Embedded newform 143.4.j.a.23.7

• Label: 143.4.j.a.23.7
• 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			23.7
Character	\(\chi\)	\(=\)	143.23
Dual form			143.4.j.a.56.7

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-3.43971 + 1.98592i) q^{2} +(-0.953208 - 1.65100i) q^{3} +(3.88775 - 6.73378i) q^{4} +18.9601i q^{5} +(6.55752 + 3.78599i) q^{6} +(20.6923 + 11.9467i) q^{7} -0.891668i q^{8} +(11.6828 - 20.2352i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 12 q^{3} + 152 q^{4} + 90 q^{6} - 36 q^{7} - 360 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−3.43971	+	1.98592i	−1.21612	+	0.702129i	−0.964086	−	0.265589i	\(-0.914433\pi\)
							−0.252036	+	0.967718i	\(0.581100\pi\)
\(3\)	−0.953208	−	1.65100i	−0.183445	−	0.317736i	0.759606	−	0.650383i	\(-0.225392\pi\)
							−0.943051	+	0.332647i	\(0.892058\pi\)
\(5\)			18.9601i			1.69585i	0.530120	+	0.847923i	\(0.322147\pi\)
							−0.530120	+	0.847923i	\(0.677853\pi\)
\(7\)	20.6923	+	11.9467i	1.11728	+	0.645062i	0.940705	−	0.339226i	\(-0.110165\pi\)
							0.176575	+	0.984287i	\(0.443498\pi\)
\(11\)	9.52628	−	5.50000i	0.261116	−	0.150756i
							\(13\)	45.9871	−	9.06585i	0.981117	−	0.193417i
\(17\)	−52.2228	+	90.4526i	−0.745053	+	1.29047i								0.205117	+	0.978737i	\(0.434243\pi\)
							−0.950170	+	0.311732i	\(0.899091\pi\)
\(19\)	29.9585	+	17.2966i	0.361735	+	0.208848i	0.669841	−	0.742504i	\(-0.266362\pi\)
							−0.308107	+	0.951352i	\(0.599695\pi\)
\(23\)	36.6739	+	63.5210i	0.332480	+	0.575872i	0.982997	−	0.183619i	\(-0.0587814\pi\)
							−0.650518	+	0.759491i	\(0.725448\pi\)
\(29\)	−16.5397	−	28.6475i	−0.105908	−	0.183438i	0.808201	−	0.588907i	\(-0.200442\pi\)
							−0.914109	+	0.405469i	\(0.867108\pi\)
\(31\)			82.7750i			0.479575i	0.970825	+	0.239788i	\(0.0770778\pi\)
							−0.970825	+	0.239788i	\(0.922922\pi\)
\(37\)	221.476	−	127.869i	0.984067	−	0.568151i	0.0805716	−	0.996749i	\(-0.474325\pi\)
							0.903496	+	0.428597i	\(0.140992\pi\)
\(41\)	−336.344	+	194.189i	−1.28117	+	0.739687i	−0.977063	−	0.212950i	\(-0.931693\pi\)
							−0.304112	+	0.952636i	\(0.598360\pi\)
\(43\)	−116.874	+	202.432i	−0.414492	+	0.717921i	−0.995375	−	0.0960659i	\(-0.969374\pi\)
							0.580883	+	0.813987i	\(0.302707\pi\)
\(47\)			2.58080i			0.00800953i	0.999992	+	0.00400477i	\(0.00127476\pi\)
							−0.999992	+	0.00400477i	\(0.998725\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.j.a.23.7	✓	72
13.2	odd	12		1859.4.a.l.1.7		36
13.4	even	6	inner	143.4.j.a.56.7	yes	72
13.11	odd	12		1859.4.a.m.1.30		36

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.j.a.23.7	✓	72	1.1	even	1	trivial
143.4.j.a.56.7	yes	72	13.4	even	6	inner
1859.4.a.l.1.7		36	13.2	odd	12
1859.4.a.m.1.30		36	13.11	odd	12