Embedded newform 143.4.h.b.14.13

• Label: 143.4.h.b.14.13
• Level: $143$
• Weight: $4$
• Character: 143.14
• Analytic conductor: $8.437$
• Analytic rank: $0$
• Dimension: $76$
• CM: no
• 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:	\(76\)
Relative dimension:	\(19\) over \(\Q(\zeta_{5})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			14.13
Character	\(\chi\)	\(=\)	143.14
Dual form			143.4.h.b.92.13

$q$-expansion

\(f(q)\)	\(=\)	\(q+(1.57062 - 1.14112i) q^{2} +(0.990304 + 3.04784i) q^{3} +(-1.30744 + 4.02390i) q^{4} +(-16.0734 - 11.6780i) q^{5} +(5.03336 + 3.65695i) q^{6} +(8.77337 - 27.0017i) q^{7} +(7.33766 + 22.5830i) q^{8} +(13.5348 - 9.83362i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{2} - 12 q^{3} - 148 q^{4} - 16 q^{5} + 77 q^{6} + 56 q^{7} - 34 q^{8} - 241 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(67\)	\(79\)
\(\chi(n)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	1.57062	−	1.14112i	0.555299	−	0.403448i	−0.274436	−	0.961605i	\(-0.588491\pi\)
							0.829735	+	0.558157i	\(0.188491\pi\)
\(3\)	0.990304	+	3.04784i	0.190584	+	0.586558i	1.00000		0.000678609i	\(-0.000216008\pi\)
							−0.809416	+	0.587236i	\(0.800216\pi\)
\(5\)	−16.0734	−	11.6780i	−1.43765	−	1.04452i	−0.988526	−	0.151048i	\(-0.951735\pi\)
							−0.449126	−	0.893468i	\(-0.648265\pi\)
\(7\)	8.77337	−	27.0017i	0.473718	−	1.45795i	−0.373962	−	0.927444i	\(-0.622001\pi\)
							0.847679	−	0.530509i	\(-0.177999\pi\)
\(11\)	−29.7624	−	21.0997i	−0.815792	−	0.578346i
							\(13\)	10.5172	−	7.64121i	0.224381	−	0.163022i
\(17\)	6.10817	+	4.43785i	0.0871441	+	0.0633139i								0.630504	−	0.776186i	\(-0.282848\pi\)
							−0.543360	+	0.839500i	\(0.682848\pi\)
\(19\)	−49.6352	−	152.761i	−0.599321	−	1.84452i	−0.531923	−	0.846793i	\(-0.678530\pi\)
							−0.0673976	−	0.997726i	\(-0.521470\pi\)
\(23\)	−32.6850			−0.296317			−0.148159	−	0.988964i	\(-0.547335\pi\)
							−0.148159	+	0.988964i	\(0.547335\pi\)
\(29\)	45.5600	−	140.219i	0.291734	−	0.897864i	−0.692565	−	0.721355i	\(-0.743520\pi\)
							0.984299	−	0.176509i	\(-0.0564804\pi\)
\(31\)	−131.253	+	95.3610i	−0.760444	+	0.552495i	−0.899047	−	0.437853i	\(-0.855739\pi\)
							0.138602	+	0.990348i	\(0.455739\pi\)
\(37\)	−15.7619	+	48.5103i	−0.0700337	+	0.215542i	−0.979948	−	0.199256i	\(-0.936148\pi\)
							0.909914	+	0.414797i	\(0.136148\pi\)
\(41\)	−36.6749	−	112.874i	−0.139699	−	0.429949i	0.856592	−	0.515994i	\(-0.172577\pi\)
							−0.996291	+	0.0860449i	\(0.972577\pi\)
\(43\)	255.704			0.906850			0.453425	−	0.891294i	\(-0.350202\pi\)
							0.453425	+	0.891294i	\(0.350202\pi\)
\(47\)	121.706	+	374.572i	0.377716	+	1.16249i	0.941628	+	0.336655i	\(0.109296\pi\)
							−0.563912	+	0.825835i	\(0.690704\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.h.b.14.13	✓	76
11.2	odd	10		1573.4.a.r.1.25		38
11.4	even	5	inner	143.4.h.b.92.13	yes	76
11.9	even	5		1573.4.a.q.1.14		38

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.b.14.13	✓	76	1.1	even	1	trivial
143.4.h.b.92.13	yes	76	11.4	even	5	inner
1573.4.a.q.1.14		38	11.9	even	5
1573.4.a.r.1.25		38	11.2	odd	10