Embedded newform 201.2.i.b.25.3

• Label: 201.2.i.b.25.3
• 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			25.3
Character	\(\chi\)	\(=\)	201.25
Dual form			201.2.i.b.193.3

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.197156 - 1.37125i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.0775356 - 0.0227665i) q^{4} +(-1.53079 + 0.983778i) q^{5} +(1.16543 + 0.748976i) q^{6} +(-0.598366 - 4.16172i) q^{7} +(-1.19749 - 2.62215i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q - 2 q^{2} - 7 q^{3} - 12 q^{4} - 2 q^{5} + 9 q^{6} - 10 q^{7} + 15 q^{8} - 7 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.197156	−	1.37125i	−0.139410	−	0.969619i	−0.932669	−	0.360734i	\(-0.882526\pi\)
							0.793259	−	0.608885i	\(-0.208383\pi\)
\(3\)	−0.654861	+	0.755750i	−0.378084	+	0.436332i
							\(5\)	−1.53079	+	0.983778i	−0.684589	+	0.439959i	−0.836159	−	0.548488i	\(-0.815204\pi\)
0.151569	+	0.988447i	\(0.451567\pi\)
\(7\)	−0.598366	−	4.16172i	−0.226161	−	1.57298i	−0.714060	−	0.700084i	\(-0.753146\pi\)
							0.487899	−	0.872900i	\(-0.337763\pi\)
\(11\)	1.22973	−	0.790301i	0.370778	−	0.238285i	−0.341960	−	0.939714i	\(-0.611091\pi\)
							0.712739	+	0.701430i	\(0.247455\pi\)
\(13\)	2.67719	−	5.86223i	0.742519	−	1.62589i	−0.0368471	−	0.999321i	\(-0.511731\pi\)
							0.779366	−	0.626569i	\(-0.215541\pi\)
\(17\)	2.70936	+	0.795540i	0.657116	+	0.192947i	0.593258	−	0.805012i	\(-0.297841\pi\)
							0.0638580	+	0.997959i	\(0.479660\pi\)
\(19\)	−0.156739	+	1.09014i	−0.0359584	+	0.250096i	−0.999870	−	0.0161264i	\(-0.994867\pi\)
							0.963912	+	0.266223i	\(0.0857757\pi\)
\(23\)	−4.55698	+	5.25903i	−0.950195	+	1.09658i	0.0450305	+	0.998986i	\(0.485661\pi\)
							−0.995226	+	0.0975983i	\(0.968884\pi\)
\(29\)	−1.43643			−0.266738			−0.133369	−	0.991066i	\(-0.542580\pi\)
							−0.133369	+	0.991066i	\(0.542580\pi\)
\(31\)	2.05739	+	4.50505i	0.369517	+	0.809130i	0.999472	+	0.0324980i	\(0.0103463\pi\)
							−0.629954	+	0.776632i	\(0.716926\pi\)
\(37\)	7.28584			1.19779			0.598893	−	0.800829i	\(-0.295608\pi\)
							0.598893	+	0.800829i	\(0.295608\pi\)
\(41\)	1.62628	+	0.477518i	0.253982	+	0.0745758i	0.406245	−	0.913764i	\(-0.366838\pi\)
							−0.152263	+	0.988340i	\(0.548656\pi\)
\(43\)	−3.14278	−	0.922804i	−0.479270	−	0.140726i	0.0331696	−	0.999450i	\(-0.489440\pi\)
							−0.512439	+	0.858723i	\(0.671258\pi\)
\(47\)	8.84898	−	10.2123i	1.29076	−	1.48961i	0.517235	−	0.855843i	\(-0.326961\pi\)
							0.773522	−	0.633769i	\(-0.218493\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.2.i.b.25.3	✓	70
3.2	odd	2		603.2.u.e.226.5		70
67.59	even	11	inner	201.2.i.b.193.3	yes	70
201.59	odd	22		603.2.u.e.595.5		70

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.2.i.b.25.3	✓	70	1.1	even	1	trivial
201.2.i.b.193.3	yes	70	67.59	even	11	inner
603.2.u.e.226.5		70	3.2	odd	2
603.2.u.e.595.5		70	201.59	odd	22