Embedded newform 143.4.h.b.14.3

• Label: 143.4.h.b.14.3
• Level: $143$
• Weight: $4$
• Character: 143.14
• Analytic conductor: $8.437$
• Analytic rank: $0$
• Dimension: $76$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.43727313082\)
Analytic rank:	\(0\)
Dimension:	\(76\)
Relative dimension:	\(19\) over \(\Q(\zeta_{5})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			14.3
Character	\(\chi\)	\(=\)	143.14
Dual form			143.4.h.b.92.3

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-3.52735 + 2.56277i) q^{2} +(-2.18335 - 6.71965i) q^{3} +(3.40227 - 10.4711i) q^{4} +(-10.8529 - 7.88510i) q^{5} +(24.9223 + 18.1071i) q^{6} +(8.14177 - 25.0578i) q^{7} +(4.05543 + 12.4813i) q^{8} +(-18.5432 + 13.4724i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{2} - 12 q^{3} - 148 q^{4} - 16 q^{5} + 77 q^{6} + 56 q^{7} - 34 q^{8} - 241 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).

\(n\)	\(67\)	\(79\)
\(\chi(n)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−3.52735	+	2.56277i	−1.24711	+	0.906076i	−0.998050	−	0.0624132i	\(-0.980120\pi\)
							−0.249056	+	0.968489i	\(0.580120\pi\)
\(3\)	−2.18335	−	6.71965i	−0.420185	−	1.29320i	−0.907530	−	0.419987i	\(-0.862035\pi\)
							0.487345	−	0.873210i	\(-0.337965\pi\)
\(5\)	−10.8529	−	7.88510i	−0.970713	−	0.705265i	−0.0150994	−	0.999886i	\(-0.504806\pi\)
							−0.955614	+	0.294621i	\(0.904806\pi\)
\(7\)	8.14177	−	25.0578i	0.439614	−	1.35299i	−0.448669	−	0.893698i	\(-0.648102\pi\)
							0.888284	−	0.459295i	\(-0.151898\pi\)
\(11\)	13.1785	−	34.0195i	0.361224	−	0.932479i
							\(13\)	10.5172	−	7.64121i	0.224381	−	0.163022i
\(17\)	−91.1886	−	66.2524i	−1.30097	−	0.945210i								−0.301005	−	0.953623i	\(-0.597322\pi\)
							−0.999965	+	0.00841300i	\(0.997322\pi\)
\(19\)	27.8267	+	85.6418i	0.335994	+	1.03408i	0.966230	+	0.257680i	\(0.0829580\pi\)
							−0.630236	+	0.776403i	\(0.717042\pi\)
\(23\)	−34.7421			−0.314966			−0.157483	−	0.987522i	\(-0.550338\pi\)
							−0.157483	+	0.987522i	\(0.550338\pi\)
\(29\)	75.8954	−	233.582i	0.485980	−	1.49569i	−0.344577	−	0.938758i	\(-0.611978\pi\)
							0.830557	−	0.556934i	\(-0.188022\pi\)
\(31\)	147.328	−	107.040i	0.853578	−	0.620161i	−0.0725522	−	0.997365i	\(-0.523114\pi\)
							0.926130	+	0.377204i	\(0.123114\pi\)
\(37\)	−75.8714	+	233.508i	−0.337113	+	1.03753i	0.628559	+	0.777762i	\(0.283645\pi\)
							−0.965672	+	0.259765i	\(0.916355\pi\)
\(41\)	89.1899	+	274.498i	0.339735	+	1.04560i	0.964342	+	0.264658i	\(0.0852589\pi\)
							−0.624608	+	0.780939i	\(0.714741\pi\)
\(43\)	−166.681			−0.591132			−0.295566	−	0.955322i	\(-0.595508\pi\)
							−0.295566	+	0.955322i	\(0.595508\pi\)
\(47\)	150.487	+	463.150i	0.467037	+	1.43739i	0.856403	+	0.516309i	\(0.172694\pi\)
							−0.389366	+	0.921083i	\(0.627306\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.h.b.14.3	✓	76
11.2	odd	10		1573.4.a.r.1.6		38
11.4	even	5	inner	143.4.h.b.92.3	yes	76
11.9	even	5		1573.4.a.q.1.33		38

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.b.14.3	✓	76	1.1	even	1	trivial
143.4.h.b.92.3	yes	76	11.4	even	5	inner
1573.4.a.q.1.33		38	11.9	even	5
1573.4.a.r.1.6		38	11.2	odd	10