Embedded newform 143.4.h.a.92.17

• Label: 143.4.h.a.92.17
• Level: $143$
• Weight: $4$
• Character: 143.92
• Analytic conductor: $8.437$
• Analytic rank: $0$
• Dimension: $68$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.43727313082\)
Analytic rank:	\(0\)
Dimension:	\(68\)
Relative dimension:	\(17\) over \(\Q(\zeta_{5})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			92.17
Character	\(\chi\)	\(=\)	143.92
Dual form			143.4.h.a.14.17

$q$-expansion

\(f(q)\)	\(=\)	\(q+(4.42470 + 3.21473i) q^{2} +(-2.05208 + 6.31565i) q^{3} +(6.77132 + 20.8400i) q^{4} +(10.1327 - 7.36185i) q^{5} +(-29.3829 + 21.3480i) q^{6} +(-1.00225 - 3.08462i) q^{7} +(-23.5132 + 72.3663i) q^{8} +(-13.8329 - 10.0502i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{2} + 12 q^{3} - 16 q^{4} + 24 q^{5} + 7 q^{6} + 8 q^{7} - 34 q^{8} - 55 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).

\(n\)	\(67\)	\(79\)
\(\chi(n)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	4.42470	+	3.21473i	1.56437	+	1.13658i	0.932312	+	0.361656i	\(0.117789\pi\)
							0.632056	+	0.774923i	\(0.282211\pi\)
\(3\)	−2.05208	+	6.31565i	−0.394923	+	1.21545i	0.534099	+	0.845422i	\(0.320651\pi\)
							−0.929022	+	0.370025i	\(0.879349\pi\)
\(5\)	10.1327	−	7.36185i	0.906298	−	0.658464i	−0.0337779	−	0.999429i	\(-0.510754\pi\)
							0.940076	+	0.340965i	\(0.110754\pi\)
\(7\)	−1.00225	−	3.08462i	−0.0541166	−	0.166554i	0.920345	−	0.391107i	\(-0.127908\pi\)
							−0.974462	+	0.224553i	\(0.927908\pi\)
\(11\)	7.92955	−	35.6107i	0.217350	−	0.976094i
							\(13\)	−10.5172	−	7.64121i	−0.224381	−	0.163022i
\(17\)	94.8323	−	68.8997i	1.35295	−	0.982978i								0.354095	−	0.935210i	\(-0.384789\pi\)
							0.998858	−	0.0477685i	\(-0.0152110\pi\)
\(19\)	24.5521	−	75.5635i	0.296454	−	0.912392i	−0.686275	−	0.727342i	\(-0.740755\pi\)
							0.982729	−	0.185050i	\(-0.0592447\pi\)
\(23\)	−178.384			−1.61720			−0.808600	−	0.588358i	\(-0.799774\pi\)
							−0.808600	+	0.588358i	\(0.799774\pi\)
\(29\)	35.7092	+	109.902i	0.228656	+	0.703732i	0.997900	+	0.0647761i	\(0.0206333\pi\)
							−0.769244	+	0.638956i	\(0.779367\pi\)
\(31\)	−9.59702	−	6.97264i	−0.0556024	−	0.0403975i	0.559637	−	0.828738i	\(-0.310941\pi\)
							−0.615239	+	0.788340i	\(0.710941\pi\)
\(37\)	−11.8608	−	36.5039i	−0.0527003	−	0.162195i	0.921242	−	0.388989i	\(-0.127176\pi\)
							−0.973943	+	0.226794i	\(0.927176\pi\)
\(41\)	−111.480	+	343.101i	−0.424642	+	1.30691i	0.478695	+	0.877981i	\(0.341110\pi\)
							−0.903337	+	0.428932i	\(0.858890\pi\)
\(43\)	270.693			0.960005			0.480003	−	0.877267i	\(-0.340636\pi\)
							0.480003	+	0.877267i	\(0.340636\pi\)
\(47\)	44.1558	−	135.898i	0.137038	−	0.421759i	−0.858863	−	0.512205i	\(-0.828829\pi\)
							0.995901	+	0.0904451i	\(0.0288290\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.h.a.92.17	yes	68
11.3	even	5	inner	143.4.h.a.14.17	✓	68
11.5	even	5		1573.4.a.o.1.1		34
11.6	odd	10		1573.4.a.p.1.34		34

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.14.17	✓	68	11.3	even	5	inner
143.4.h.a.92.17	yes	68	1.1	even	1	trivial
1573.4.a.o.1.1		34	11.5	even	5
1573.4.a.p.1.34		34	11.6	odd	10