Embedded newform 143.4.h.a.27.8

• Label: 143.4.h.a.27.8
• 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			27.8
Character	\(\chi\)	\(=\)	143.27
Dual form			143.4.h.a.53.8

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.175549 - 0.540283i) q^{2} +(-5.19733 - 3.77608i) q^{3} +(6.21105 - 4.51259i) q^{4} +(1.29337 - 3.98059i) q^{5} +(-1.12777 + 3.47091i) q^{6} +(26.2833 - 19.0959i) q^{7} +(-7.20515 - 5.23485i) q^{8} +(4.40999 + 13.5726i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{2} + 12 q^{3} - 16 q^{4} + 24 q^{5} + 7 q^{6} + 8 q^{7} - 34 q^{8} - 55 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.175549	−	0.540283i	−0.0620658	−	0.191019i	0.915216	−	0.402964i	\(-0.132020\pi\)
							−0.977282	+	0.211945i	\(0.932020\pi\)
\(3\)	−5.19733	−	3.77608i	−1.00023	−	0.726707i	−0.0380900	−	0.999274i	\(-0.512127\pi\)
							−0.962137	+	0.272567i	\(0.912127\pi\)
\(5\)	1.29337	−	3.98059i	0.115683	−	0.356034i	−0.876406	−	0.481573i	\(-0.840066\pi\)
							0.992089	+	0.125538i	\(0.0400658\pi\)
\(7\)	26.2833	−	19.0959i	1.41916	−	1.03108i	0.427255	−	0.904131i	\(-0.359481\pi\)
							0.991909	−	0.126952i	\(-0.0405193\pi\)
\(11\)	5.04016	+	36.1330i	0.138151	+	0.990411i
							\(13\)	4.01722	+	12.3637i	0.0857059	+	0.263776i
\(17\)	26.5251	−	81.6358i	0.378428	−	1.16468i								−0.562708	−	0.826656i	\(-0.690241\pi\)
							0.941136	−	0.338027i	\(-0.109759\pi\)
\(19\)	−80.9601	−	58.8209i	−0.977553	−	0.710234i	−0.0203928	−	0.999792i	\(-0.506492\pi\)
							−0.957160	+	0.289558i	\(0.906492\pi\)
\(23\)	−82.5402			−0.748297			−0.374148	−	0.927369i	\(-0.622065\pi\)
							−0.374148	+	0.927369i	\(0.622065\pi\)
\(29\)	−209.890	+	152.494i	−1.34398	+	0.976462i	−0.344697	+	0.938714i	\(0.612018\pi\)
							−0.999287	+	0.0377481i	\(0.987982\pi\)
\(31\)	−24.2206	−	74.5433i	−0.140327	−	0.431883i	0.856053	−	0.516888i	\(-0.172910\pi\)
							−0.996381	+	0.0850045i	\(0.972910\pi\)
\(37\)	44.1083	−	32.0466i	0.195983	−	0.142390i	−0.485466	−	0.874255i	\(-0.661350\pi\)
							0.681449	+	0.731866i	\(0.261350\pi\)
\(41\)	149.976	+	108.964i	0.571277	+	0.415057i	0.835569	−	0.549386i	\(-0.185138\pi\)
							−0.264292	+	0.964443i	\(0.585138\pi\)
\(43\)	337.190			1.19584			0.597919	−	0.801557i	\(-0.295994\pi\)
							0.597919	+	0.801557i	\(0.295994\pi\)
\(47\)	34.0450	+	24.7352i	0.105659	+	0.0767658i	0.639360	−	0.768907i	\(-0.279199\pi\)
							−0.533701	+	0.845673i	\(0.679199\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.h.a.27.8	✓	68
11.3	even	5		1573.4.a.o.1.16		34
11.8	odd	10		1573.4.a.p.1.19		34
11.9	even	5	inner	143.4.h.a.53.8	yes	68

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.27.8	✓	68	1.1	even	1	trivial
143.4.h.a.53.8	yes	68	11.9	even	5	inner
1573.4.a.o.1.16		34	11.3	even	5
1573.4.a.p.1.19		34	11.8	odd	10