Embedded newform 141.4.e.b.4.2

• Label: 141.4.e.b.4.2
• Level: $141$
• Weight: $4$
• Character: 141.4
• Analytic conductor: $8.319$
• Analytic rank: $0$
• Dimension: $264$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 141 = 3 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	141.e (of order \(23\), degree \(22\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.31926931081\)
Analytic rank:	\(0\)
Dimension:	\(264\)
Relative dimension:	\(12\) over \(\Q(\zeta_{23})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{23}]$

Embedding invariants

Embedding label			4.2
Character	\(\chi\)	\(=\)	141.4
Dual form			141.4.e.b.106.2

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-4.11775 - 1.15374i) q^{2} +(-1.38020 + 2.66366i) q^{3} +(8.78940 + 5.34495i) q^{4} +(14.7477 - 11.9981i) q^{5} +(8.75646 - 9.37588i) q^{6} +(-7.88427 - 1.08367i) q^{7} +(-6.67529 - 7.14749i) q^{8} +(-5.19012 - 7.35273i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 264 q + 2 q^{2} + 36 q^{3} - 46 q^{4} - 2 q^{5} - 6 q^{6} - 4 q^{7} + 66 q^{8} - 108 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/141\mathbb{Z}\right)^\times\).

\(n\)	\(52\)	\(95\)
\(\chi(n)\)	\(e\left(\frac{18}{23}\right)\)	\(1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−4.11775	−	1.15374i	−1.45584	−	0.407909i	−0.551307	−	0.834302i	\(-0.685871\pi\)
							−0.904538	+	0.426394i	\(0.859784\pi\)
\(3\)	−1.38020	+	2.66366i	−0.265619	+	0.512621i
							\(5\)	14.7477	−	11.9981i	1.31907	−	1.07314i	0.327328	−	0.944911i	\(-0.393852\pi\)
0.991744	−	0.128234i	\(-0.0409310\pi\)
\(7\)	−7.88427	−	1.08367i	−0.425711	−	0.0585126i	−0.0798688	−	0.996805i	\(-0.525450\pi\)
							−0.345842	+	0.938293i	\(0.612407\pi\)
\(11\)	2.96215	+	43.3051i	0.0811928	+	1.18700i	0.842533	+	0.538645i	\(0.181063\pi\)
							−0.761340	+	0.648353i	\(0.775458\pi\)
\(13\)	7.51119	−	21.1345i	0.160248	−	0.450896i	−0.834769	−	0.550601i	\(-0.814399\pi\)
							0.995017	+	0.0997050i	\(0.0317899\pi\)
\(17\)	−0.469785	+	6.86802i	−0.00670234	+	0.0979847i	−0.999816	−	0.0191677i	\(-0.993898\pi\)
							0.993114	+	0.117152i	\(0.0373766\pi\)
\(19\)	7.69868	+	6.26334i	0.0929579	+	0.0756268i	0.676433	−	0.736504i	\(-0.263525\pi\)
							−0.583475	+	0.812131i	\(0.698307\pi\)
\(23\)	175.857	−	49.2727i	1.59429	−	0.446699i	0.645799	−	0.763508i	\(-0.276525\pi\)
							0.948489	+	0.316809i	\(0.102612\pi\)
\(29\)	−21.1631	−	59.5473i	−0.135514	−	0.381299i	0.855015	−	0.518603i	\(-0.173548\pi\)
							−0.990529	+	0.137304i	\(0.956156\pi\)
\(31\)	−92.2178	−	177.972i	−0.534284	−	1.03112i	−0.990009	−	0.141001i	\(-0.954968\pi\)
							0.455725	−	0.890121i	\(-0.349380\pi\)
\(37\)	209.557	−	91.0233i	0.931105	−	0.404436i	0.122287	−	0.992495i	\(-0.460977\pi\)
							0.808818	+	0.588059i	\(0.200108\pi\)
\(41\)	302.166	−	323.540i	1.15098	−	1.23240i	0.182533	−	0.983200i	\(-0.441570\pi\)
							0.968451	−	0.249203i	\(-0.0801688\pi\)
\(43\)	317.715	+	193.207i	1.12677	+	0.685205i	0.954015	−	0.299760i	\(-0.0969066\pi\)
							0.172756	+	0.984965i	\(0.444733\pi\)
\(47\)	319.699	−	40.1968i	0.992188	−	0.124751i

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	141.4.e.b.4.2	✓	264
47.12	even	23	inner	141.4.e.b.106.2	yes	264

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
141.4.e.b.4.2	✓	264	1.1	even	1	trivial
141.4.e.b.106.2	yes	264	47.12	even	23	inner