Embedded newform 143.4.h.b.14.7

• Label: 143.4.h.b.14.7
• 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			14.7
Character	\(\chi\)	\(=\)	143.14
Dual form			143.4.h.b.92.7

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.16976 + 0.849884i) q^{2} +(0.145177 + 0.446808i) q^{3} +(-1.82609 + 5.62012i) q^{4} +(-0.581588 - 0.422548i) q^{5} +(-0.549558 - 0.399277i) q^{6} +(9.00894 - 27.7267i) q^{7} +(-6.21484 - 19.1273i) q^{8} +(21.6649 - 15.7405i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{2} - 12 q^{3} - 148 q^{4} - 16 q^{5} + 77 q^{6} + 56 q^{7} - 34 q^{8} - 241 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.16976	+	0.849884i	−0.413574	+	0.300479i	−0.775047	−	0.631903i	\(-0.782274\pi\)
							0.361473	+	0.932383i	\(0.382274\pi\)
\(3\)	0.145177	+	0.446808i	0.0279393	+	0.0859883i	0.964054	−	0.265707i	\(-0.0856054\pi\)
							−0.936115	+	0.351695i	\(0.885605\pi\)
\(5\)	−0.581588	−	0.422548i	−0.0520188	−	0.0377939i	0.561472	−	0.827496i	\(-0.310235\pi\)
							−0.613491	+	0.789702i	\(0.710235\pi\)
\(7\)	9.00894	−	27.7267i	0.486437	−	1.49710i	−0.343451	−	0.939171i	\(-0.611596\pi\)
							0.829888	−	0.557929i	\(-0.188404\pi\)
\(11\)	0.981630	+	36.4697i	0.0269066	+	0.999638i
							\(13\)	10.5172	−	7.64121i	0.224381	−	0.163022i
\(17\)	83.5542	+	60.7057i	1.19205	+	0.866076i								0.993480	−	0.114011i	\(-0.0363698\pi\)
							0.198571	+	0.980086i	\(0.436370\pi\)
\(19\)	28.6895	+	88.2972i	0.346412	+	1.06615i	0.960824	+	0.277160i	\(0.0893932\pi\)
							−0.614412	+	0.788985i	\(0.710607\pi\)
\(23\)	83.1287			0.753632			0.376816	−	0.926288i	\(-0.377019\pi\)
							0.376816	+	0.926288i	\(0.377019\pi\)
\(29\)	72.8203	−	224.118i	0.466290	−	1.43509i	−0.391064	−	0.920364i	\(-0.627893\pi\)
							0.857353	−	0.514728i	\(-0.172107\pi\)
\(31\)	57.9131	−	42.0763i	0.335532	−	0.243778i	−0.407242	−	0.913320i	\(-0.633510\pi\)
							0.742774	+	0.669542i	\(0.233510\pi\)
\(37\)	−97.3193	+	299.518i	−0.432411	+	1.33082i	0.463306	+	0.886198i	\(0.346663\pi\)
							−0.895717	+	0.444625i	\(0.853337\pi\)
\(41\)	82.3364	+	253.406i	0.313629	+	0.965251i	0.976315	+	0.216354i	\(0.0694164\pi\)
							−0.662686	+	0.748897i	\(0.730584\pi\)
\(43\)	296.705			1.05226			0.526128	−	0.850405i	\(-0.323643\pi\)
							0.526128	+	0.850405i	\(0.323643\pi\)
\(47\)	−123.395	−	379.771i	−0.382958	−	1.17862i	−0.937951	−	0.346769i	\(-0.887279\pi\)
							0.554992	−	0.831855i	\(-0.312721\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.h.b.14.7	✓	76
11.2	odd	10		1573.4.a.r.1.14		38
11.4	even	5	inner	143.4.h.b.92.7	yes	76
11.9	even	5		1573.4.a.q.1.25		38

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.b.14.7	✓	76	1.1	even	1	trivial
143.4.h.b.92.7	yes	76	11.4	even	5	inner
1573.4.a.q.1.25		38	11.9	even	5
1573.4.a.r.1.14		38	11.2	odd	10