Embedded newform 483.2.v.a.41.2

• Label: 483.2.v.a.41.2
• Level: $483$
• Weight: $2$
• Character: 483.41
• Analytic conductor: $3.857$
• Analytic rank: $0$
• Dimension: $600$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.v (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.85677441763\)
Analytic rank:	\(0\)
Dimension:	\(600\)
Relative dimension:	\(60\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			41.2
Character	\(\chi\)	\(=\)	483.41
Dual form			483.2.v.a.377.2

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.783018 + 2.66671i) q^{2} +(1.29371 - 1.15165i) q^{3} +(-4.81573 - 3.09488i) q^{4} +(-0.328519 + 2.28490i) q^{5} +(2.05813 + 4.35173i) q^{6} +(2.09878 - 1.61094i) q^{7} +(7.82307 - 6.77873i) q^{8} +(0.347391 - 2.97982i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 600 q + 20 q^{4} - 18 q^{7} - 26 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(323\)	\(346\)	\(442\)
\(\chi(n)\)	\(-1\)	\(-1\)	\(e\left(\frac{6}{11}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.783018	+	2.66671i	−0.553677	+	1.88565i	−0.0987737	+	0.995110i	\(0.531492\pi\)
							−0.454903	+	0.890541i	\(0.650326\pi\)
\(3\)	1.29371	−	1.15165i	0.746926	−	0.664907i
							\(5\)	−0.328519	+	2.28490i	−0.146918	+	1.02184i	0.774307	+	0.632810i	\(0.218099\pi\)
−0.921225	+	0.389029i	\(0.872811\pi\)
\(7\)	2.09878	−	1.61094i	0.793265	−	0.608876i
							\(11\)	0.892863	+	3.04081i	0.269208	+	0.916840i	0.977503	+	0.210922i	\(0.0676467\pi\)
−0.708294	+	0.705917i	\(0.750535\pi\)
\(13\)	1.39374	+	0.636498i	0.386553	+	0.176533i	0.599206	−	0.800595i	\(-0.295483\pi\)
							−0.212653	+	0.977128i	\(0.568210\pi\)
\(17\)	3.01474	−	1.93745i	0.731181	−	0.469902i	−0.121329	−	0.992612i	\(-0.538716\pi\)
							0.852510	+	0.522711i	\(0.175079\pi\)
\(19\)	−2.67355	+	4.16012i	−0.613354	+	0.954398i	0.386135	+	0.922442i	\(0.373810\pi\)
							−0.999489	+	0.0319557i	\(0.989826\pi\)
\(23\)	4.76812	+	0.514855i	0.994221	+	0.107355i
							\(29\)	2.38941	+	3.71800i	0.443703	+	0.690415i	0.989015	−	0.147818i	\(-0.0472251\pi\)
−0.545312	+	0.838233i	\(0.683589\pi\)
\(31\)	−2.75156	+	2.38424i	−0.494195	+	0.428222i	−0.865967	−	0.500102i	\(-0.833296\pi\)
							0.371772	+	0.928324i	\(0.378750\pi\)
\(37\)	−0.721075	−	5.01519i	−0.118544	−	0.824492i	−0.959161	−	0.282861i	\(-0.908716\pi\)
							0.840617	−	0.541630i	\(-0.182193\pi\)
\(41\)	−1.21612	+	8.45831i	−0.189926	+	1.32097i	0.642267	+	0.766481i	\(0.277994\pi\)
							−0.832193	+	0.554485i	\(0.812915\pi\)
\(43\)	4.85917	−	5.60778i	0.741017	−	0.855179i	−0.252649	−	0.967558i	\(-0.581302\pi\)
							0.993665	+	0.112379i	\(0.0358472\pi\)
\(47\)	−4.42066			−0.644820			−0.322410	−	0.946600i	\(-0.604493\pi\)
							−0.322410	+	0.946600i	\(0.604493\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.v.a.41.2	yes	600
3.2	odd	2	inner	483.2.v.a.41.59	yes	600
7.6	odd	2	inner	483.2.v.a.41.1	✓	600
21.20	even	2	inner	483.2.v.a.41.60	yes	600
23.9	even	11	inner	483.2.v.a.377.60	yes	600
69.32	odd	22	inner	483.2.v.a.377.1	yes	600
161.55	odd	22	inner	483.2.v.a.377.59	yes	600
483.377	even	22	inner	483.2.v.a.377.2	yes	600

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.v.a.41.1	✓	600	7.6	odd	2	inner
483.2.v.a.41.2	yes	600	1.1	even	1	trivial
483.2.v.a.41.59	yes	600	3.2	odd	2	inner
483.2.v.a.41.60	yes	600	21.20	even	2	inner
483.2.v.a.377.1	yes	600	69.32	odd	22	inner
483.2.v.a.377.2	yes	600	483.377	even	22	inner
483.2.v.a.377.59	yes	600	161.55	odd	22	inner
483.2.v.a.377.60	yes	600	23.9	even	11	inner