Embedded newform 143.4.o.a.32.3

• Label: 143.4.o.a.32.3
• 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			32.3
Character	\(\chi\)	\(=\)	143.32
Dual form			143.4.o.a.76.3

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-4.78621 + 1.28246i) q^{2} +(-3.24999 + 5.62914i) q^{3} +(14.3349 - 8.27626i) q^{4} +(13.3984 - 13.3984i) q^{5} +(8.33597 - 31.1102i) q^{6} +(-2.07549 - 0.556126i) q^{7} +(-29.9659 + 29.9659i) q^{8} +(-7.62484 - 13.2066i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 4 q^{3} - 12 q^{4} - 8 q^{5} - 652 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−4.78621	+	1.28246i	−1.69218	+	0.453418i	−0.970951	−	0.239278i	\(-0.923089\pi\)
							−0.721230	+	0.692696i	\(0.756423\pi\)
\(3\)	−3.24999	+	5.62914i	−0.625460	+	1.08333i	0.362991	+	0.931793i	\(0.381755\pi\)
							−0.988452	+	0.151537i	\(0.951578\pi\)
\(5\)	13.3984	−	13.3984i	1.19839	−	1.19839i	0.223746	−	0.974648i	\(-0.428172\pi\)
							0.974648	−	0.223746i	\(-0.0718285\pi\)
\(7\)	−2.07549	−	0.556126i	−0.112066	−	0.0300280i	0.202350	−	0.979313i	\(-0.435142\pi\)
							−0.314416	+	0.949285i	\(0.601809\pi\)
\(11\)	−20.1548	+	30.4103i	−0.552446	+	0.833549i
							\(13\)	−30.9436	−	35.2064i	−0.660170	−	0.751116i
\(17\)	−42.9276	−	74.3527i	−0.612439	−	1.06078i								−0.990828	−	0.135129i	\(-0.956855\pi\)
							0.378389	−	0.925647i	\(-0.376478\pi\)
\(19\)	−22.5437	+	84.1344i	−0.272205	+	1.01588i	0.685487	+	0.728085i	\(0.259589\pi\)
							−0.957691	+	0.287797i	\(0.907077\pi\)
\(23\)	−15.6199	−	9.01815i	−0.141607	−	0.0817571i	0.427522	−	0.904005i	\(-0.359387\pi\)
							−0.569130	+	0.822248i	\(0.692720\pi\)
\(29\)	51.8455	+	29.9330i	0.331982	+	0.191670i	0.656721	−	0.754134i	\(-0.271943\pi\)
							−0.324739	+	0.945804i	\(0.605276\pi\)
\(31\)	−171.311	+	171.311i	−0.992527	+	0.992527i	−0.999972	−	0.00744576i	\(-0.997630\pi\)
							0.00744576	+	0.999972i	\(0.497630\pi\)
\(37\)	−248.770	+	66.6576i	−1.10534	+	0.296174i	−0.764936	−	0.644106i	\(-0.777229\pi\)
							−0.340401	+	0.940280i	\(0.610563\pi\)
\(41\)	247.903	−	66.4254i	0.944292	−	0.253022i	0.246353	−	0.969180i	\(-0.420768\pi\)
							0.697938	+	0.716158i	\(0.254101\pi\)
\(43\)	−160.160	−	277.405i	−0.568004	−	0.983811i	−0.996763	−	0.0803927i	\(-0.974383\pi\)
							0.428760	−	0.903419i	\(-0.358951\pi\)
\(47\)	−280.340	−	280.340i	−0.870038	−	0.870038i	0.122438	−	0.992476i	\(-0.460929\pi\)
							−0.992476	+	0.122438i	\(0.960929\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.o.a.32.3	✓	160
11.10	odd	2	inner	143.4.o.a.32.38	yes	160
13.11	odd	12	inner	143.4.o.a.76.38	yes	160
143.76	even	12	inner	143.4.o.a.76.3	yes	160

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.o.a.32.3	✓	160	1.1	even	1	trivial
143.4.o.a.32.38	yes	160	11.10	odd	2	inner
143.4.o.a.76.3	yes	160	143.76	even	12	inner
143.4.o.a.76.38	yes	160	13.11	odd	12	inner