Embedded newform 143.4.h.a.14.11

• Label: 143.4.h.a.14.11
• Level: $143$
• Weight: $4$
• Character: 143.14
• Analytic conductor: $8.437$
• Analytic rank: $0$
• Dimension: $68$
• 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:	\(68\)
Relative dimension:	\(17\) over \(\Q(\zeta_{5})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			14.11
Character	\(\chi\)	\(=\)	143.14
Dual form			143.4.h.a.92.11

$q$-expansion

\(f(q)\)	\(=\)	\(q+(1.64125 - 1.19244i) q^{2} +(-1.40236 - 4.31601i) q^{3} +(-1.20034 + 3.69426i) q^{4} +(9.87094 + 7.17166i) q^{5} +(-7.44820 - 5.41143i) q^{6} +(3.82371 - 11.7682i) q^{7} +(7.45035 + 22.9298i) q^{8} +(5.18214 - 3.76505i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{2} + 12 q^{3} - 16 q^{4} + 24 q^{5} + 7 q^{6} + 8 q^{7} - 34 q^{8} - 55 q^{9}+O(q^{10}) \)

Character values

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

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

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	1.64125	−	1.19244i	0.580270	−	0.421591i	−0.258551	−	0.965998i	\(-0.583245\pi\)
							0.838822	+	0.544406i	\(0.183245\pi\)
\(3\)	−1.40236	−	4.31601i	−0.269883	−	0.830616i	−0.990528	−	0.137311i	\(-0.956154\pi\)
							0.720644	−	0.693305i	\(-0.243846\pi\)
\(5\)	9.87094	+	7.17166i	0.882884	+	0.641453i	0.934013	−	0.357239i	\(-0.116282\pi\)
							−0.0511289	+	0.998692i	\(0.516282\pi\)
\(7\)	3.82371	−	11.7682i	0.206461	−	0.635421i	−0.793189	−	0.608975i	\(-0.791581\pi\)
							0.999650	−	0.0264462i	\(-0.00841907\pi\)
\(11\)	31.3447	−	18.6683i	0.859163	−	0.511702i
							\(13\)	−10.5172	+	7.64121i	−0.224381	+	0.163022i
\(17\)	88.3055	+	64.1577i	1.25984	+	0.915325i								0.998750	−	0.0499899i	\(-0.0159189\pi\)
							0.261087	+	0.965315i	\(0.415919\pi\)
\(19\)	−36.5116	−	112.371i	−0.440860	−	1.35683i	−0.886961	−	0.461845i	\(-0.847188\pi\)
							0.446101	−	0.894983i	\(-0.352812\pi\)
\(23\)	70.2429			0.636811			0.318405	−	0.947955i	\(-0.396853\pi\)
							0.318405	+	0.947955i	\(0.396853\pi\)
\(29\)	20.4293	−	62.8750i	0.130815	−	0.402607i	−0.864101	−	0.503319i	\(-0.832112\pi\)
							0.994916	+	0.100712i	\(0.0321121\pi\)
\(31\)	19.8052	−	14.3893i	0.114745	−	0.0833675i	−0.528933	−	0.848664i	\(-0.677408\pi\)
							0.643678	+	0.765296i	\(0.277408\pi\)
\(37\)	−51.0342	+	157.067i	−0.226756	+	0.697883i	0.771353	+	0.636408i	\(0.219581\pi\)
							−0.998109	+	0.0614753i	\(0.980419\pi\)
\(41\)	140.039	+	430.995i	0.533424	+	1.64171i	0.747030	+	0.664790i	\(0.231479\pi\)
							−0.213606	+	0.976920i	\(0.568521\pi\)
\(43\)	−409.892			−1.45367			−0.726837	−	0.686810i	\(-0.759010\pi\)
							−0.726837	+	0.686810i	\(0.759010\pi\)
\(47\)	142.949	+	439.951i	0.443643	+	1.36539i	0.883965	+	0.467553i	\(0.154864\pi\)
							−0.440322	+	0.897840i	\(0.645136\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.h.a.14.11	✓	68
11.2	odd	10		1573.4.a.p.1.23		34
11.4	even	5	inner	143.4.h.a.92.11	yes	68
11.9	even	5		1573.4.a.o.1.12		34

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.14.11	✓	68	1.1	even	1	trivial
143.4.h.a.92.11	yes	68	11.4	even	5	inner
1573.4.a.o.1.12		34	11.9	even	5
1573.4.a.p.1.23		34	11.2	odd	10