Embedded newform 201.3.o.b.17.14

• Label: 201.3.o.b.17.14
• Level: $201$
• Weight: $3$
• Character: 201.17
• Analytic conductor: $5.477$
• Analytic rank: $0$
• Dimension: $840$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.o (of order \(66\), degree \(20\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.47685331364\)
Analytic rank:	\(0\)
Dimension:	\(840\)
Relative dimension:	\(42\) over \(\Q(\zeta_{66})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			17.14
Character	\(\chi\)	\(=\)	201.17
Dual form			201.3.o.b.71.14

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.152393 - 1.59594i) q^{2} +(0.135358 - 2.99694i) q^{3} +(1.40393 - 0.270585i) q^{4} +(0.199274 + 0.0286513i) q^{5} +(-4.80356 + 0.240692i) q^{6} +(-2.27333 - 3.19244i) q^{7} +(-2.45247 - 8.35236i) q^{8} +(-8.96336 - 0.811320i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 16 q^{3} - 126 q^{4} - 25 q^{6} - 34 q^{7} - 24 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(68\)	\(136\)
\(\chi(n)\)	\(-1\)	\(e\left(\frac{32}{33}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.152393	−	1.59594i	−0.0761967	−	0.797968i	−0.950116	−	0.311897i	\(-0.899036\pi\)
							0.873919	−	0.486071i	\(-0.161570\pi\)
\(3\)	0.135358	−	2.99694i	0.0451193	−	0.998982i
							\(5\)	0.199274	+	0.0286513i	0.0398548	+	0.00573026i	0.162213	−	0.986756i	\(-0.448137\pi\)
−0.122359	+	0.992486i	\(0.539046\pi\)
\(7\)	−2.27333	−	3.19244i	−0.324761	−	0.456063i	0.619627	−	0.784897i	\(-0.287284\pi\)
							−0.944388	+	0.328833i	\(0.893345\pi\)
\(11\)	−0.648068	+	0.824086i	−0.0589153	+	0.0749169i	−0.814618	−	0.579998i	\(-0.803053\pi\)
							0.755702	+	0.654915i	\(0.227296\pi\)
\(13\)	2.13201	+	8.78828i	0.164001	+	0.676021i	0.993135	+	0.116972i	\(0.0373187\pi\)
							−0.829134	+	0.559049i	\(0.811166\pi\)
\(17\)	4.30932	−	22.3589i	0.253489	−	1.31523i	−0.602452	−	0.798155i	\(-0.705810\pi\)
							0.855942	−	0.517073i	\(-0.172978\pi\)
\(19\)	17.7735	−	24.9594i	0.935449	−	1.31365i	−0.0140550	−	0.999901i	\(-0.504474\pi\)
							0.949504	−	0.313754i	\(-0.101587\pi\)
\(23\)	−18.2915	+	35.4806i	−0.795285	+	1.54264i	0.0440547	+	0.999029i	\(0.485972\pi\)
							−0.839339	+	0.543608i	\(0.817058\pi\)
\(29\)	35.8986	+	20.7261i	1.23788	+	0.714692i	0.968661	−	0.248387i	\(-0.0799004\pi\)
							0.269221	+	0.963078i	\(0.413234\pi\)
\(31\)	−9.90092	+	40.8121i	−0.319384	+	1.31652i	0.555228	+	0.831698i	\(0.312631\pi\)
							−0.874613	+	0.484822i	\(0.838884\pi\)
\(37\)	−15.7059	−	27.2035i	−0.424485	−	0.735229i	0.571887	−	0.820332i	\(-0.306211\pi\)
							−0.996372	+	0.0851030i	\(0.972878\pi\)
\(41\)	20.9696	−	7.25766i	0.511455	−	0.177016i	−0.0591373	−	0.998250i	\(-0.518835\pi\)
							0.570592	+	0.821234i	\(0.306714\pi\)
\(43\)	42.8809	−	49.4872i	0.997230	−	1.15086i	0.00868092	−	0.999962i	\(-0.497237\pi\)
							0.988549	−	0.150902i	\(-0.0482178\pi\)
\(47\)	47.3922	−	2.25757i	1.00835	−	0.0480334i	0.463097	−	0.886308i	\(-0.346738\pi\)
							0.545249	+	0.838274i	\(0.316435\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.o.b.17.14	✓	840
3.2	odd	2	inner	201.3.o.b.17.29	yes	840
67.4	even	33	inner	201.3.o.b.71.29	yes	840
201.71	odd	66	inner	201.3.o.b.71.14	yes	840

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.o.b.17.14	✓	840	1.1	even	1	trivial
201.3.o.b.17.29	yes	840	3.2	odd	2	inner
201.3.o.b.71.14	yes	840	201.71	odd	66	inner
201.3.o.b.71.29	yes	840	67.4	even	33	inner