Embedded newform 143.4.j.a.23.13

• Label: 143.4.j.a.23.13
• 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			23.13
Character	\(\chi\)	\(=\)	143.23
Dual form			143.4.j.a.56.13

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.40127 + 0.809025i) q^{2} +(1.16324 + 2.01478i) q^{3} +(-2.69096 + 4.66087i) q^{4} -8.11969i q^{5} +(-3.26002 - 1.88217i) q^{6} +(-7.84996 - 4.53218i) q^{7} -21.6526i q^{8} +(10.7938 - 18.6954i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 12 q^{3} + 152 q^{4} + 90 q^{6} - 36 q^{7} - 360 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.40127	+	0.809025i	−0.495425	+	0.286034i	−0.726822	−	0.686826i	\(-0.759004\pi\)
							0.231397	+	0.972859i	\(0.425670\pi\)
\(3\)	1.16324	+	2.01478i	0.223865	+	0.387745i	0.955978	−	0.293438i	\(-0.0947993\pi\)
							−0.732113	+	0.681183i	\(0.761466\pi\)
\(5\)		−	8.11969i		−	0.726247i	−0.931741	−	0.363123i	\(-0.881710\pi\)
							0.931741	−	0.363123i	\(-0.118290\pi\)
\(7\)	−7.84996	−	4.53218i	−0.423858	−	0.244715i	0.272869	−	0.962051i	\(-0.412028\pi\)
							−0.696727	+	0.717337i	\(0.745361\pi\)
\(11\)	−9.52628	+	5.50000i	−0.261116	+	0.150756i
							\(13\)	40.0707	−	24.3175i	0.854892	−	0.518806i
\(17\)	−1.63384	+	2.82989i	−0.0233096	+	0.0403734i								−0.877445	−	0.479677i	\(-0.840754\pi\)
							0.854135	+	0.520051i	\(0.174087\pi\)
\(19\)	81.2728	+	46.9229i	0.981330	+	0.566571i	0.902671	−	0.430330i	\(-0.141603\pi\)
							0.0786586	+	0.996902i	\(0.474936\pi\)
\(23\)	−23.9217	−	41.4336i	−0.216871	−	0.375631i	0.736979	−	0.675916i	\(-0.236252\pi\)
							−0.953850	+	0.300285i	\(0.902918\pi\)
\(29\)	−115.351	−	199.794i	−0.738626	−	1.27934i	−0.953114	−	0.302611i	\(-0.902142\pi\)
							0.214488	−	0.976727i	\(-0.431192\pi\)
\(31\)		−	149.802i		−	0.867912i	−0.900934	−	0.433956i	\(-0.857117\pi\)
							0.900934	−	0.433956i	\(-0.142883\pi\)
\(37\)	308.353	−	178.028i	1.37008	−	0.791015i	0.379141	−	0.925339i	\(-0.376220\pi\)
							0.990937	+	0.134324i	\(0.0428863\pi\)
\(41\)	105.769	−	61.0657i	0.402886	−	0.232607i	−0.284842	−	0.958574i	\(-0.591941\pi\)
							0.687729	+	0.725968i	\(0.258608\pi\)
\(43\)	−181.483	+	314.338i	−0.643626	+	1.11479i	0.340991	+	0.940066i	\(0.389237\pi\)
							−0.984617	+	0.174726i	\(0.944096\pi\)
\(47\)		−	292.845i		−	0.908847i	−0.890786	−	0.454423i	\(-0.849845\pi\)
							0.890786	−	0.454423i	\(-0.150155\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.j.a.23.13	✓	72
13.2	odd	12		1859.4.a.m.1.13		36
13.4	even	6	inner	143.4.j.a.56.13	yes	72
13.11	odd	12		1859.4.a.l.1.24		36

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.j.a.23.13	✓	72	1.1	even	1	trivial
143.4.j.a.56.13	yes	72	13.4	even	6	inner
1859.4.a.l.1.24		36	13.11	odd	12
1859.4.a.m.1.13		36	13.2	odd	12