Embedded newform 201.4.i.b.22.11

• Label: 201.4.i.b.22.11
• Level: $201$
• Weight: $4$
• Character: 201.22
• 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			22.11
Character	\(\chi\)	\(=\)	201.22
Dual form			201.4.i.b.64.11

$q$-expansion

\(f(q)\)	\(=\)	\(q+(1.28293 - 0.376701i) q^{2} +(0.426945 + 2.96946i) q^{3} +(-5.22603 + 3.35857i) q^{4} +(-3.87080 + 8.47587i) q^{5} +(1.66634 + 3.64877i) q^{6} +(-3.40266 + 0.999110i) q^{7} +(-12.4443 + 14.3615i) q^{8} +(-8.63544 + 2.53559i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 170 q + 2 q^{2} + 51 q^{3} - 74 q^{4} - 4 q^{5} + 27 q^{6} + 12 q^{7} - 237 q^{8} - 153 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(68\)	\(136\)
\(\chi(n)\)	\(1\)	\(e\left(\frac{10}{11}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	1.28293	−	0.376701i	0.453583	−	0.133184i	−0.0469579	−	0.998897i	\(-0.514953\pi\)
							0.500541	+	0.865713i	\(0.333134\pi\)
\(3\)	0.426945	+	2.96946i	0.0821655	+	0.571474i
							\(5\)	−3.87080	+	8.47587i	−0.346215	+	0.758105i	0.653784	+	0.756681i	\(0.273180\pi\)
−0.999999	+	0.00142373i	\(0.999547\pi\)
\(7\)	−3.40266	+	0.999110i	−0.183726	+	0.0539469i	−0.372301	−	0.928112i	\(-0.621431\pi\)
							0.188575	+	0.982059i	\(0.439613\pi\)
\(11\)	20.9696	−	45.9171i	0.574780	−	1.25859i	−0.369433	−	0.929257i	\(-0.620448\pi\)
							0.944213	−	0.329336i	\(-0.106825\pi\)
\(13\)	−15.2628	−	17.6143i	−0.325627	−	0.375794i	0.569206	−	0.822195i	\(-0.307251\pi\)
							−0.894833	+	0.446401i	\(0.852705\pi\)
\(17\)	−72.2580	−	46.4374i	−1.03089	−	0.662513i	−0.0881728	−	0.996105i	\(-0.528103\pi\)
							−0.942717	+	0.333592i	\(0.891739\pi\)
\(19\)	−49.5399	−	14.5462i	−0.598170	−	0.175639i	−0.0313893	−	0.999507i	\(-0.509993\pi\)
							−0.566781	+	0.823869i	\(0.691811\pi\)
\(23\)	12.0593	+	83.8746i	0.109328	+	0.760394i	0.968555	+	0.248799i	\(0.0800359\pi\)
							−0.859227	+	0.511595i	\(0.829055\pi\)
\(29\)	−151.440			−0.969711			−0.484855	−	0.874594i	\(-0.661128\pi\)
							−0.484855	+	0.874594i	\(0.661128\pi\)
\(31\)	−50.2379	+	57.9777i	−0.291064	+	0.335906i	−0.882383	−	0.470532i	\(-0.844062\pi\)
							0.591319	+	0.806438i	\(0.298608\pi\)
\(37\)	−212.239			−0.943022			−0.471511	−	0.881860i	\(-0.656291\pi\)
							−0.471511	+	0.881860i	\(0.656291\pi\)
\(41\)	257.764	+	165.655i	0.981854	+	0.630999i	0.929963	−	0.367654i	\(-0.119839\pi\)
							0.0518911	+	0.998653i	\(0.483475\pi\)
\(43\)	13.0556	+	8.39034i	0.0463015	+	0.0297562i	0.563587	−	0.826057i	\(-0.309421\pi\)
							−0.517285	+	0.855813i	\(0.673057\pi\)
\(47\)	13.4679	+	93.6716i	0.0417979	+	0.290711i	0.999989	+	0.00458346i	\(0.00145896\pi\)
							−0.958192	+	0.286127i	\(0.907632\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.i.b.22.11	✓	170
67.64	even	11	inner	201.4.i.b.64.11	yes	170

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.i.b.22.11	✓	170	1.1	even	1	trivial
201.4.i.b.64.11	yes	170	67.64	even	11	inner