Embedded newform 143.4.o.a.32.1

• Label: 143.4.o.a.32.1
• Level: $143$
• Weight: $4$
• Character: 143.32
• Analytic conductor: $8.437$
• Analytic rank: $0$
• Dimension: $160$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.o (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.43727313082\)
Analytic rank:	\(0\)
Dimension:	\(160\)
Relative dimension:	\(40\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			32.1
Character	\(\chi\)	\(=\)	143.32
Dual form			143.4.o.a.76.1

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-5.35695 + 1.43539i) q^{2} +(1.66657 - 2.88658i) q^{3} +(19.7084 - 11.3787i) q^{4} +(-3.25582 + 3.25582i) q^{5} +(-4.78435 + 17.8554i) q^{6} +(5.43090 + 1.45520i) q^{7} +(-57.8717 + 57.8717i) q^{8} +(7.94512 + 13.7614i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 4 q^{3} - 12 q^{4} - 8 q^{5} - 652 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(67\)	\(79\)
\(\chi(n)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−5.35695	+	1.43539i	−1.89397	+	0.507488i	−0.895981	+	0.444093i	\(0.853526\pi\)
							−0.997989	+	0.0633949i	\(0.979807\pi\)
\(3\)	1.66657	−	2.88658i	0.320731	−	0.555522i	−0.659908	−	0.751346i	\(-0.729405\pi\)
							0.980639	+	0.195824i	\(0.0627383\pi\)
\(5\)	−3.25582	+	3.25582i	−0.291210	+	0.291210i	−0.837558	−	0.546348i	\(-0.816017\pi\)
							0.546348	+	0.837558i	\(0.316017\pi\)
\(7\)	5.43090	+	1.45520i	0.293241	+	0.0785737i	0.402440	−	0.915446i	\(-0.368162\pi\)
							−0.109199	+	0.994020i	\(0.534829\pi\)
\(11\)	−35.1442	−	9.79214i	−0.963306	−	0.268404i
							\(13\)	46.0590	−	8.69302i	0.982651	−	0.185462i
\(17\)	−15.2204	−	26.3625i	−0.217146	−	0.376108i								0.736788	−	0.676124i	\(-0.236341\pi\)
							−0.953934	+	0.300015i	\(0.903008\pi\)
\(19\)	−16.0972	+	60.0757i	−0.194366	+	0.725384i	0.798064	+	0.602573i	\(0.205858\pi\)
							−0.992430	+	0.122811i	\(0.960809\pi\)
\(23\)	24.4428	+	14.1120i	0.221594	+	0.127938i	0.606688	−	0.794940i	\(-0.292498\pi\)
							−0.385094	+	0.922877i	\(0.625831\pi\)
\(29\)	119.219	+	68.8311i	0.763393	+	0.440745i	0.830513	−	0.557000i	\(-0.188047\pi\)
							−0.0671194	+	0.997745i	\(0.521381\pi\)
\(31\)	−118.229	+	118.229i	−0.684984	+	0.684984i	−0.961119	−	0.276135i	\(-0.910946\pi\)
							0.276135	+	0.961119i	\(0.410946\pi\)
\(37\)	325.410	−	87.1932i	1.44586	−	0.387418i	0.551281	−	0.834319i	\(-0.314139\pi\)
							0.894583	+	0.446901i	\(0.147472\pi\)
\(41\)	210.470	−	56.3953i	0.801705	−	0.214816i	0.165372	−	0.986231i	\(-0.447117\pi\)
							0.636332	+	0.771415i	\(0.280451\pi\)
\(43\)	159.677	+	276.569i	0.566292	+	0.980847i	0.996928	+	0.0783213i	\(0.0249560\pi\)
							−0.430636	+	0.902526i	\(0.641711\pi\)
\(47\)	321.443	+	321.443i	0.997603	+	0.997603i	0.999997	−	0.00239453i	\(-0.000762204\pi\)
							−0.00239453	+	0.999997i	\(0.500762\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.o.a.32.1	✓	160
11.10	odd	2	inner	143.4.o.a.32.40	yes	160
13.11	odd	12	inner	143.4.o.a.76.40	yes	160
143.76	even	12	inner	143.4.o.a.76.1	yes	160

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.o.a.32.1	✓	160	1.1	even	1	trivial
143.4.o.a.32.40	yes	160	11.10	odd	2	inner
143.4.o.a.76.1	yes	160	143.76	even	12	inner
143.4.o.a.76.40	yes	160	13.11	odd	12	inner