Embedded newform 143.4.j.a.23.20

• Label: 143.4.j.a.23.20
• Level: $143$
• Weight: $4$
• Character: 143.23
• Analytic conductor: $8.437$
• Analytic rank: $0$
• Dimension: $72$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.j (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.43727313082\)
Analytic rank:	\(0\)
Dimension:	\(72\)
Relative dimension:	\(36\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.20
Character	\(\chi\)	\(=\)	143.23
Dual form			143.4.j.a.56.20

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.200845 - 0.115958i) q^{2} +(-4.34402 - 7.52406i) q^{3} +(-3.97311 + 6.88162i) q^{4} -0.297636i q^{5} +(-1.74495 - 1.00745i) q^{6} +(-6.82685 - 3.94148i) q^{7} +3.69817i q^{8} +(-24.2410 + 41.9867i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 12 q^{3} + 152 q^{4} + 90 q^{6} - 36 q^{7} - 360 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(67\)	\(79\)
\(\chi(n)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.200845	−	0.115958i	0.0710093	−	0.0409972i	−0.464075	−	0.885796i	\(-0.653613\pi\)
							0.535084	+	0.844799i	\(0.320280\pi\)
\(3\)	−4.34402	−	7.52406i	−0.836007	−	1.44801i	−0.893208	−	0.449644i	\(-0.851551\pi\)
							0.0572007	−	0.998363i	\(-0.481782\pi\)
\(5\)		−	0.297636i		−	0.0266214i	−0.999911	−	0.0133107i	\(-0.995763\pi\)
							0.999911	−	0.0133107i	\(-0.00423705\pi\)
\(7\)	−6.82685	−	3.94148i	−0.368615	−	0.212820i	0.304238	−	0.952596i	\(-0.401598\pi\)
							−0.672853	+	0.739776i	\(0.734931\pi\)
\(11\)	9.52628	−	5.50000i	0.261116	−	0.150756i
							\(13\)	16.1394	+	44.0059i	0.344328	+	0.938850i
\(17\)	−7.67711	+	13.2971i	−0.109528	+	0.189708i								−0.915579	−	0.402138i	\(-0.868267\pi\)
							0.806051	+	0.591846i	\(0.201601\pi\)
\(19\)	104.641	+	60.4143i	1.26348	+	0.729473i	0.973747	−	0.227633i	\(-0.0730986\pi\)
							0.289738	+	0.957106i	\(0.406432\pi\)
\(23\)	78.2404	+	135.516i	0.709315	+	1.22857i	0.965111	+	0.261839i	\(0.0843291\pi\)
							−0.255796	+	0.966731i	\(0.582338\pi\)
\(29\)	−108.600	−	188.100i	−0.695394	−	1.20446i	−0.970048	−	0.242915i	\(-0.921896\pi\)
							0.274654	−	0.961543i	\(-0.411437\pi\)
\(31\)			209.889i			1.21604i	0.793923	+	0.608019i	\(0.208036\pi\)
							−0.793923	+	0.608019i	\(0.791964\pi\)
\(37\)	−157.727	+	91.0638i	−0.700816	+	0.404616i	−0.807651	−	0.589661i	\(-0.799261\pi\)
							0.106836	+	0.994277i	\(0.465928\pi\)
\(41\)	−248.488	+	143.465i	−0.946521	+	0.546474i	−0.891999	−	0.452038i	\(-0.850697\pi\)
							−0.0545227	+	0.998513i	\(0.517364\pi\)
\(43\)	−209.639	+	363.106i	−0.743481	+	1.28775i	0.207420	+	0.978252i	\(0.433493\pi\)
							−0.950901	+	0.309495i	\(0.899840\pi\)
\(47\)			196.098i			0.608592i	0.952578	+	0.304296i	\(0.0984211\pi\)
							−0.952578	+	0.304296i	\(0.901579\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.j.a.23.20	✓	72
13.2	odd	12		1859.4.a.l.1.18		36
13.4	even	6	inner	143.4.j.a.56.20	yes	72
13.11	odd	12		1859.4.a.m.1.19		36

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.j.a.23.20	✓	72	1.1	even	1	trivial
143.4.j.a.56.20	yes	72	13.4	even	6	inner
1859.4.a.l.1.18		36	13.2	odd	12
1859.4.a.m.1.19		36	13.11	odd	12