Embedded newform 201.3.k.a.14.11

• Label: 201.3.k.a.14.11
• Level: $201$
• Weight: $3$
• Character: 201.14
• Analytic conductor: $5.477$
• Analytic rank: $0$
• Dimension: $440$
• CM: no
• Inner twists: $4$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(5.47685331364\)
Analytic rank:	\(0\)
Dimension:	\(440\)
Relative dimension:	\(44\) over \(\Q(\zeta_{22})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			14.11
Character	\(\chi\)	\(=\)	201.14
Dual form			201.3.k.a.158.11

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.96120 + 0.895652i) q^{2} +(-1.45460 - 2.62376i) q^{3} +(0.424688 - 0.490116i) q^{4} +(-1.45741 + 0.209544i) q^{5} +(5.20275 + 3.84292i) q^{6} +(2.99885 + 6.56656i) q^{7} +(2.03578 - 6.93324i) q^{8} +(-4.76826 + 7.63307i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 11 q^{3} + 70 q^{4} - 17 q^{6} - 30 q^{7} - 15 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(68\)	\(136\)
\(\chi(n)\)	\(-1\)	\(e\left(\frac{4}{11}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.96120	+	0.895652i	−0.980602	+	0.447826i	−0.840205	−	0.542269i	\(-0.817565\pi\)
							−0.140397	+	0.990095i	\(0.544838\pi\)
\(3\)	−1.45460	−	2.62376i	−0.484868	−	0.874587i
							\(5\)	−1.45741	+	0.209544i	−0.291482	+	0.0419088i	−0.286505	−	0.958079i	\(-0.592493\pi\)
−0.00497732	+	0.999988i	\(0.501584\pi\)
\(7\)	2.99885	+	6.56656i	0.428407	+	0.938080i	0.993583	+	0.113110i	\(0.0360811\pi\)
							−0.565176	+	0.824971i	\(0.691192\pi\)
\(11\)	−14.1833	+	2.03924i	−1.28939	+	0.185386i	−0.752682	−	0.658384i	\(-0.771240\pi\)
							−0.536705	+	0.843770i	\(0.680331\pi\)
\(13\)	10.6979	−	3.14118i	0.822914	−	0.241629i	0.156944	−	0.987608i	\(-0.449836\pi\)
							0.665970	+	0.745978i	\(0.268018\pi\)
\(17\)	10.6877	−	9.26093i	0.628687	−	0.544760i	−0.281183	−	0.959654i	\(-0.590727\pi\)
							0.909870	+	0.414894i	\(0.136181\pi\)
\(19\)	11.1150	−	24.3386i	0.585002	−	1.28098i	−0.353413	−	0.935467i	\(-0.614979\pi\)
							0.938415	−	0.345509i	\(-0.112294\pi\)
\(23\)	14.4960	−	22.5563i	0.630263	−	0.980708i	−0.368433	−	0.929654i	\(-0.620106\pi\)
							0.998696	−	0.0510535i	\(-0.0162579\pi\)
\(29\)		−	37.9801i		−	1.30966i	−0.755776	−	0.654830i	\(-0.772740\pi\)
							0.755776	−	0.654830i	\(-0.227260\pi\)
\(31\)	43.8897	+	12.8872i	1.41580	+	0.415715i	0.898078	−	0.439836i	\(-0.144963\pi\)
							0.517718	+	0.855551i	\(0.326782\pi\)
\(37\)	43.5878			1.17805			0.589025	−	0.808115i	\(-0.299512\pi\)
							0.589025	+	0.808115i	\(0.299512\pi\)
\(41\)	24.7292	−	21.4279i	0.603150	−	0.522633i	−0.298888	−	0.954288i	\(-0.596616\pi\)
							0.902039	+	0.431655i	\(0.142070\pi\)
\(43\)	−55.2897	−	63.8077i	−1.28581	−	1.48390i	−0.786665	−	0.617380i	\(-0.788194\pi\)
							−0.499142	−	0.866520i	\(-0.666352\pi\)
\(47\)	−32.2205	+	50.1361i	−0.685543	+	1.06673i	0.307791	+	0.951454i	\(0.400410\pi\)
							−0.993334	+	0.115272i	\(0.963226\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.k.a.14.11	✓	440
3.2	odd	2	inner	201.3.k.a.14.34	yes	440
67.24	even	11	inner	201.3.k.a.158.34	yes	440
201.158	odd	22	inner	201.3.k.a.158.11	yes	440

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.k.a.14.11	✓	440	1.1	even	1	trivial
201.3.k.a.14.34	yes	440	3.2	odd	2	inner
201.3.k.a.158.11	yes	440	201.158	odd	22	inner
201.3.k.a.158.34	yes	440	67.24	even	11	inner