Embedded newform 201.3.l.a.43.5

• Label: 201.3.l.a.43.5
• 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			43.5
Character	\(\chi\)	\(=\)	201.43
Dual form			201.3.l.a.187.5

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-2.27098 - 1.03712i) q^{2} +(-0.936417 - 1.45709i) q^{3} +(1.46229 + 1.68758i) q^{4} +(2.84282 + 0.408736i) q^{5} +(0.615402 + 4.28021i) q^{6} +(-0.295181 - 0.134805i) q^{7} +(1.24287 + 4.23283i) q^{8} +(-1.24625 + 2.72890i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q + 52 q^{4} + 66 q^{8} + 66 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−2.27098	−	1.03712i	−1.13549	−	0.518561i	−0.243179	−	0.969981i	\(-0.578190\pi\)
							−0.892312	+	0.451420i	\(0.850918\pi\)
\(3\)	−0.936417	−	1.45709i	−0.312139	−	0.485698i
							\(5\)	2.84282	+	0.408736i	0.568564	+	0.0817472i	0.420601	−	0.907246i	\(-0.361819\pi\)
0.147963	+	0.988993i	\(0.452728\pi\)
\(7\)	−0.295181	−	0.134805i	−0.0421687	−	0.0192578i	0.394219	−	0.919017i	\(-0.371015\pi\)
							−0.436388	+	0.899759i	\(0.643742\pi\)
\(11\)	13.3941	+	1.92578i	1.21765	+	0.175071i	0.721032	−	0.692901i	\(-0.243668\pi\)
							0.496613	+	0.867972i	\(0.334577\pi\)
\(13\)	−5.56680	+	18.9588i	−0.428216	+	1.45837i	0.409525	+	0.912299i	\(0.365695\pi\)
							−0.837740	+	0.546069i	\(0.816124\pi\)
\(17\)	4.53801	−	5.23715i	0.266942	−	0.308067i	−0.606415	−	0.795148i	\(-0.707393\pi\)
							0.873357	+	0.487081i	\(0.161938\pi\)
\(19\)	5.24478	+	11.4845i	0.276041	+	0.604446i	0.995978	−	0.0895934i	\(-0.0285567\pi\)
							−0.719937	+	0.694039i	\(0.755829\pi\)
\(23\)	28.7116	−	18.4518i	1.24833	−	0.802254i	0.261688	−	0.965152i	\(-0.415721\pi\)
							0.986643	+	0.162899i	\(0.0520844\pi\)
\(29\)	46.0639			1.58841			0.794206	−	0.607649i	\(-0.207887\pi\)
							0.794206	+	0.607649i	\(0.207887\pi\)
\(31\)	−15.2561	−	51.9574i	−0.492131	−	1.67604i	−0.713340	−	0.700818i	\(-0.752819\pi\)
							0.221209	−	0.975226i	\(-0.429000\pi\)
\(37\)	32.0600			0.866487			0.433244	−	0.901277i	\(-0.357369\pi\)
							0.433244	+	0.901277i	\(0.357369\pi\)
\(41\)	2.86709	+	2.48434i	0.0699289	+	0.0605938i	0.689124	−	0.724643i	\(-0.257996\pi\)
							−0.619195	+	0.785237i	\(0.712541\pi\)
\(43\)	59.2589	+	51.3481i	1.37811	+	1.19414i	0.958034	+	0.286655i	\(0.0925434\pi\)
							0.420080	+	0.907487i	\(0.362002\pi\)
\(47\)	−61.8661	+	39.7589i	−1.31630	+	0.845935i	−0.994886	−	0.101004i	\(-0.967795\pi\)
							−0.321414	+	0.946939i	\(0.604158\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.l.a.43.5	✓	220
67.53	odd	22	inner	201.3.l.a.187.5	yes	220

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.l.a.43.5	✓	220	1.1	even	1	trivial
201.3.l.a.187.5	yes	220	67.53	odd	22	inner