Embedded newform 143.4.j.a.23.19

• Label: 143.4.j.a.23.19
• 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			23.19
Character	\(\chi\)	\(=\)	143.23
Dual form			143.4.j.a.56.19

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.204845 + 0.118267i) q^{2} +(3.87126 + 6.70523i) q^{3} +(-3.97203 + 6.87975i) q^{4} +11.7890i q^{5} +(-1.58602 - 0.915689i) q^{6} +(4.94948 + 2.85759i) q^{7} -3.77132i q^{8} +(-16.4734 + 28.5327i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 12 q^{3} + 152 q^{4} + 90 q^{6} - 36 q^{7} - 360 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.204845	+	0.118267i	−0.0724237	+	0.0418138i	−0.535775	−	0.844361i	\(-0.679980\pi\)
							0.463351	+	0.886175i	\(0.346647\pi\)
\(3\)	3.87126	+	6.70523i	0.745025	+	1.29042i	0.950183	+	0.311693i	\(0.100896\pi\)
							−0.205158	+	0.978729i	\(0.565771\pi\)
\(5\)			11.7890i			1.05444i	0.849730	+	0.527219i	\(0.176765\pi\)
							−0.849730	+	0.527219i	\(0.823235\pi\)
\(7\)	4.94948	+	2.85759i	0.267247	+	0.154295i	0.627636	−	0.778507i	\(-0.284023\pi\)
							−0.360389	+	0.932802i	\(0.617356\pi\)
\(11\)	9.52628	−	5.50000i	0.261116	−	0.150756i
							\(13\)	36.8564	−	28.9587i	0.786317	−	0.617823i
\(17\)	6.86220	−	11.8857i	0.0979017	−	0.169571i								−0.812914	−	0.582383i	\(-0.802120\pi\)
							0.910816	+	0.412813i	\(0.135454\pi\)
\(19\)	8.40425	+	4.85219i	0.101477	+	0.0585879i	0.549880	−	0.835244i	\(-0.314674\pi\)
							−0.448403	+	0.893832i	\(0.648007\pi\)
\(23\)	−41.8610	−	72.5053i	−0.379505	−	0.657322i	0.611485	−	0.791256i	\(-0.290572\pi\)
							−0.990990	+	0.133934i	\(0.957239\pi\)
\(29\)	83.5473	+	144.708i	0.534978	+	0.926608i	0.999164	+	0.0408711i	\(0.0130133\pi\)
							−0.464187	+	0.885737i	\(0.653653\pi\)
\(31\)			145.260i			0.841595i	0.907155	+	0.420798i	\(0.138250\pi\)
							−0.907155	+	0.420798i	\(0.861750\pi\)
\(37\)	−116.391	+	67.1985i	−0.517152	+	0.298578i	−0.735768	−	0.677233i	\(-0.763179\pi\)
							0.218617	+	0.975811i	\(0.429846\pi\)
\(41\)	−198.191	+	114.426i	−0.754934	+	0.435862i	−0.827474	−	0.561504i	\(-0.810223\pi\)
							0.0725397	+	0.997366i	\(0.476890\pi\)
\(43\)	−106.258	+	184.044i	−0.376840	+	0.652707i	−0.990601	−	0.136786i	\(-0.956323\pi\)
							0.613760	+	0.789492i	\(0.289656\pi\)
\(47\)		−	89.4784i		−	0.277697i	−0.990314	−	0.138849i	\(-0.955660\pi\)
							0.990314	−	0.138849i	\(-0.0443401\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.j.a.23.19	✓	72
13.2	odd	12		1859.4.a.l.1.17		36
13.4	even	6	inner	143.4.j.a.56.19	yes	72
13.11	odd	12		1859.4.a.m.1.20		36

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.j.a.23.19	✓	72	1.1	even	1	trivial
143.4.j.a.56.19	yes	72	13.4	even	6	inner
1859.4.a.l.1.17		36	13.2	odd	12
1859.4.a.m.1.20		36	13.11	odd	12