Embedded newform 201.3.l.a.43.2

• Label: 201.3.l.a.43.2
• 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			43.2
Character	\(\chi\)	\(=\)	201.43
Dual form			201.3.l.a.187.2

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-3.31598 - 1.51436i) q^{2} +(-0.936417 - 1.45709i) q^{3} +(6.08302 + 7.02018i) q^{4} +(-3.45931 - 0.497373i) q^{5} +(0.898581 + 6.24977i) q^{6} +(4.95524 + 2.26298i) q^{7} +(-5.43199 - 18.4997i) q^{8} +(-1.24625 + 2.72890i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q + 52 q^{4} + 66 q^{8} + 66 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−3.31598	−	1.51436i	−1.65799	−	0.757179i	−0.999991	−	0.00416151i	\(-0.998675\pi\)
							−0.658000	−	0.753018i	\(-0.728597\pi\)
\(3\)	−0.936417	−	1.45709i	−0.312139	−	0.485698i
							\(5\)	−3.45931	−	0.497373i	−0.691862	−	0.0994747i	−0.212590	−	0.977141i	\(-0.568190\pi\)
−0.479271	+	0.877667i	\(0.659099\pi\)
\(7\)	4.95524	+	2.26298i	0.707892	+	0.323283i	0.736623	−	0.676304i	\(-0.236419\pi\)
							−0.0287309	+	0.999587i	\(0.509147\pi\)
\(11\)	4.48097	+	0.644267i	0.407361	+	0.0585697i	0.342950	−	0.939354i	\(-0.388574\pi\)
							0.0644114	+	0.997923i	\(0.479483\pi\)
\(13\)	4.03808	−	13.7524i	0.310621	−	1.05788i	−0.645220	−	0.763997i	\(-0.723234\pi\)
							0.955842	−	0.293882i	\(-0.0949474\pi\)
\(17\)	12.6650	−	14.6162i	0.744998	−	0.859774i	−0.249075	−	0.968484i	\(-0.580127\pi\)
							0.994073	+	0.108710i	\(0.0346721\pi\)
\(19\)	4.31849	+	9.45617i	0.227289	+	0.497693i	0.988576	−	0.150721i	\(-0.0481596\pi\)
							−0.761287	+	0.648415i	\(0.775432\pi\)
\(23\)	−8.84783	+	5.68616i	−0.384688	+	0.247224i	−0.718664	−	0.695357i	\(-0.755246\pi\)
							0.333976	+	0.942582i	\(0.391610\pi\)
\(29\)	−36.0207			−1.24209			−0.621047	−	0.783773i	\(-0.713292\pi\)
							−0.621047	+	0.783773i	\(0.713292\pi\)
\(31\)	−12.3871	−	42.1866i	−0.399584	−	1.36086i	−0.876285	−	0.481793i	\(-0.839986\pi\)
							0.476701	−	0.879066i	\(-0.341833\pi\)
\(37\)	−27.2906			−0.737583			−0.368792	−	0.929512i	\(-0.620228\pi\)
							−0.368792	+	0.929512i	\(0.620228\pi\)
\(41\)	−1.90783	−	1.65315i	−0.0465326	−	0.0403207i	0.631284	−	0.775552i	\(-0.282528\pi\)
							−0.677817	+	0.735231i	\(0.737074\pi\)
\(43\)	−10.2354	−	8.86905i	−0.238033	−	0.206257i	0.527673	−	0.849448i	\(-0.323065\pi\)
							−0.765706	+	0.643191i	\(0.777610\pi\)
\(47\)	69.6465	−	44.7591i	1.48184	−	0.952321i	0.484866	−	0.874589i	\(-0.338868\pi\)
							0.996974	−	0.0777323i	\(-0.0247680\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.l.a.43.2	✓	220
67.53	odd	22	inner	201.3.l.a.187.2	yes	220

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.l.a.43.2	✓	220	1.1	even	1	trivial
201.3.l.a.187.2	yes	220	67.53	odd	22	inner