Embedded newform 201.3.g.b.29.18

• Label: 201.3.g.b.29.18
• Level: $201$
• Weight: $3$
• Character: 201.29
• Analytic conductor: $5.477$
• Analytic rank: $0$
• Dimension: $84$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.g (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.47685331364\)
Analytic rank:	\(0\)
Dimension:	\(84\)
Relative dimension:	\(42\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.18
Character	\(\chi\)	\(=\)	201.29
Dual form			201.3.g.b.104.18

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.718547 - 0.414853i) q^{2} +(2.98530 - 0.296617i) q^{3} +(-1.65579 - 2.86792i) q^{4} +4.81931i q^{5} +(-2.26813 - 1.02533i) q^{6} +(-2.30167 - 3.98661i) q^{7} +6.06647i q^{8} +(8.82404 - 1.77098i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 6 q^{3} + 82 q^{4} + 3 q^{6} - 10 q^{7} + 2 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(68\)	\(136\)
\(\chi(n)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.718547	−	0.414853i	−0.359273	−	0.207427i	0.309489	−	0.950903i	\(-0.399842\pi\)
							−0.668762	+	0.743477i	\(0.733175\pi\)
\(3\)	2.98530	−	0.296617i	0.995100	−	0.0988723i
							\(5\)			4.81931i			0.963862i	0.876209	+	0.481931i	\(0.160064\pi\)
−0.876209	+	0.481931i	\(0.839936\pi\)
\(7\)	−2.30167	−	3.98661i	−0.328810	−	0.569516i	0.653466	−	0.756956i	\(-0.273314\pi\)
							−0.982276	+	0.187440i	\(0.939981\pi\)
\(11\)	16.3119	−	9.41765i	1.48290	−	0.856150i	0.483084	−	0.875574i	\(-0.339516\pi\)
							0.999811	+	0.0194235i	\(0.00618309\pi\)
\(13\)	9.01783	−	15.6193i	0.693679	−	1.20149i	−0.276945	−	0.960886i	\(-0.589322\pi\)
							0.970624	−	0.240602i	\(-0.0773448\pi\)
\(17\)	0.286183	+	0.165228i	0.0168343	+	0.00971929i	0.508394	−	0.861125i	\(-0.330240\pi\)
							−0.491559	+	0.870844i	\(0.663573\pi\)
\(19\)	3.37330	−	5.84272i	0.177542	−	0.307512i	−0.763496	−	0.645812i	\(-0.776519\pi\)
							0.941038	+	0.338301i	\(0.109852\pi\)
\(23\)	−34.9465	−	20.1764i	−1.51941	−	0.877234i	−0.999738	−	0.0228700i	\(-0.992720\pi\)
							−0.519675	−	0.854364i	\(-0.673947\pi\)
\(29\)	−14.2415	+	8.22235i	−0.491087	+	0.283529i	−0.725025	−	0.688722i	\(-0.758172\pi\)
							0.233938	+	0.972251i	\(0.424839\pi\)
\(31\)	25.6526	+	44.4316i	0.827503	+	1.43328i	0.899991	+	0.435908i	\(0.143573\pi\)
							−0.0724880	+	0.997369i	\(0.523094\pi\)
\(37\)	0.843539	−	1.46105i	0.0227983	−	0.0394879i	−0.854401	−	0.519614i	\(-0.826076\pi\)
							0.877199	+	0.480126i	\(0.159409\pi\)
\(41\)	−39.6382	+	22.8851i	−0.966786	+	0.558174i	−0.898255	−	0.439475i	\(-0.855165\pi\)
							−0.0685313	+	0.997649i	\(0.521831\pi\)
\(43\)	−8.27336			−0.192404			−0.0962019	−	0.995362i	\(-0.530669\pi\)
							−0.0962019	+	0.995362i	\(0.530669\pi\)
\(47\)	60.9448	−	35.1865i	1.29670	−	0.748649i	0.316866	−	0.948470i	\(-0.397369\pi\)
							0.979832	+	0.199821i	\(0.0640360\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.g.b.29.18	✓	84
3.2	odd	2	inner	201.3.g.b.29.25	yes	84
67.37	even	3	inner	201.3.g.b.104.25	yes	84
201.104	odd	6	inner	201.3.g.b.104.18	yes	84

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.g.b.29.18	✓	84	1.1	even	1	trivial
201.3.g.b.29.25	yes	84	3.2	odd	2	inner
201.3.g.b.104.18	yes	84	201.104	odd	6	inner
201.3.g.b.104.25	yes	84	67.37	even	3	inner