Embedded newform 201.3.l.a.43.6

• Label: 201.3.l.a.43.6
• 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			43.6
Character	\(\chi\)	\(=\)	201.43
Dual form			201.3.l.a.187.6

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.91347 - 0.873852i) q^{2} +(0.936417 + 1.45709i) q^{3} +(0.278305 + 0.321181i) q^{4} +(9.57220 + 1.37628i) q^{5} +(-0.518521 - 3.60640i) q^{6} +(5.09555 + 2.32706i) q^{7} +(2.11871 + 7.21565i) q^{8} +(-1.24625 + 2.72890i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q + 52 q^{4} + 66 q^{8} + 66 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.91347	−	0.873852i	−0.956735	−	0.436926i	−0.125035	−	0.992152i	\(-0.539904\pi\)
							−0.831699	+	0.555226i	\(0.812632\pi\)
\(3\)	0.936417	+	1.45709i	0.312139	+	0.485698i
							\(5\)	9.57220	+	1.37628i	1.91444	+	0.275255i	0.993444	−	0.114316i	\(-0.0364677\pi\)
0.920996	+	0.389571i	\(0.127377\pi\)
\(7\)	5.09555	+	2.32706i	0.727936	+	0.332437i	0.744679	−	0.667423i	\(-0.232603\pi\)
							−0.0167434	+	0.999860i	\(0.505330\pi\)
\(11\)	−16.6233	−	2.39007i	−1.51121	−	0.217279i	−0.663674	−	0.748022i	\(-0.731004\pi\)
							−0.847533	+	0.530743i	\(0.821913\pi\)
\(13\)	−3.14365	+	10.7063i	−0.241819	+	0.823562i	0.745729	+	0.666249i	\(0.232101\pi\)
							−0.987549	+	0.157313i	\(0.949717\pi\)
\(17\)	15.4897	−	17.8761i	0.911160	−	1.05154i	−0.0873065	−	0.996181i	\(-0.527826\pi\)
							0.998467	−	0.0553536i	\(-0.0176286\pi\)
\(19\)	12.0382	+	26.3599i	0.633588	+	1.38736i	0.905212	+	0.424960i	\(0.139712\pi\)
							−0.271625	+	0.962403i	\(0.587561\pi\)
\(23\)	−11.4371	+	7.35016i	−0.497264	+	0.319572i	−0.765121	−	0.643887i	\(-0.777321\pi\)
							0.267857	+	0.963459i	\(0.413685\pi\)
\(29\)	1.51524			0.0522495			0.0261247	−	0.999659i	\(-0.491683\pi\)
							0.0261247	+	0.999659i	\(0.491683\pi\)
\(31\)	0.0492576	+	0.167756i	0.00158895	+	0.00541148i	0.960284	−	0.279026i	\(-0.0900115\pi\)
							−0.958695	+	0.284437i	\(0.908193\pi\)
\(37\)	9.70948			0.262418			0.131209	−	0.991355i	\(-0.458114\pi\)
							0.131209	+	0.991355i	\(0.458114\pi\)
\(41\)	−46.0884	−	39.9358i	−1.12411	−	0.974044i	−0.124273	−	0.992248i	\(-0.539660\pi\)
							−0.999834	+	0.0182039i	\(0.994205\pi\)
\(43\)	30.3068	+	26.2610i	0.704810	+	0.610721i	0.931713	−	0.363196i	\(-0.118315\pi\)
							−0.226903	+	0.973917i	\(0.572860\pi\)
\(47\)	67.5166	−	43.3903i	1.43652	−	0.923197i	0.436802	−	0.899558i	\(-0.356111\pi\)
							0.999721	−	0.0236394i	\(-0.00752534\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.l.a.43.6	✓	220
67.53	odd	22	inner	201.3.l.a.187.6	yes	220

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.l.a.43.6	✓	220	1.1	even	1	trivial
201.3.l.a.187.6	yes	220	67.53	odd	22	inner