Embedded newform 143.4.j.a.23.15

• Label: 143.4.j.a.23.15
• 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			23.15
Character	\(\chi\)	\(=\)	143.23
Dual form			143.4.j.a.56.15

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.753305 + 0.434921i) q^{2} +(4.96974 + 8.60785i) q^{3} +(-3.62169 + 6.27295i) q^{4} -11.3907i q^{5} +(-7.48747 - 4.32289i) q^{6} +(-24.1895 - 13.9658i) q^{7} -13.2593i q^{8} +(-35.8967 + 62.1749i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 12 q^{3} + 152 q^{4} + 90 q^{6} - 36 q^{7} - 360 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.753305	+	0.434921i	−0.266334	+	0.153768i	−0.627220	−	0.778842i	\(-0.715807\pi\)
							0.360887	+	0.932610i	\(0.382474\pi\)
\(3\)	4.96974	+	8.60785i	0.956428	+	1.65658i	0.731067	+	0.682306i	\(0.239023\pi\)
							0.225361	+	0.974275i	\(0.427644\pi\)
\(5\)		−	11.3907i		−	1.01881i	−0.860527	−	0.509405i	\(-0.829865\pi\)
							0.860527	−	0.509405i	\(-0.170135\pi\)
\(7\)	−24.1895	−	13.9658i	−1.30611	−	0.754084i	−0.324667	−	0.945828i	\(-0.605252\pi\)
							−0.981445	+	0.191744i	\(0.938586\pi\)
\(11\)	−9.52628	+	5.50000i	−0.261116	+	0.150756i
							\(13\)	−1.65484	+	46.8429i	−0.0353054	+	0.999377i
\(17\)	4.23204	−	7.33011i	0.0603777	−	0.104577i								−0.834257	−	0.551376i	\(-0.814103\pi\)
							0.894634	+	0.446799i	\(0.147436\pi\)
\(19\)	−85.1937	−	49.1866i	−1.02867	−	0.593904i	−0.112068	−	0.993701i	\(-0.535747\pi\)
							−0.916604	+	0.399796i	\(0.869081\pi\)
\(23\)	64.4034	+	111.550i	0.583872	+	1.01130i	0.995015	+	0.0997246i	\(0.0317962\pi\)
							−0.411144	+	0.911571i	\(0.634870\pi\)
\(29\)	36.4935	+	63.2087i	0.233679	+	0.404743i	0.958888	−	0.283785i	\(-0.0915903\pi\)
							−0.725209	+	0.688529i	\(0.758257\pi\)
\(31\)			201.514i			1.16752i	0.811927	+	0.583759i	\(0.198419\pi\)
							−0.811927	+	0.583759i	\(0.801581\pi\)
\(37\)	−183.352	+	105.858i	−0.814672	+	0.470351i	−0.848576	−	0.529074i	\(-0.822539\pi\)
							0.0339038	+	0.999425i	\(0.489206\pi\)
\(41\)	98.8781	−	57.0873i	0.376638	−	0.217452i	−0.299716	−	0.954028i	\(-0.596892\pi\)
							0.676355	+	0.736576i	\(0.263559\pi\)
\(43\)	150.785	−	261.168i	0.534757	−	0.926227i	−0.464418	−	0.885616i	\(-0.653736\pi\)
							0.999175	−	0.0406104i	\(-0.0129302\pi\)
\(47\)			118.192i			0.366811i	0.983037	+	0.183405i	\(0.0587121\pi\)
							−0.983037	+	0.183405i	\(0.941288\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.j.a.23.15	✓	72
13.2	odd	12		1859.4.a.m.1.16		36
13.4	even	6	inner	143.4.j.a.56.15	yes	72
13.11	odd	12		1859.4.a.l.1.21		36

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.j.a.23.15	✓	72	1.1	even	1	trivial
143.4.j.a.56.15	yes	72	13.4	even	6	inner
1859.4.a.l.1.21		36	13.11	odd	12
1859.4.a.m.1.16		36	13.2	odd	12