Embedded newform 201.3.l.a.43.19

• Label: 201.3.l.a.43.19
• 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			43.19
Character	\(\chi\)	\(=\)	201.43
Dual form			201.3.l.a.187.19

$q$-expansion

\(f(q)\)	\(=\)	\(q+(2.26882 + 1.03614i) q^{2} +(-0.936417 - 1.45709i) q^{3} +(1.45454 + 1.67863i) q^{4} +(6.52672 + 0.938401i) q^{5} +(-0.614817 - 4.27615i) q^{6} +(2.05853 + 0.940098i) q^{7} +(-1.25001 - 4.25713i) q^{8} +(-1.24625 + 2.72890i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q + 52 q^{4} + 66 q^{8} + 66 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	2.26882	+	1.03614i	1.13441	+	0.518069i	0.891969	−	0.452097i	\(-0.149324\pi\)
							0.242443	+	0.970166i	\(0.422051\pi\)
\(3\)	−0.936417	−	1.45709i	−0.312139	−	0.485698i
							\(5\)	6.52672	+	0.938401i	1.30534	+	0.187680i	0.759666	−	0.650314i	\(-0.225363\pi\)
0.545679	+	0.837994i	\(0.316272\pi\)
\(7\)	2.05853	+	0.940098i	0.294075	+	0.134300i	0.556990	−	0.830519i	\(-0.311956\pi\)
							−0.262914	+	0.964819i	\(0.584684\pi\)
\(11\)	4.38943	+	0.631104i	0.399039	+	0.0573731i	0.338913	−	0.940818i	\(-0.389941\pi\)
							0.0601257	+	0.998191i	\(0.480850\pi\)
\(13\)	0.211309	−	0.719653i	0.0162545	−	0.0553579i	−0.950966	−	0.309294i	\(-0.899907\pi\)
							0.967221	+	0.253936i	\(0.0817254\pi\)
\(17\)	12.1908	−	14.0690i	0.717107	−	0.827585i	−0.273849	−	0.961773i	\(-0.588297\pi\)
							0.990956	+	0.134187i	\(0.0428424\pi\)
\(19\)	12.5726	+	27.5302i	0.661717	+	1.44896i	0.880913	+	0.473278i	\(0.156929\pi\)
							−0.219196	+	0.975681i	\(0.570343\pi\)
\(23\)	−28.2848	+	18.1775i	−1.22977	+	0.790327i	−0.983856	−	0.178964i	\(-0.942726\pi\)
							−0.245917	+	0.969291i	\(0.579089\pi\)
\(29\)	−11.6104			−0.400360			−0.200180	−	0.979759i	\(-0.564153\pi\)
							−0.200180	+	0.979759i	\(0.564153\pi\)
\(31\)	−1.46934	−	5.00411i	−0.0473980	−	0.161423i	0.932393	−	0.361445i	\(-0.117717\pi\)
							−0.979791	+	0.200023i	\(0.935898\pi\)
\(37\)	−61.0082			−1.64887			−0.824436	−	0.565956i	\(-0.808507\pi\)
							−0.824436	+	0.565956i	\(0.808507\pi\)
\(41\)	−18.7423	−	16.2403i	−0.457128	−	0.396104i	0.395630	−	0.918410i	\(-0.370526\pi\)
							−0.852758	+	0.522306i	\(0.825072\pi\)
\(43\)	−4.35933	−	3.77738i	−0.101380	−	0.0878461i	0.602696	−	0.797971i	\(-0.294093\pi\)
							−0.704076	+	0.710125i	\(0.748639\pi\)
\(47\)	−38.3807	+	24.6658i	−0.816610	+	0.524804i	−0.880997	−	0.473121i	\(-0.843127\pi\)
							0.0643869	+	0.997925i	\(0.479491\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.l.a.43.19	✓	220
67.53	odd	22	inner	201.3.l.a.187.19	yes	220

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.l.a.43.19	✓	220	1.1	even	1	trivial
201.3.l.a.187.19	yes	220	67.53	odd	22	inner