\(0.359505\pi\)
\(37\)	−4.95530	+	8.58282i	−0.814646	+	1.41101i	0.0949365	+	0.995483i	\(0.469735\pi\)
							−0.909582	+	0.415524i	\(0.863598\pi\)
\(41\)	−3.69476			−0.577025			−0.288512	−	0.957476i	\(-0.593161\pi\)
							−0.288512	+	0.957476i	\(0.593161\pi\)
\(43\)	7.11692			1.08532			0.542660	−	0.839952i	\(-0.317417\pi\)
							0.542660	+	0.839952i	\(0.317417\pi\)
\(47\)	0.184503	−	0.319569i	0.0269126	−	0.0466140i	−0.852255	−	0.523126i	\(-0.824766\pi\)
							0.879168	+	0.476512i	\(0.158099\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.n.a.47.14	✓	116
3.2	odd	2	inner	483.2.n.a.47.45	yes	116
7.3	odd	6	inner	483.2.n.a.185.45	yes	116
21.17	even	6	inner	483.2.n.a.185.14	yes	116

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.n.a.47.14	✓	116	1.1	even	1	trivial
483.2.n.a.47.45	yes	116	3.2	odd	2	inner
483.2.n.a.185.14	yes	116	21.17	even	6	inner
483.2.n.a.185.45	yes	116	7.3	odd	6	inner