Embedded newform 201.4.i.a.25.2

• Label: 201.4.i.a.25.2
• Level: $201$
• Weight: $4$
• Character: 201.25
• 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			25.2
Character	\(\chi\)	\(=\)	201.25
Dual form			201.4.i.a.193.2

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.687211 - 4.77966i) q^{2} +(-1.96458 + 2.26725i) q^{3} +(-14.6969 + 4.31540i) q^{4} +(-18.1078 + 11.6372i) q^{5} +(12.1867 + 7.83195i) q^{6} +(-0.920492 - 6.40216i) q^{7} +(14.6783 + 32.1410i) q^{8} +(-1.28083 - 8.90839i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 170 q + 2 q^{2} - 51 q^{3} - 82 q^{4} + 4 q^{5} - 27 q^{6} - 16 q^{7} - 177 q^{8} - 153 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(68\)	\(136\)
\(\chi(n)\)	\(1\)	\(e\left(\frac{5}{11}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.687211	−	4.77966i	−0.242966	−	1.68986i	−0.637077	−	0.770800i	\(-0.719857\pi\)
							0.394111	−	0.919063i	\(-0.371053\pi\)
\(3\)	−1.96458	+	2.26725i	−0.378084	+	0.436332i
							\(5\)	−18.1078	+	11.6372i	−1.61961	+	1.04086i	−0.663362	+	0.748299i	\(0.730871\pi\)
−0.956247	+	0.292561i	\(0.905493\pi\)
\(7\)	−0.920492	−	6.40216i	−0.0497019	−	0.345684i	−0.999465	−	0.0327139i	\(-0.989585\pi\)
							0.949763	−	0.312971i	\(-0.101324\pi\)
\(11\)	6.51744	−	4.18851i	0.178644	−	0.114807i	−0.448263	−	0.893902i	\(-0.647957\pi\)
							0.626907	+	0.779094i	\(0.284321\pi\)
\(13\)	−5.19123	+	11.3672i	−0.110753	+	0.242515i	−0.956890	−	0.290450i	\(-0.906195\pi\)
							0.846137	+	0.532965i	\(0.178922\pi\)
\(17\)	48.3420	+	14.1945i	0.689686	+	0.202510i	0.607751	−	0.794127i	\(-0.292072\pi\)
							0.0819352	+	0.996638i	\(0.473890\pi\)
\(19\)	19.0779	−	132.689i	0.230356	−	1.60216i	−0.466215	−	0.884672i	\(-0.654383\pi\)
							0.696570	−	0.717488i	\(-0.254708\pi\)
\(23\)	−55.5093	+	64.0612i	−0.503239	+	0.580769i	−0.949355	−	0.314207i	\(-0.898262\pi\)
							0.446116	+	0.894975i	\(0.352807\pi\)
\(29\)	38.2307			0.244802			0.122401	−	0.992481i	\(-0.460941\pi\)
							0.122401	+	0.992481i	\(0.460941\pi\)
\(31\)	72.8008	+	159.411i	0.421787	+	0.923585i	0.994589	+	0.103891i	\(0.0331294\pi\)
							−0.572801	+	0.819694i	\(0.694143\pi\)
\(37\)	310.904			1.38141			0.690706	−	0.723135i	\(-0.257300\pi\)
							0.690706	+	0.723135i	\(0.257300\pi\)
\(41\)	−281.730	−	82.7233i	−1.07314	−	0.315103i	−0.303010	−	0.952987i	\(-0.597991\pi\)
							−0.770132	+	0.637885i	\(0.779810\pi\)
\(43\)	131.265	+	38.5428i	0.465528	+	0.136691i	0.506081	−	0.862486i	\(-0.331094\pi\)
							−0.0405530	+	0.999177i	\(0.512912\pi\)
\(47\)	−263.864	+	304.516i	−0.818906	+	0.945068i	−0.999257	−	0.0385342i	\(-0.987731\pi\)
							0.180351	+	0.983602i	\(0.442277\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.i.a.25.2	✓	170
67.59	even	11	inner	201.4.i.a.193.2	yes	170

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.i.a.25.2	✓	170	1.1	even	1	trivial
201.4.i.a.193.2	yes	170	67.59	even	11	inner