Embedded newform 201.4.i.b.25.1

• Label: 201.4.i.b.25.1
• Level: $201$
• Weight: $4$
• Character: 201.25
• Analytic conductor: $11.859$
• Analytic rank: $0$
• Dimension: $170$
• CM: no
• 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			25.1
Character	\(\chi\)	\(=\)	201.25
Dual form			201.4.i.b.193.1

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.715229 - 4.97453i) q^{2} +(1.96458 - 2.26725i) q^{3} +(-16.5584 + 4.86199i) q^{4} +(10.1409 - 6.51716i) q^{5} +(-12.6836 - 8.15127i) q^{6} +(-4.69471 - 32.6525i) q^{7} +(19.3272 + 42.3208i) q^{8} +(-1.28083 - 8.90839i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 170 q + 2 q^{2} + 51 q^{3} - 74 q^{4} - 4 q^{5} + 27 q^{6} + 12 q^{7} - 237 q^{8} - 153 q^{9}+O(q^{10}) \)

Character values

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

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

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.715229	−	4.97453i	−0.252872	−	1.75876i	−0.580788	−	0.814055i	\(-0.697256\pi\)
							0.327917	−	0.944707i	\(-0.393653\pi\)
\(3\)	1.96458	−	2.26725i	0.378084	−	0.436332i
							\(5\)	10.1409	−	6.51716i	0.907030	−	0.582912i	−0.00183756	−	0.999998i	\(-0.500585\pi\)
0.908867	+	0.417086i	\(0.136949\pi\)
\(7\)	−4.69471	−	32.6525i	−0.253491	−	1.76307i	−0.576907	−	0.816810i	\(-0.695740\pi\)
							0.323416	−	0.946257i	\(-0.395169\pi\)
\(11\)	50.7773	−	32.6326i	1.39181	−	0.894463i	0.392135	−	0.919908i	\(-0.371737\pi\)
							0.999676	+	0.0254450i	\(0.00810026\pi\)
\(13\)	1.10113	−	2.41113i	0.0234921	−	0.0514405i	−0.897522	−	0.440969i	\(-0.854635\pi\)
							0.921014	+	0.389529i	\(0.127362\pi\)
\(17\)	59.5924	+	17.4979i	0.850192	+	0.249639i	0.677670	−	0.735367i	\(-0.262990\pi\)
							0.172523	+	0.985006i	\(0.444808\pi\)
\(19\)	−6.25196	+	43.4833i	−0.0754893	+	0.525040i	0.916629	+	0.399738i	\(0.130899\pi\)
							−0.992119	+	0.125302i	\(0.960010\pi\)
\(23\)	−82.4767	+	95.1832i	−0.747721	+	0.862916i	−0.994345	−	0.106195i	\(-0.966133\pi\)
							0.246624	+	0.969111i	\(0.420679\pi\)
\(29\)	−131.007			−0.838874			−0.419437	−	0.907784i	\(-0.637773\pi\)
							−0.419437	+	0.907784i	\(0.637773\pi\)
\(31\)	77.6156	+	169.955i	0.449683	+	0.984669i	0.989719	+	0.143027i	\(0.0456835\pi\)
							−0.540036	+	0.841642i	\(0.681589\pi\)
\(37\)	278.638			1.23805			0.619025	−	0.785371i	\(-0.287528\pi\)
							0.619025	+	0.785371i	\(0.287528\pi\)
\(41\)	−122.150	−	35.8665i	−0.465284	−	0.136620i	0.0406838	−	0.999172i	\(-0.487046\pi\)
							−0.505968	+	0.862552i	\(0.668865\pi\)
\(43\)	486.963	+	142.985i	1.72700	+	0.507094i	0.986331	−	0.164773i	\(-0.0526892\pi\)
							0.740672	+	0.671867i	\(0.234507\pi\)
\(47\)	265.064	−	305.900i	0.822628	−	0.949364i	−0.176763	−	0.984253i	\(-0.556563\pi\)
							0.999391	+	0.0348899i	\(0.0111081\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.i.b.25.1	✓	170
67.59	even	11	inner	201.4.i.b.193.1	yes	170

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.i.b.25.1	✓	170	1.1	even	1	trivial
201.4.i.b.193.1	yes	170	67.59	even	11	inner