Embedded newform 201.4.i.b.64.7

• Label: 201.4.i.b.64.7
• Level: $201$
• Weight: $4$
• Character: 201.64
• Analytic conductor: $11.859$
• Analytic rank: $0$
• Dimension: $170$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.i (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(11.8593839112\)
Analytic rank:	\(0\)
Dimension:	\(170\)
Relative dimension:	\(17\) over \(\Q(\zeta_{11})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			64.7
Character	\(\chi\)	\(=\)	201.64
Dual form			201.4.i.b.22.7

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.26486 - 0.371395i) q^{2} +(0.426945 - 2.96946i) q^{3} +(-5.26810 - 3.38560i) q^{4} +(-4.40899 - 9.65433i) q^{5} +(-1.64287 + 3.59738i) q^{6} +(-28.6135 - 8.40167i) q^{7} +(12.3122 + 14.2090i) q^{8} +(-8.63544 - 2.53559i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 170 q + 2 q^{2} + 51 q^{3} - 74 q^{4} - 4 q^{5} + 27 q^{6} + 12 q^{7} - 237 q^{8} - 153 q^{9}+O(q^{10}) \)

Character values

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

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

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.26486	−	0.371395i	−0.447194	−	0.131308i	0.0503787	−	0.998730i	\(-0.483957\pi\)
							−0.497573	+	0.867422i	\(0.665775\pi\)
\(3\)	0.426945	−	2.96946i	0.0821655	−	0.571474i
							\(5\)	−4.40899	−	9.65433i	−0.394352	−	0.863510i	−0.997812	−	0.0661168i	\(-0.978939\pi\)
0.603460	−	0.797393i	\(-0.293788\pi\)
\(7\)	−28.6135	−	8.40167i	−1.54498	−	0.453647i	−0.605385	−	0.795933i	\(-0.706981\pi\)
							−0.939596	+	0.342285i	\(0.888799\pi\)
\(11\)	−3.35429	−	7.34488i	−0.0919416	−	0.201324i	0.858074	−	0.513526i	\(-0.171661\pi\)
							−0.950016	+	0.312202i	\(0.898934\pi\)
\(13\)	−11.1627	+	12.8825i	−0.238153	+	0.274843i	−0.862227	−	0.506522i	\(-0.830931\pi\)
							0.624074	+	0.781365i	\(0.285476\pi\)
\(17\)	43.4785	−	27.9419i	0.620299	−	0.398642i	−0.192408	−	0.981315i	\(-0.561630\pi\)
							0.812707	+	0.582673i	\(0.197993\pi\)
\(19\)	87.9929	−	25.8371i	1.06247	−	0.311970i	0.296626	−	0.954994i	\(-0.404139\pi\)
							0.765846	+	0.643024i	\(0.222320\pi\)
\(23\)	−5.99273	+	41.6804i	−0.0543292	+	0.377868i	0.944458	+	0.328632i	\(0.106588\pi\)
							−0.998787	+	0.0492357i	\(0.984321\pi\)
\(29\)	−132.340			−0.847412			−0.423706	−	0.905800i	\(-0.639271\pi\)
							−0.423706	+	0.905800i	\(0.639271\pi\)
\(31\)	−11.2199	−	12.9484i	−0.0650047	−	0.0750195i	0.722316	−	0.691563i	\(-0.243078\pi\)
							−0.787321	+	0.616544i	\(0.788532\pi\)
\(37\)	274.554			1.21990			0.609952	−	0.792439i	\(-0.291189\pi\)
							0.609952	+	0.792439i	\(0.291189\pi\)
\(41\)	−322.120	+	207.014i	−1.22699	+	0.788541i	−0.983420	−	0.181342i	\(-0.941956\pi\)
							−0.243573	+	0.969882i	\(0.578320\pi\)
\(43\)	−305.278	+	196.190i	−1.08266	+	0.695785i	−0.955171	−	0.296055i	\(-0.904329\pi\)
							−0.127492	+	0.991840i	\(0.540693\pi\)
\(47\)	−52.7326	+	366.763i	−0.163656	+	1.13825i	0.728012	+	0.685564i	\(0.240444\pi\)
							−0.891668	+	0.452689i	\(0.850465\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.i.b.64.7	yes	170
67.22	even	11	inner	201.4.i.b.22.7	✓	170

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.i.b.22.7	✓	170	67.22	even	11	inner
201.4.i.b.64.7	yes	170	1.1	even	1	trivial