Embedded newform 201.3.l.a.43.9

• Label: 201.3.l.a.43.9
• Level: $201$
• Weight: $3$
• Character: 201.43
• Analytic conductor: $5.477$
• Analytic rank: $0$
• Dimension: $220$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.l (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.47685331364\)
Analytic rank:	\(0\)
Dimension:	\(220\)
Relative dimension:	\(22\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			43.9
Character	\(\chi\)	\(=\)	201.43
Dual form			201.3.l.a.187.9

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.00045 - 0.456891i) q^{2} +(0.936417 + 1.45709i) q^{3} +(-1.82729 - 2.10880i) q^{4} +(-2.48696 - 0.357570i) q^{5} +(-0.271107 - 1.88559i) q^{6} +(-2.35904 - 1.07734i) q^{7} +(2.10407 + 7.16579i) q^{8} +(-1.24625 + 2.72890i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q + 52 q^{4} + 66 q^{8} + 66 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(68\)	\(136\)
\(\chi(n)\)	\(1\)	\(e\left(\frac{3}{22}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.00045	−	0.456891i	−0.500226	−	0.228445i	0.149290	−	0.988793i	\(-0.452301\pi\)
							−0.649516	+	0.760348i	\(0.725028\pi\)
\(3\)	0.936417	+	1.45709i	0.312139	+	0.485698i
							\(5\)	−2.48696	−	0.357570i	−0.497391	−	0.0715141i	−0.110946	−	0.993826i	\(-0.535388\pi\)
−0.386445	+	0.922312i	\(0.626297\pi\)
\(7\)	−2.35904	−	1.07734i	−0.337006	−	0.153905i	0.239722	−	0.970841i	\(-0.422944\pi\)
							−0.576728	+	0.816936i	\(0.695671\pi\)
\(11\)	15.0960	+	2.17048i	1.37236	+	0.197316i	0.788749	−	0.614715i	\(-0.210729\pi\)
							0.583614	+	0.812031i	\(0.301638\pi\)
\(13\)	−5.82023	+	19.8219i	−0.447710	+	1.52476i	0.358728	+	0.933442i	\(0.383211\pi\)
							−0.806438	+	0.591318i	\(0.798608\pi\)
\(17\)	−0.000245214	0	0.000282992i	−1.44243e−5	0	1.66466e-5i	−0.755757	−	0.654852i	\(-0.772731\pi\)
							0.755742	+	0.654869i	\(0.227276\pi\)
\(19\)	11.2640	+	24.6646i	0.592840	+	1.29814i	0.933710	+	0.358029i	\(0.116551\pi\)
							−0.340870	+	0.940110i	\(0.610722\pi\)
\(23\)	7.73072	−	4.96823i	0.336118	−	0.216010i	−0.361684	−	0.932301i	\(-0.617798\pi\)
							0.697802	+	0.716291i	\(0.254162\pi\)
\(29\)	−45.0143			−1.55222			−0.776109	−	0.630598i	\(-0.782809\pi\)
							−0.776109	+	0.630598i	\(0.782809\pi\)
\(31\)	17.2463	+	58.7355i	0.556332	+	1.89469i	0.430351	+	0.902662i	\(0.358390\pi\)
							0.125981	+	0.992033i	\(0.459792\pi\)
\(37\)	25.3209			0.684349			0.342175	−	0.939636i	\(-0.388837\pi\)
							0.342175	+	0.939636i	\(0.388837\pi\)
\(41\)	52.8070	+	45.7575i	1.28798	+	1.11604i	0.986709	+	0.162497i	\(0.0519548\pi\)
							0.301267	+	0.953540i	\(0.402591\pi\)
\(43\)	−14.1262	−	12.2404i	−0.328516	−	0.284661i	0.474948	−	0.880014i	\(-0.342467\pi\)
							−0.803464	+	0.595353i	\(0.797012\pi\)
\(47\)	14.9545	−	9.61069i	0.318181	−	0.204483i	−0.371795	−	0.928315i	\(-0.621257\pi\)
							0.689976	+	0.723832i	\(0.257621\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.l.a.43.9	✓	220
67.53	odd	22	inner	201.3.l.a.187.9	yes	220

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.l.a.43.9	✓	220	1.1	even	1	trivial
201.3.l.a.187.9	yes	220	67.53	odd	22	inner