Embedded newform 201.3.l.a.43.4

• Label: 201.3.l.a.43.4
• 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			43.4
Character	\(\chi\)	\(=\)	201.43
Dual form			201.3.l.a.187.4

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-2.54688 - 1.16312i) q^{2} +(0.936417 + 1.45709i) q^{3} +(2.51429 + 2.90164i) q^{4} +(1.62480 + 0.233611i) q^{5} +(-0.690165 - 4.80020i) q^{6} +(-7.97050 - 3.64000i) q^{7} +(0.126668 + 0.431390i) q^{8} +(-1.24625 + 2.72890i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q + 52 q^{4} + 66 q^{8} + 66 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−2.54688	−	1.16312i	−1.27344	−	0.581560i	−0.340043	−	0.940410i	\(-0.610442\pi\)
							−0.933395	+	0.358850i	\(0.883169\pi\)
\(3\)	0.936417	+	1.45709i	0.312139	+	0.485698i
							\(5\)	1.62480	+	0.233611i	0.324960	+	0.0467223i	0.302865	−	0.953034i	\(-0.402057\pi\)
0.0220959	+	0.999756i	\(0.492966\pi\)
\(7\)	−7.97050	−	3.64000i	−1.13864	−	0.520001i	−0.245331	−	0.969439i	\(-0.578897\pi\)
							−0.893311	+	0.449439i	\(0.851624\pi\)
\(11\)	−0.0524937	−	0.00754745i	−0.00477215	−	0.000686132i	0.139928	−	0.990162i	\(-0.455313\pi\)
							−0.144701	+	0.989475i	\(0.546222\pi\)
\(13\)	3.66893	−	12.4952i	0.282226	−	0.961173i	−0.689347	−	0.724431i	\(-0.742102\pi\)
							0.971573	−	0.236741i	\(-0.0760794\pi\)
\(17\)	−1.52696	+	1.76221i	−0.0898215	+	0.103659i	−0.798881	−	0.601489i	\(-0.794574\pi\)
							0.709059	+	0.705149i	\(0.249120\pi\)
\(19\)	−6.48463	−	14.1994i	−0.341296	−	0.747335i	0.658691	−	0.752414i	\(-0.271111\pi\)
							−0.999987	+	0.00507885i	\(0.998383\pi\)
\(23\)	22.6587	−	14.5619i	0.985161	−	0.633125i	0.0543102	−	0.998524i	\(-0.482704\pi\)
							0.930851	+	0.365400i	\(0.119068\pi\)
\(29\)	−54.6563			−1.88470			−0.942351	−	0.334627i	\(-0.891390\pi\)
							−0.942351	+	0.334627i	\(0.891390\pi\)
\(31\)	−12.6916	−	43.2235i	−0.409406	−	1.39431i	−0.863947	−	0.503582i	\(-0.832015\pi\)
							0.454542	−	0.890725i	\(-0.349803\pi\)
\(37\)	−0.413774			−0.0111831			−0.00559154	−	0.999984i	\(-0.501780\pi\)
							−0.00559154	+	0.999984i	\(0.501780\pi\)
\(41\)	−16.2233	−	14.0575i	−0.395689	−	0.342867i	0.434178	−	0.900827i	\(-0.357039\pi\)
							−0.829868	+	0.557960i	\(0.811584\pi\)
\(43\)	−10.2719	−	8.90063i	−0.238881	−	0.206991i	0.527190	−	0.849747i	\(-0.323246\pi\)
							−0.766071	+	0.642756i	\(0.777791\pi\)
\(47\)	17.6704	−	11.3561i	0.375967	−	0.241619i	−0.338987	−	0.940791i	\(-0.610084\pi\)
							0.714954	+	0.699172i	\(0.246448\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.l.a.43.4	✓	220
67.53	odd	22	inner	201.3.l.a.187.4	yes	220

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.l.a.43.4	✓	220	1.1	even	1	trivial
201.3.l.a.187.4	yes	220	67.53	odd	22	inner