Embedded newform 143.4.o.a.32.2

• Label: 143.4.o.a.32.2
• 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			32.2
Character	\(\chi\)	\(=\)	143.32
Dual form			143.4.o.a.76.2

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-4.87783 + 1.30701i) q^{2} +(-4.77756 + 8.27498i) q^{3} +(15.1567 - 8.75074i) q^{4} +(-11.5708 + 11.5708i) q^{5} +(12.4886 - 46.6082i) q^{6} +(20.5354 + 5.50244i) q^{7} +(-33.9281 + 33.9281i) q^{8} +(-32.1502 - 55.6857i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 4 q^{3} - 12 q^{4} - 8 q^{5} - 652 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−4.87783	+	1.30701i	−1.72457	+	0.462098i	−0.978921	−	0.204238i	\(-0.934528\pi\)
							−0.745651	+	0.666336i	\(0.767862\pi\)
\(3\)	−4.77756	+	8.27498i	−0.919442	+	1.59252i	−0.119178	+	0.992873i	\(0.538026\pi\)
							−0.800264	+	0.599647i	\(0.795308\pi\)
\(5\)	−11.5708	+	11.5708i	−1.03492	+	1.03492i	−0.0355515	+	0.999368i	\(0.511319\pi\)
							−0.999368	+	0.0355515i	\(0.988681\pi\)
\(7\)	20.5354	+	5.50244i	1.10881	+	0.297104i	0.766346	−	0.642428i	\(-0.222073\pi\)
							0.342461	+	0.939532i	\(0.388739\pi\)
\(11\)	19.7391	−	30.6817i	0.541052	−	0.840989i
							\(13\)	−4.84102	−	46.6215i	−0.103281	−	0.994652i
\(17\)	0.695475	+	1.20460i	0.00992220	+	0.0171858i								0.870944	−	0.491383i	\(-0.163508\pi\)
							−0.861022	+	0.508568i	\(0.830175\pi\)
\(19\)	19.0088	−	70.9417i	0.229522	−	0.856587i	−0.751021	−	0.660279i	\(-0.770438\pi\)
							0.980542	−	0.196308i	\(-0.0628952\pi\)
\(23\)	90.2819	+	52.1243i	0.818481	+	0.472550i	0.849892	−	0.526956i	\(-0.176667\pi\)
							−0.0314112	+	0.999507i	\(0.510000\pi\)
\(29\)	−102.356	−	59.0954i	−0.655416	−	0.378405i	0.135112	−	0.990830i	\(-0.456861\pi\)
							−0.790528	+	0.612426i	\(0.790194\pi\)
\(31\)	5.98325	−	5.98325i	0.0346653	−	0.0346653i	−0.689562	−	0.724227i	\(-0.742197\pi\)
							0.724227	+	0.689562i	\(0.242197\pi\)
\(37\)	86.8630	−	23.2749i	0.385951	−	0.103415i	−0.0606257	−	0.998161i	\(-0.519310\pi\)
							0.446577	+	0.894745i	\(0.352643\pi\)
\(41\)	−40.9487	+	10.9722i	−0.155979	+	0.0417943i	−0.335963	−	0.941875i	\(-0.609062\pi\)
							0.179985	+	0.983669i	\(0.442395\pi\)
\(43\)	−118.603	−	205.427i	−0.420624	−	0.728542i	0.575377	−	0.817888i	\(-0.304855\pi\)
							−0.996001	+	0.0893468i	\(0.971522\pi\)
\(47\)	−175.113	−	175.113i	−0.543464	−	0.543464i	0.381078	−	0.924543i	\(-0.375553\pi\)
							−0.924543	+	0.381078i	\(0.875553\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.o.a.32.2	✓	160
11.10	odd	2	inner	143.4.o.a.32.39	yes	160
13.11	odd	12	inner	143.4.o.a.76.39	yes	160
143.76	even	12	inner	143.4.o.a.76.2	yes	160

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.o.a.32.2	✓	160	1.1	even	1	trivial
143.4.o.a.32.39	yes	160	11.10	odd	2	inner
143.4.o.a.76.2	yes	160	143.76	even	12	inner
143.4.o.a.76.39	yes	160	13.11	odd	12	inner