Embedded newform 201.4.j.b.5.18

• Label: 201.4.j.b.5.18
• Level: $201$
• Weight: $4$
• Character: 201.5
• Analytic conductor: $11.859$
• Analytic rank: $0$
• Dimension: $640$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.j (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(11.8593839112\)
Analytic rank:	\(0\)
Dimension:	\(640\)
Relative dimension:	\(64\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.18
Character	\(\chi\)	\(=\)	201.5
Dual form			201.4.j.b.161.18

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.98603 + 2.29200i) q^{2} +(4.03838 - 3.26978i) q^{3} +(-0.170435 - 1.18540i) q^{4} +(19.1936 - 5.63576i) q^{5} +(-0.526014 + 15.7499i) q^{6} +(24.7274 + 21.4264i) q^{7} +(-17.3551 - 11.1534i) q^{8} +(5.61708 - 26.4092i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 11 q^{3} - 290 q^{4} + 35 q^{6} - 22 q^{7} - 33 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(68\)	\(136\)
\(\chi(n)\)	\(-1\)	\(e\left(\frac{5}{22}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.98603	+	2.29200i	−0.702168	+	0.810345i	−0.989044	−	0.147623i	\(-0.952838\pi\)
							0.286876	+	0.957968i	\(0.407383\pi\)
\(3\)	4.03838	−	3.26978i	0.777187	−	0.629269i
							\(5\)	19.1936	−	5.63576i	1.71673	−	0.504078i	0.732470	−	0.680799i	\(-0.238367\pi\)
0.984261	+	0.176721i	\(0.0565492\pi\)
\(7\)	24.7274	+	21.4264i	1.33515	+	1.15692i	0.974543	+	0.224201i	\(0.0719773\pi\)
							0.360611	+	0.932716i	\(0.382568\pi\)
\(11\)	26.9483	−	7.91273i	0.738656	−	0.216889i	0.109303	−	0.994008i	\(-0.465138\pi\)
							0.629353	+	0.777120i	\(0.283320\pi\)
\(13\)	9.42108	+	14.6595i	0.200995	+	0.312755i	0.927089	−	0.374841i	\(-0.122303\pi\)
							−0.726094	+	0.687595i	\(0.758666\pi\)
\(17\)	−127.176	−	18.2851i	−1.81439	−	0.260870i	−0.850273	−	0.526342i	\(-0.823563\pi\)
							−0.964119	+	0.265472i	\(0.914472\pi\)
\(19\)	−58.3859	−	67.3809i	−0.704981	−	0.813591i	0.284436	−	0.958695i	\(-0.408194\pi\)
							−0.989416	+	0.145104i	\(0.953648\pi\)
\(23\)	93.2892	−	42.6038i	0.845746	−	0.386239i	0.0550761	−	0.998482i	\(-0.482460\pi\)
							0.790670	+	0.612243i	\(0.209733\pi\)
\(29\)			74.1937i			0.475084i	0.971377	+	0.237542i	\(0.0763417\pi\)
							−0.971377	+	0.237542i	\(0.923658\pi\)
\(31\)	−125.960	+	195.997i	−0.729776	+	1.13555i	0.255867	+	0.966712i	\(0.417639\pi\)
							−0.985643	+	0.168842i	\(0.945997\pi\)
\(37\)	−196.042			−0.871058			−0.435529	−	0.900175i	\(-0.643439\pi\)
							−0.435529	+	0.900175i	\(0.643439\pi\)
\(41\)	−34.8113	+	242.118i	−0.132600	+	0.922256i	0.809547	+	0.587056i	\(0.199713\pi\)
							−0.942147	+	0.335200i	\(0.891196\pi\)
\(43\)	114.423	+	16.4516i	0.405799	+	0.0583451i	0.342192	−	0.939630i	\(-0.388831\pi\)
							0.0636068	+	0.997975i	\(0.479740\pi\)
\(47\)	−105.904	+	48.3648i	−0.328674	+	0.150101i	−0.572917	−	0.819614i	\(-0.694188\pi\)
							0.244242	+	0.969714i	\(0.421461\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.j.b.5.18	✓	640
3.2	odd	2	inner	201.4.j.b.5.47	yes	640
67.27	odd	22	inner	201.4.j.b.161.47	yes	640
201.161	even	22	inner	201.4.j.b.161.18	yes	640

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.j.b.5.18	✓	640	1.1	even	1	trivial
201.4.j.b.5.47	yes	640	3.2	odd	2	inner
201.4.j.b.161.18	yes	640	201.161	even	22	inner
201.4.j.b.161.47	yes	640	67.27	odd	22	inner