Embedded newform 201.3.l.a.43.14

• Label: 201.3.l.a.43.14
• Level: $201$
• Weight: $3$
• Character: 201.43
• Analytic conductor: $5.477$
• Analytic rank: $0$
• Dimension: $220$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.l (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.47685331364\)
Analytic rank:	\(0\)
Dimension:	\(220\)
Relative dimension:	\(22\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			43.14
Character	\(\chi\)	\(=\)	201.43
Dual form			201.3.l.a.187.14

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.191268 + 0.0873493i) q^{2} +(0.936417 + 1.45709i) q^{3} +(-2.59049 - 2.98958i) q^{4} +(8.50765 + 1.22322i) q^{5} +(0.0518308 + 0.360491i) q^{6} +(-5.30827 - 2.42421i) q^{7} +(-0.471300 - 1.60510i) q^{8} +(-1.24625 + 2.72890i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q + 52 q^{4} + 66 q^{8} + 66 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).

\(n\)	\(68\)	\(136\)
\(\chi(n)\)	\(1\)	\(e\left(\frac{3}{22}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.191268	+	0.0873493i	0.0956341	+	0.0436746i	0.462658	−	0.886537i	\(-0.346896\pi\)
							−0.367024	+	0.930212i	\(0.619623\pi\)
\(3\)	0.936417	+	1.45709i	0.312139	+	0.485698i
							\(5\)	8.50765	+	1.22322i	1.70153	+	0.244643i	0.923504	−	0.383588i	\(-0.125312\pi\)
0.778027	+	0.628231i	\(0.216221\pi\)
\(7\)	−5.30827	−	2.42421i	−0.758324	−	0.346315i	−0.00155637	−	0.999999i	\(-0.500495\pi\)
							−0.756768	+	0.653684i	\(0.773223\pi\)
\(11\)	20.3087	+	2.91995i	1.84625	+	0.265450i	0.974481	−	0.224470i	\(-0.0720651\pi\)
							0.871767	+	0.489920i	\(0.162974\pi\)
\(13\)	5.36188	−	18.2609i	0.412452	−	1.40468i	−0.447489	−	0.894290i	\(-0.647682\pi\)
							0.859941	−	0.510394i	\(-0.170500\pi\)
\(17\)	−7.85755	+	9.06810i	−0.462209	+	0.533418i	−0.938228	−	0.346017i	\(-0.887534\pi\)
							0.476019	+	0.879435i	\(0.342079\pi\)
\(19\)	0.0150702	+	0.0329991i	0.000793168	+	0.00173680i	0.910028	−	0.414546i	\(-0.136060\pi\)
							−0.909235	+	0.416283i	\(0.863332\pi\)
\(23\)	3.44628	−	2.21479i	0.149838	−	0.0962953i	−0.463573	−	0.886059i	\(-0.653433\pi\)
							0.613412	+	0.789763i	\(0.289797\pi\)
\(29\)	48.2119			1.66248			0.831239	−	0.555915i	\(-0.187632\pi\)
							0.831239	+	0.555915i	\(0.187632\pi\)
\(31\)	1.38170	+	4.70564i	0.0445710	+	0.151795i	0.978772	−	0.204952i	\(-0.0657040\pi\)
							−0.934201	+	0.356747i	\(0.883886\pi\)
\(37\)	−29.8990			−0.808081			−0.404040	−	0.914741i	\(-0.632394\pi\)
							−0.404040	+	0.914741i	\(0.632394\pi\)
\(41\)	−41.0840	−	35.5995i	−1.00205	−	0.868279i	−0.0107532	−	0.999942i	\(-0.503423\pi\)
							−0.991295	+	0.131663i	\(0.957968\pi\)
\(43\)	18.9834	+	16.4492i	0.441475	+	0.382540i	0.847043	−	0.531525i	\(-0.178381\pi\)
							−0.405568	+	0.914065i	\(0.632926\pi\)
\(47\)	−70.5563	+	45.3438i	−1.50120	+	0.964761i	−0.506464	+	0.862261i	\(0.669048\pi\)
							−0.994733	+	0.102500i	\(0.967316\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.l.a.43.14	✓	220
67.53	odd	22	inner	201.3.l.a.187.14	yes	220

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.l.a.43.14	✓	220	1.1	even	1	trivial
201.3.l.a.187.14	yes	220	67.53	odd	22	inner