Embedded newform 201.4.i.b.64.11

• Label: 201.4.i.b.64.11
• Level: $201$
• Weight: $4$
• Character: 201.64
• 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			64.11
Character	\(\chi\)	\(=\)	201.64
Dual form			201.4.i.b.22.11

$q$-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 \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).

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

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	0.500541	−	0.865713i	\(-0.333134\pi\)
							−0.0469579	+	0.998897i	\(0.514953\pi\)
\(3\)	0.426945	−	2.96946i	0.0821655	−	0.571474i
							\(5\)	−3.87080	−	8.47587i	−0.346215	−	0.758105i	−0.999999	−	0.00142373i	\(-0.999547\pi\)
0.653784	−	0.756681i	\(-0.273180\pi\)
\(7\)	−3.40266	−	0.999110i	−0.183726	−	0.0539469i	0.188575	−	0.982059i	\(-0.439613\pi\)
							−0.372301	+	0.928112i	\(0.621431\pi\)
\(11\)	20.9696	+	45.9171i	0.574780	+	1.25859i	0.944213	+	0.329336i	\(0.106825\pi\)
							−0.369433	+	0.929257i	\(0.620448\pi\)
\(13\)	−15.2628	+	17.6143i	−0.325627	+	0.375794i	−0.894833	−	0.446401i	\(-0.852705\pi\)
							0.569206	+	0.822195i	\(0.307251\pi\)
\(17\)	−72.2580	+	46.4374i	−1.03089	+	0.662513i	−0.942717	−	0.333592i	\(-0.891739\pi\)
							−0.0881728	+	0.996105i	\(0.528103\pi\)
\(19\)	−49.5399	+	14.5462i	−0.598170	+	0.175639i	−0.566781	−	0.823869i	\(-0.691811\pi\)
							−0.0313893	+	0.999507i	\(0.509993\pi\)
\(23\)	12.0593	−	83.8746i	0.109328	−	0.760394i	−0.859227	−	0.511595i	\(-0.829055\pi\)
							0.968555	−	0.248799i	\(-0.0800359\pi\)
\(29\)	−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	0.591319	−	0.806438i	\(-0.298608\pi\)
							−0.882383	+	0.470532i	\(0.844062\pi\)
\(37\)	−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	0.0518911	−	0.998653i	\(-0.483475\pi\)
							0.929963	+	0.367654i	\(0.119839\pi\)
\(43\)	13.0556	−	8.39034i	0.0463015	−	0.0297562i	−0.517285	−	0.855813i	\(-0.673057\pi\)
							0.563587	+	0.826057i	\(0.309421\pi\)
\(47\)	13.4679	−	93.6716i	0.0417979	−	0.290711i	−0.958192	−	0.286127i	\(-0.907632\pi\)
							0.999989	−	0.00458346i	\(-0.00145896\pi\)

(See \(a_n\) instead)

Twists

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

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.i.b.22.11	✓	170	67.22	even	11	inner
201.4.i.b.64.11	yes	170	1.1	even	1	trivial