Embedded newform 143.4.h.a.14.7

• Label: 143.4.h.a.14.7
• Level: $143$
• Weight: $4$
• Character: 143.14
• Analytic conductor: $8.437$
• Analytic rank: $0$
• Dimension: $68$
• 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:	\(68\)
Relative dimension:	\(17\) over \(\Q(\zeta_{5})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			14.7
Character	\(\chi\)	\(=\)	143.14
Dual form			143.4.h.a.92.7

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.92631 + 1.39955i) q^{2} +(-1.97595 - 6.08135i) q^{3} +(-0.720198 + 2.21654i) q^{4} +(4.29934 + 3.12365i) q^{5} +(12.3174 + 8.94913i) q^{6} +(1.64214 - 5.05400i) q^{7} +(-7.60110 - 23.3938i) q^{8} +(-11.2350 + 8.16270i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{2} + 12 q^{3} - 16 q^{4} + 24 q^{5} + 7 q^{6} + 8 q^{7} - 34 q^{8} - 55 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.92631	+	1.39955i	−0.681053	+	0.494814i	−0.873707	−	0.486453i	\(-0.838291\pi\)
							0.192654	+	0.981267i	\(0.438291\pi\)
\(3\)	−1.97595	−	6.08135i	−0.380272	−	1.17036i	−0.939852	−	0.341581i	\(-0.889038\pi\)
							0.559581	−	0.828776i	\(-0.310962\pi\)
\(5\)	4.29934	+	3.12365i	0.384545	+	0.279388i	0.763216	−	0.646143i	\(-0.223619\pi\)
							−0.378672	+	0.925531i	\(0.623619\pi\)
\(7\)	1.64214	−	5.05400i	0.0886674	−	0.272890i	−0.896884	−	0.442265i	\(-0.854175\pi\)
							0.985552	+	0.169375i	\(0.0541749\pi\)
\(11\)	21.4169	+	29.5350i	0.587040	+	0.809558i
							\(13\)	−10.5172	+	7.64121i	−0.224381	+	0.163022i
\(17\)	−82.4546	−	59.9068i	−1.17636	−	0.854678i								−0.184606	−	0.982813i	\(-0.559101\pi\)
							−0.991757	+	0.128135i	\(0.959101\pi\)
\(19\)	−25.4152	−	78.2198i	−0.306876	−	0.944466i	−0.978971	−	0.204001i	\(-0.934605\pi\)
							0.672095	−	0.740465i	\(-0.265395\pi\)
\(23\)	−131.682			−1.19381			−0.596904	−	0.802313i	\(-0.703603\pi\)
							−0.596904	+	0.802313i	\(0.703603\pi\)
\(29\)	68.0299	−	209.375i	0.435615	−	1.34069i	−0.456840	−	0.889549i	\(-0.651019\pi\)
							0.892455	−	0.451137i	\(-0.148981\pi\)
\(31\)	−223.963	+	162.719i	−1.29758	+	0.942746i	−0.999929	−	0.0119296i	\(-0.996203\pi\)
							−0.297649	+	0.954675i	\(0.596203\pi\)
\(37\)	63.2837	−	194.767i	0.281183	−	0.865393i	−0.706334	−	0.707879i	\(-0.749652\pi\)
							0.987517	−	0.157514i	\(-0.0503479\pi\)
\(41\)	81.0800	+	249.539i	0.308843	+	0.950522i	0.978215	+	0.207594i	\(0.0665633\pi\)
							−0.669372	+	0.742927i	\(0.733437\pi\)
\(43\)	−113.404			−0.402184			−0.201092	−	0.979572i	\(-0.564449\pi\)
							−0.201092	+	0.979572i	\(0.564449\pi\)
\(47\)	−172.187	−	529.938i	−0.534385	−	1.64467i	−0.744975	−	0.667093i	\(-0.767539\pi\)
							0.210590	−	0.977574i	\(-0.432461\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.h.a.14.7	✓	68
11.2	odd	10		1573.4.a.p.1.11		34
11.4	even	5	inner	143.4.h.a.92.7	yes	68
11.9	even	5		1573.4.a.o.1.24		34

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.14.7	✓	68	1.1	even	1	trivial
143.4.h.a.92.7	yes	68	11.4	even	5	inner
1573.4.a.o.1.24		34	11.9	even	5
1573.4.a.p.1.11		34	11.2	odd	10