Embedded newform 143.4.h.b.14.14

• Label: 143.4.h.b.14.14
• 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			14.14
Character	\(\chi\)	\(=\)	143.14
Dual form			143.4.h.b.92.14

$q$-expansion

\(f(q)\)	\(=\)	\(q+(2.37777 - 1.72755i) q^{2} +(0.497021 + 1.52967i) q^{3} +(0.197213 - 0.606958i) q^{4} +(2.32261 + 1.68747i) q^{5} +(3.82439 + 2.77858i) q^{6} +(-3.54970 + 10.9248i) q^{7} +(6.68618 + 20.5780i) q^{8} +(19.7506 - 14.3496i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{2} - 12 q^{3} - 148 q^{4} - 16 q^{5} + 77 q^{6} + 56 q^{7} - 34 q^{8} - 241 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	2.37777	−	1.72755i	0.840667	−	0.610781i	−0.0818897	−	0.996641i	\(-0.526096\pi\)
							0.922557	+	0.385861i	\(0.126096\pi\)
\(3\)	0.497021	+	1.52967i	0.0956518	+	0.294386i	0.987423	−	0.158101i	\(-0.0505370\pi\)
							−0.891771	+	0.452487i	\(0.850537\pi\)
\(5\)	2.32261	+	1.68747i	0.207740	+	0.150932i	0.686791	−	0.726855i	\(-0.259019\pi\)
							−0.479050	+	0.877787i	\(0.659019\pi\)
\(7\)	−3.54970	+	10.9248i	−0.191666	+	0.589886i	0.808334	+	0.588724i	\(0.200370\pi\)
							−0.999999	+	0.00116139i	\(0.999630\pi\)
\(11\)	4.95734	+	36.1445i	0.135881	+	0.990725i
							\(13\)	10.5172	−	7.64121i	0.224381	−	0.163022i
\(17\)	46.4069	+	33.7166i	0.662078	+	0.481028i								0.867364	−	0.497674i	\(-0.165812\pi\)
							−0.205286	+	0.978702i	\(0.565812\pi\)
\(19\)	−6.78812	−	20.8917i	−0.0819633	−	0.252257i	0.901674	−	0.432416i	\(-0.142339\pi\)
							−0.983638	+	0.180159i	\(0.942339\pi\)
\(23\)	−14.7872			−0.134058			−0.0670290	−	0.997751i	\(-0.521352\pi\)
							−0.0670290	+	0.997751i	\(0.521352\pi\)
\(29\)	−12.4650	+	38.3634i	−0.0798172	+	0.245652i	−0.983000	−	0.183603i	\(-0.941224\pi\)
							0.903183	+	0.429255i	\(0.141224\pi\)
\(31\)	−51.8841	+	37.6960i	−0.300602	+	0.218400i	−0.727853	−	0.685733i	\(-0.759482\pi\)
							0.427251	+	0.904133i	\(0.359482\pi\)
\(37\)	86.4450	−	266.050i	0.384094	−	1.18212i	−0.553042	−	0.833153i	\(-0.686533\pi\)
							0.937136	−	0.348965i	\(-0.113467\pi\)
\(41\)	−129.099	−	397.325i	−0.491752	−	1.51346i	−0.821957	−	0.569549i	\(-0.807118\pi\)
							0.330205	−	0.943909i	\(-0.392882\pi\)
\(43\)	−229.613			−0.814319			−0.407160	−	0.913357i	\(-0.633481\pi\)
							−0.407160	+	0.913357i	\(0.633481\pi\)
\(47\)	6.92459	+	21.3117i	0.0214905	+	0.0661411i	0.961227	−	0.275760i	\(-0.0889294\pi\)
							−0.939736	+	0.341901i	\(0.888929\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.h.b.14.14	✓	76
11.2	odd	10		1573.4.a.r.1.28		38
11.4	even	5	inner	143.4.h.b.92.14	yes	76
11.9	even	5		1573.4.a.q.1.11		38

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.b.14.14	✓	76	1.1	even	1	trivial
143.4.h.b.92.14	yes	76	11.4	even	5	inner
1573.4.a.q.1.11		38	11.9	even	5
1573.4.a.r.1.28		38	11.2	odd	10