Embedded newform 201.2.i.b.25.1

• Label: 201.2.i.b.25.1
• Level: $201$
• Weight: $2$
• Character: 201.25
• Analytic conductor: $1.605$
• Analytic rank: $0$
• Dimension: $70$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	201.i (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.60499308063\)
Analytic rank:	\(0\)
Dimension:	\(70\)
Relative dimension:	\(7\) over \(\Q(\zeta_{11})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			25.1
Character	\(\chi\)	\(=\)	201.25
Dual form			201.2.i.b.193.1

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.354867 - 2.46816i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(-4.04687 + 1.18827i) q^{4} +(3.46834 - 2.22897i) q^{5} +(2.09770 + 1.34811i) q^{6} +(-0.450350 - 3.13225i) q^{7} +(2.29723 + 5.03024i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q - 2 q^{2} - 7 q^{3} - 12 q^{4} - 2 q^{5} + 9 q^{6} - 10 q^{7} + 15 q^{8} - 7 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(68\)	\(136\)
\(\chi(n)\)	\(1\)	\(e\left(\frac{5}{11}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.354867	−	2.46816i	−0.250929	−	1.74525i	−0.592661	−	0.805452i	\(-0.701923\pi\)
							0.341732	−	0.939797i	\(-0.388986\pi\)
\(3\)	−0.654861	+	0.755750i	−0.378084	+	0.436332i
							\(5\)	3.46834	−	2.22897i	1.55109	−	0.996824i	0.566074	−	0.824354i	\(-0.308461\pi\)
0.985015	−	0.172470i	\(-0.0551749\pi\)
\(7\)	−0.450350	−	3.13225i	−0.170216	−	1.18388i	−0.878426	−	0.477879i	\(-0.841406\pi\)
							0.708210	−	0.706002i	\(-0.249503\pi\)
\(11\)	−1.10308	+	0.708904i	−0.332590	+	0.213743i	−0.696268	−	0.717782i	\(-0.745157\pi\)
							0.363678	+	0.931525i	\(0.381521\pi\)
\(13\)	−1.74321	+	3.81709i	−0.483479	+	1.05867i	0.498013	+	0.867169i	\(0.334063\pi\)
							−0.981492	+	0.191502i	\(0.938664\pi\)
\(17\)	−1.69909	−	0.498898i	−0.412090	−	0.121001i	0.0691149	−	0.997609i	\(-0.477982\pi\)
							−0.481205	+	0.876608i	\(0.659801\pi\)
\(19\)	0.854407	−	5.94253i	0.196015	−	1.36331i	−0.619692	−	0.784845i	\(-0.712743\pi\)
							0.815707	−	0.578466i	\(-0.196348\pi\)
\(23\)	−0.837780	+	0.966850i	−0.174689	+	0.201602i	−0.836342	−	0.548209i	\(-0.815310\pi\)
							0.661652	+	0.749811i	\(0.269855\pi\)
\(29\)	8.11136			1.50624			0.753121	−	0.657882i	\(-0.228548\pi\)
							0.753121	+	0.657882i	\(0.228548\pi\)
\(31\)	2.01939	+	4.42184i	0.362692	+	0.794185i	0.999727	+	0.0233505i	\(0.00743337\pi\)
							−0.637035	+	0.770835i	\(0.719839\pi\)
\(37\)	−4.34980			−0.715102			−0.357551	−	0.933894i	\(-0.616388\pi\)
							−0.357551	+	0.933894i	\(0.616388\pi\)
\(41\)	10.2292	+	3.00357i	1.59754	+	0.469079i	0.954859	−	0.297058i	\(-0.0960055\pi\)
							0.642677	+	0.766137i	\(0.277824\pi\)
\(43\)	−1.43611	−	0.421681i	−0.219005	−	0.0643057i	0.170389	−	0.985377i	\(-0.445497\pi\)
							−0.389394	+	0.921071i	\(0.627316\pi\)
\(47\)	−3.55761	+	4.10570i	−0.518931	+	0.598878i	−0.953363	−	0.301826i	\(-0.902404\pi\)
							0.434432	+	0.900705i	\(0.356949\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.2.i.b.25.1	✓	70
3.2	odd	2		603.2.u.e.226.7		70
67.59	even	11	inner	201.2.i.b.193.1	yes	70
201.59	odd	22		603.2.u.e.595.7		70

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.2.i.b.25.1	✓	70	1.1	even	1	trivial
201.2.i.b.193.1	yes	70	67.59	even	11	inner
603.2.u.e.226.7		70	3.2	odd	2
603.2.u.e.595.7		70	201.59	odd	22