Embedded newform 483.2.bf.a.145.5

• Label: 483.2.bf.a.145.5
• Level: $483$
• Weight: $2$
• Character: 483.145
• Analytic conductor: $3.857$
• Analytic rank: $0$
• Dimension: $640$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.bf (of order \(66\), degree \(20\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.85677441763\)
Analytic rank:	\(0\)
Dimension:	\(640\)
Relative dimension:	\(32\) over \(\Q(\zeta_{66})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			145.5
Character	\(\chi\)	\(=\)	483.145
Dual form			483.2.bf.a.10.5

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.647644 - 1.87125i) q^{2} +(0.458227 - 0.888835i) q^{3} +(-1.51001 + 1.18748i) q^{4} +(-3.91898 - 0.374217i) q^{5} +(-1.96000 - 0.281805i) q^{6} +(-1.01941 + 2.44148i) q^{7} +(-0.131596 - 0.0845715i) q^{8} +(-0.580057 - 0.814576i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(323\)	\(346\)	\(442\)
\(\chi(n)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{22}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.647644	−	1.87125i	−0.457954	−	1.32317i	−0.903760	−	0.428041i	\(-0.859204\pi\)
							0.445806	−	0.895130i	\(-0.352917\pi\)
\(3\)	0.458227	−	0.888835i	0.264557	−	0.513169i
							\(5\)	−3.91898	−	0.374217i	−1.75262	−	0.167355i	−0.831213	−	0.555954i	\(-0.812353\pi\)
−0.921407	+	0.388599i	\(0.872959\pi\)
\(7\)	−1.01941	+	2.44148i	−0.385301	+	0.922791i
							\(11\)	0.645660	+	0.223465i	0.194674	+	0.0673772i	0.422665	−	0.906286i	\(-0.361095\pi\)
−0.227991	+	0.973663i	\(0.573216\pi\)
\(13\)	−0.0976592	+	0.332597i	−0.0270858	+	0.0922457i	−0.971927	−	0.235284i	\(-0.924398\pi\)
							0.944841	+	0.327530i	\(0.106216\pi\)
\(17\)	5.85483	−	2.34392i	1.42000	−	0.568484i	0.470545	−	0.882376i	\(-0.344057\pi\)
							0.949459	+	0.313892i	\(0.101633\pi\)
\(19\)	1.61603	+	0.646960i	0.370742	+	0.148423i	0.549549	−	0.835461i	\(-0.314800\pi\)
							−0.178807	+	0.983884i	\(0.557224\pi\)
\(23\)	−4.15203	+	2.40013i	−0.865759	+	0.500461i
							\(29\)	−0.951297	+	6.61641i	−0.176651	+	1.22864i	0.687792	+	0.725908i	\(0.258580\pi\)
−0.864444	+	0.502730i	\(0.832329\pi\)
\(31\)	−4.91106	−	0.233942i	−0.882052	−	0.0420173i	−0.398333	−	0.917241i	\(-0.630411\pi\)
							−0.483719	+	0.875224i	\(0.660714\pi\)
\(37\)	−8.88359	+	6.32597i	−1.46045	+	1.03998i	−0.473176	+	0.880968i	\(0.656893\pi\)
							−0.987276	+	0.159016i	\(0.949168\pi\)
\(41\)	−10.0291	+	4.58013i	−1.56628	+	0.715295i	−0.994463	−	0.105087i	\(-0.966488\pi\)
							−0.571815	+	0.820382i	\(0.693761\pi\)
\(43\)	2.14542	+	3.33833i	0.327173	+	0.509091i	0.965406	−	0.260753i	\(-0.0839707\pi\)
							−0.638233	+	0.769843i	\(0.720334\pi\)
\(47\)	−6.49244	−	3.74841i	−0.947020	−	0.546762i	−0.0548659	−	0.998494i	\(-0.517473\pi\)
							−0.892154	+	0.451732i	\(0.850806\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.bf.a.145.5	yes	640
7.3	odd	6	inner	483.2.bf.a.283.28	yes	640
23.10	odd	22	inner	483.2.bf.a.355.28	yes	640
161.10	even	66	inner	483.2.bf.a.10.5	✓	640

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.bf.a.10.5	✓	640	161.10	even	66	inner
483.2.bf.a.145.5	yes	640	1.1	even	1	trivial
483.2.bf.a.283.28	yes	640	7.3	odd	6	inner
483.2.bf.a.355.28	yes	640	23.10	odd	22	inner