Embedded newform 143.4.o.a.32.19

• Label: 143.4.o.a.32.19
• 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			32.19
Character	\(\chi\)	\(=\)	143.32
Dual form			143.4.o.a.76.19

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.740490 + 0.198414i) q^{2} +(-0.446262 + 0.772948i) q^{3} +(-6.41925 + 3.70615i) q^{4} +(7.28686 - 7.28686i) q^{5} +(0.177089 - 0.660905i) q^{6} +(-5.35131 - 1.43388i) q^{7} +(8.35464 - 8.35464i) q^{8} +(13.1017 + 22.6928i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 4 q^{3} - 12 q^{4} - 8 q^{5} - 652 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.740490	+	0.198414i	−0.261803	+	0.0701498i	−0.387333	−	0.921940i	\(-0.626604\pi\)
							0.125530	+	0.992090i	\(0.459937\pi\)
\(3\)	−0.446262	+	0.772948i	−0.0858831	+	0.148754i	−0.905767	−	0.423776i	\(-0.860705\pi\)
							0.819884	+	0.572530i	\(0.194038\pi\)
\(5\)	7.28686	−	7.28686i	0.651757	−	0.651757i	−0.301659	−	0.953416i	\(-0.597540\pi\)
							0.953416	+	0.301659i	\(0.0975405\pi\)
\(7\)	−5.35131	−	1.43388i	−0.288944	−	0.0774222i	0.111436	−	0.993772i	\(-0.464455\pi\)
							−0.400380	+	0.916349i	\(0.631122\pi\)
\(11\)	−36.2790	+	3.85117i	−0.994413	+	0.105561i
							\(13\)	−46.0655	−	8.65849i	−0.982790	−	0.184726i
\(17\)	−49.5465	−	85.8171i	−0.706871	−	1.22434i								−0.966012	−	0.258496i	\(-0.916773\pi\)
							0.259142	−	0.965839i	\(-0.416560\pi\)
\(19\)	37.9604	−	141.670i	0.458354	−	1.71060i	−0.219684	−	0.975571i	\(-0.570503\pi\)
							0.678037	−	0.735028i	\(-0.262831\pi\)
\(23\)	−74.8828	−	43.2336i	−0.678876	−	0.391949i	0.120556	−	0.992707i	\(-0.461532\pi\)
							−0.799431	+	0.600757i	\(0.794866\pi\)
\(29\)	−161.561	−	93.2773i	−1.03452	−	0.597281i	−0.116245	−	0.993221i	\(-0.537086\pi\)
							−0.918277	+	0.395939i	\(0.870419\pi\)
\(31\)	103.651	−	103.651i	0.600526	−	0.600526i	−0.339926	−	0.940452i	\(-0.610402\pi\)
							0.940452	+	0.339926i	\(0.110402\pi\)
\(37\)	−107.548	+	28.8173i	−0.477857	+	0.128041i	−0.489705	−	0.871888i	\(-0.662895\pi\)
							0.0118475	+	0.999930i	\(0.496229\pi\)
\(41\)	−213.192	+	57.1247i	−0.812075	+	0.217595i	−0.640879	−	0.767642i	\(-0.721430\pi\)
							−0.171196	+	0.985237i	\(0.554763\pi\)
\(43\)	213.260	+	369.376i	0.756320	+	1.30999i	0.944715	+	0.327892i	\(0.106338\pi\)
							−0.188395	+	0.982093i	\(0.560328\pi\)
\(47\)	130.836	+	130.836i	0.406052	+	0.406052i	0.880359	−	0.474307i	\(-0.157301\pi\)
							−0.474307	+	0.880359i	\(0.657301\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.o.a.32.19	✓	160
11.10	odd	2	inner	143.4.o.a.32.22	yes	160
13.11	odd	12	inner	143.4.o.a.76.22	yes	160
143.76	even	12	inner	143.4.o.a.76.19	yes	160

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.o.a.32.19	✓	160	1.1	even	1	trivial
143.4.o.a.32.22	yes	160	11.10	odd	2	inner
143.4.o.a.76.19	yes	160	143.76	even	12	inner
143.4.o.a.76.22	yes	160	13.11	odd	12	inner