Embedded newform 143.4.h.a.92.6

• Label: 143.4.h.a.92.6
• 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			92.6
Character	\(\chi\)	\(=\)	143.92
Dual form			143.4.h.a.14.6

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.95153 - 1.41787i) q^{2} +(1.17190 - 3.60673i) q^{3} +(-0.674012 - 2.07439i) q^{4} +(-13.9051 + 10.1026i) q^{5} +(-7.40089 + 5.37706i) q^{6} +(-2.26259 - 6.96352i) q^{7} +(-7.58923 + 23.3573i) q^{8} +(10.2083 + 7.41675i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{2} + 12 q^{3} - 16 q^{4} + 24 q^{5} + 7 q^{6} + 8 q^{7} - 34 q^{8} - 55 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.95153	−	1.41787i	−0.689972	−	0.501294i	0.186679	−	0.982421i	\(-0.440228\pi\)
							−0.876651	+	0.481127i	\(0.840228\pi\)
\(3\)	1.17190	−	3.60673i	0.225532	−	0.694116i	−0.772705	−	0.634765i	\(-0.781097\pi\)
							0.998237	−	0.0593512i	\(-0.0189032\pi\)
\(5\)	−13.9051	+	10.1026i	−1.24371	+	0.903608i	−0.997840	−	0.0656947i	\(-0.979074\pi\)
							−0.245870	+	0.969303i	\(0.579074\pi\)
\(7\)	−2.26259	−	6.96352i	−0.122168	−	0.375995i	0.871206	−	0.490917i	\(-0.163338\pi\)
							−0.993375	+	0.114922i	\(0.963338\pi\)
\(11\)	22.2110	+	28.9426i	0.608806	+	0.793319i
							\(13\)	−10.5172	−	7.64121i	−0.224381	−	0.163022i
\(17\)	54.5169	−	39.6088i	0.777781	−	0.565091i								−0.126531	−	0.991963i	\(-0.540384\pi\)
							0.904312	+	0.426872i	\(0.140384\pi\)
\(19\)	1.08394	−	3.33602i	0.0130880	−	0.0402808i	−0.944299	−	0.329088i	\(-0.893259\pi\)
							0.957387	+	0.288807i	\(0.0932587\pi\)
\(23\)	−159.787			−1.44860			−0.724302	−	0.689483i	\(-0.757838\pi\)
							−0.724302	+	0.689483i	\(0.757838\pi\)
\(29\)	89.1612	+	274.410i	0.570925	+	1.75713i	0.649655	+	0.760230i	\(0.274914\pi\)
							−0.0787299	+	0.996896i	\(0.525086\pi\)
\(31\)	187.969	+	136.568i	1.08904	+	0.791234i	0.979237	−	0.202719i	\(-0.0649778\pi\)
							0.109804	+	0.993953i	\(0.464978\pi\)
\(37\)	82.8680	+	255.041i	0.368200	+	1.13320i	0.947953	+	0.318411i	\(0.103149\pi\)
							−0.579752	+	0.814793i	\(0.696851\pi\)
\(41\)	−61.1556	+	188.218i	−0.232949	+	0.716943i	0.764438	+	0.644697i	\(0.223017\pi\)
							−0.997387	+	0.0722455i	\(0.976983\pi\)
\(43\)	−275.508			−0.977081			−0.488541	−	0.872541i	\(-0.662471\pi\)
							−0.488541	+	0.872541i	\(0.662471\pi\)
\(47\)	−107.777	+	331.704i	−0.334488	+	1.02945i	0.632486	+	0.774572i	\(0.282035\pi\)
							−0.966974	+	0.254876i	\(0.917965\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.h.a.92.6	yes	68
11.3	even	5	inner	143.4.h.a.14.6	✓	68
11.5	even	5		1573.4.a.o.1.25		34
11.6	odd	10		1573.4.a.p.1.10		34

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.14.6	✓	68	11.3	even	5	inner
143.4.h.a.92.6	yes	68	1.1	even	1	trivial
1573.4.a.o.1.25		34	11.5	even	5
1573.4.a.p.1.10		34	11.6	odd	10