Embedded newform 143.4.h.b.14.16

• Label: 143.4.h.b.14.16
• 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			14.16
Character	\(\chi\)	\(=\)	143.14
Dual form			143.4.h.b.92.16

$q$-expansion

\(f(q)\)	\(=\)	\(q+(3.22629 - 2.34404i) q^{2} +(-0.854707 - 2.63052i) q^{3} +(2.44231 - 7.51667i) q^{4} +(11.3312 + 8.23261i) q^{5} +(-8.92357 - 6.48335i) q^{6} +(6.77683 - 20.8569i) q^{7} +(0.118933 + 0.366039i) q^{8} +(15.6544 - 11.3736i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{2} - 12 q^{3} - 148 q^{4} - 16 q^{5} + 77 q^{6} + 56 q^{7} - 34 q^{8} - 241 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	3.22629	−	2.34404i	1.14067	−	0.828743i	0.153455	−	0.988156i	\(-0.450960\pi\)
							0.987212	+	0.159413i	\(0.0509600\pi\)
\(3\)	−0.854707	−	2.63052i	−0.164488	−	0.506243i	0.834510	−	0.550993i	\(-0.185751\pi\)
							−0.998998	+	0.0447498i	\(0.985751\pi\)
\(5\)	11.3312	+	8.23261i	1.01349	+	0.736347i	0.964939	−	0.262473i	\(-0.0845382\pi\)
							0.0485556	+	0.998820i	\(0.484538\pi\)
\(7\)	6.77683	−	20.8569i	0.365915	−	1.12617i	−0.583492	−	0.812119i	\(-0.698314\pi\)
							0.949406	−	0.314050i	\(-0.101686\pi\)
\(11\)	−35.1308	−	9.83996i	−0.962940	−	0.269714i
							\(13\)	10.5172	−	7.64121i	0.224381	−	0.163022i
\(17\)	−58.2875	−	42.3484i	−0.831576	−	0.604176i								0.0884284	−	0.996083i	\(-0.471816\pi\)
							−0.920005	+	0.391907i	\(0.871816\pi\)
\(19\)	27.1881	+	83.6765i	0.328283	+	1.01035i	0.969937	+	0.243358i	\(0.0782488\pi\)
							−0.641653	+	0.766995i	\(0.721751\pi\)
\(23\)	−7.78478			−0.0705756			−0.0352878	−	0.999377i	\(-0.511235\pi\)
							−0.0352878	+	0.999377i	\(0.511235\pi\)
\(29\)	−18.3461	+	56.4636i	−0.117476	+	0.361553i	−0.992455	−	0.122607i	\(-0.960875\pi\)
							0.874980	+	0.484160i	\(0.160875\pi\)
\(31\)	−55.8344	+	40.5661i	−0.323489	+	0.235028i	−0.737663	−	0.675169i	\(-0.764071\pi\)
							0.414174	+	0.910198i	\(0.364071\pi\)
\(37\)	−45.3454	+	139.559i	−0.201480	+	0.620090i	0.798360	+	0.602180i	\(0.205701\pi\)
							−0.999840	+	0.0179099i	\(0.994299\pi\)
\(41\)	143.827	+	442.654i	0.547854	+	1.68612i	0.714106	+	0.700038i	\(0.246833\pi\)
							−0.166252	+	0.986083i	\(0.553167\pi\)
\(43\)	156.756			0.555933			0.277966	−	0.960591i	\(-0.410340\pi\)
							0.277966	+	0.960591i	\(0.410340\pi\)
\(47\)	27.6137	+	84.9862i	0.0856994	+	0.263756i	0.984718	−	0.174154i	\(-0.0557190\pi\)
							−0.899019	+	0.437910i	\(0.855719\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.h.b.14.16	✓	76
11.2	odd	10		1573.4.a.r.1.31		38
11.4	even	5	inner	143.4.h.b.92.16	yes	76
11.9	even	5		1573.4.a.q.1.8		38

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.b.14.16	✓	76	1.1	even	1	trivial
143.4.h.b.92.16	yes	76	11.4	even	5	inner
1573.4.a.q.1.8		38	11.9	even	5
1573.4.a.r.1.31		38	11.2	odd	10