Embedded newform 143.4.o.a.32.12

• Label: 143.4.o.a.32.12
• 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			32.12
Character	\(\chi\)	\(=\)	143.32
Dual form			143.4.o.a.76.12

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-2.78174 + 0.745366i) q^{2} +(0.496440 - 0.859860i) q^{3} +(0.254316 - 0.146829i) q^{4} +(-7.62492 + 7.62492i) q^{5} +(-0.740059 + 2.76194i) q^{6} +(25.1138 + 6.72922i) q^{7} +(15.6930 - 15.6930i) q^{8} +(13.0071 + 22.5289i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 4 q^{3} - 12 q^{4} - 8 q^{5} - 652 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−2.78174	+	0.745366i	−0.983494	+	0.263527i	−0.714516	−	0.699620i	\(-0.753353\pi\)
							−0.268979	+	0.963146i	\(0.586686\pi\)
\(3\)	0.496440	−	0.859860i	0.0955400	−	0.165480i	−0.814294	−	0.580453i	\(-0.802876\pi\)
							0.909834	+	0.414973i	\(0.136209\pi\)
\(5\)	−7.62492	+	7.62492i	−0.681994	+	0.681994i	−0.960449	−	0.278455i	\(-0.910178\pi\)
							0.278455	+	0.960449i	\(0.410178\pi\)
\(7\)	25.1138	+	6.72922i	1.35602	+	0.363344i	0.862352	−	0.506309i	\(-0.168990\pi\)
							0.493665	+	0.869652i	\(0.335657\pi\)
\(11\)	−24.0137	−	27.4653i	−0.658218	−	0.752827i
							\(13\)	−44.2765	−	15.3816i	−0.944622	−	0.328160i
\(17\)	31.5993	+	54.7316i	0.450821	+	0.780845i								0.998437	−	0.0558845i	\(-0.0177979\pi\)
							−0.547616	+	0.836730i	\(0.684465\pi\)
\(19\)	−23.3088	+	86.9897i	−0.281443	+	1.05036i	0.669957	+	0.742400i	\(0.266312\pi\)
							−0.951400	+	0.307958i	\(0.900354\pi\)
\(23\)	−155.633	−	89.8547i	−1.41094	−	0.814609i	−0.415467	−	0.909608i	\(-0.636382\pi\)
							−0.995477	+	0.0949997i	\(0.969715\pi\)
\(29\)	−180.036	−	103.944i	−1.15282	−	0.665581i	−0.203247	−	0.979127i	\(-0.565150\pi\)
							−0.949573	+	0.313546i	\(0.898483\pi\)
\(31\)	−222.082	+	222.082i	−1.28668	+	1.28668i	−0.349887	+	0.936792i	\(0.613780\pi\)
							−0.936792	+	0.349887i	\(0.886220\pi\)
\(37\)	105.368	−	28.2334i	0.468175	−	0.125447i	−0.0170164	−	0.999855i	\(-0.505417\pi\)
							0.485191	+	0.874408i	\(0.338750\pi\)
\(41\)	107.353	−	28.7651i	0.408920	−	0.109570i	−0.0484945	−	0.998823i	\(-0.515442\pi\)
							0.457414	+	0.889254i	\(0.348776\pi\)
\(43\)	−178.264	−	308.761i	−0.632208	−	1.09502i	−0.987099	−	0.160108i	\(-0.948816\pi\)
							0.354892	−	0.934907i	\(-0.384518\pi\)
\(47\)	−244.585	−	244.585i	−0.759073	−	0.759073i	0.217081	−	0.976154i	\(-0.430346\pi\)
							−0.976154	+	0.217081i	\(0.930346\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.o.a.32.12	✓	160
11.10	odd	2	inner	143.4.o.a.32.29	yes	160
13.11	odd	12	inner	143.4.o.a.76.29	yes	160
143.76	even	12	inner	143.4.o.a.76.12	yes	160

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.o.a.32.12	✓	160	1.1	even	1	trivial
143.4.o.a.32.29	yes	160	11.10	odd	2	inner
143.4.o.a.76.12	yes	160	143.76	even	12	inner
143.4.o.a.76.29	yes	160	13.11	odd	12	inner