Embedded newform 143.4.h.a.27.9

• Label: 143.4.h.a.27.9
• Level: $143$
• Weight: $4$
• Character: 143.27
• 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			27.9
Character	\(\chi\)	\(=\)	143.27
Dual form			143.4.h.a.53.9

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.0945359 + 0.290952i) q^{2} +(0.557249 + 0.404865i) q^{3} +(6.39642 - 4.64727i) q^{4} +(-4.52869 + 13.9379i) q^{5} +(-0.0651161 + 0.200407i) q^{6} +(-27.6482 + 20.0876i) q^{7} +(3.93681 + 2.86026i) q^{8} +(-8.19685 - 25.2273i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{2} + 12 q^{3} - 16 q^{4} + 24 q^{5} + 7 q^{6} + 8 q^{7} - 34 q^{8} - 55 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(67\)	\(79\)
\(\chi(n)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.0945359	+	0.290952i	0.0334235	+	0.102867i	0.966376	−	0.257131i	\(-0.0827773\pi\)
							−0.932953	+	0.359998i	\(0.882777\pi\)
\(3\)	0.557249	+	0.404865i	0.107243	+	0.0779163i	0.640114	−	0.768280i	\(-0.278887\pi\)
							−0.532871	+	0.846196i	\(0.678887\pi\)
\(5\)	−4.52869	+	13.9379i	−0.405059	+	1.24664i	0.515788	+	0.856716i	\(0.327499\pi\)
							−0.920846	+	0.389926i	\(0.872501\pi\)
\(7\)	−27.6482	+	20.0876i	−1.49286	+	1.08463i	−0.519741	+	0.854324i	\(0.673972\pi\)
							−0.973119	+	0.230302i	\(0.926028\pi\)
\(11\)	−34.7937	+	10.9727i	−0.953699	+	0.300764i
							\(13\)	4.01722	+	12.3637i	0.0857059	+	0.263776i
\(17\)	−22.0442	+	67.8450i	−0.314500	+	0.967931i								0.661460	+	0.749980i	\(0.269937\pi\)
							−0.975960	+	0.217950i	\(0.930063\pi\)
\(19\)	27.7048	+	20.1287i	0.334522	+	0.243045i	0.742347	−	0.670016i	\(-0.233713\pi\)
							−0.407825	+	0.913060i	\(0.633713\pi\)
\(23\)	−0.447054			−0.00405292			−0.00202646	−	0.999998i	\(-0.500645\pi\)
							−0.00202646	+	0.999998i	\(0.500645\pi\)
\(29\)	−138.414	+	100.564i	−0.886304	+	0.643938i	−0.934912	−	0.354880i	\(-0.884522\pi\)
							0.0486075	+	0.998818i	\(0.484522\pi\)
\(31\)	−9.76366	−	30.0495i	−0.0565679	−	0.174098i	0.918780	−	0.394769i	\(-0.129175\pi\)
							−0.975348	+	0.220671i	\(0.929175\pi\)
\(37\)	−217.511	+	158.031i	−0.966450	+	0.702167i	−0.954640	−	0.297764i	\(-0.903759\pi\)
							−0.0118100	+	0.999930i	\(0.503759\pi\)
\(41\)	313.480	+	227.756i	1.19408	+	0.867550i	0.993689	−	0.112166i	\(-0.0357789\pi\)
							0.200390	+	0.979716i	\(0.435779\pi\)
\(43\)	452.217			1.60378			0.801889	−	0.597474i	\(-0.203829\pi\)
							0.801889	+	0.597474i	\(0.203829\pi\)
\(47\)	−73.7040	−	53.5491i	−0.228741	−	0.166190i	0.467511	−	0.883987i	\(-0.345151\pi\)
							−0.696253	+	0.717797i	\(0.745151\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.h.a.27.9	✓	68
11.3	even	5		1573.4.a.o.1.18		34
11.8	odd	10		1573.4.a.p.1.17		34
11.9	even	5	inner	143.4.h.a.53.9	yes	68

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.27.9	✓	68	1.1	even	1	trivial
143.4.h.a.53.9	yes	68	11.9	even	5	inner
1573.4.a.o.1.18		34	11.3	even	5
1573.4.a.p.1.17		34	11.8	odd	10