Embedded newform 143.4.h.a.14.9

• Label: 143.4.h.a.14.9
• 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			14.9
Character	\(\chi\)	\(=\)	143.14
Dual form			143.4.h.a.92.9

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.0253892 + 0.0184463i) q^{2} +(1.76760 + 5.44013i) q^{3} +(-2.47183 + 7.60752i) q^{4} +(-6.11234 - 4.44088i) q^{5} +(-0.145228 - 0.105515i) q^{6} +(-1.91554 + 5.89541i) q^{7} +(-0.155155 - 0.477519i) q^{8} +(-4.62709 + 3.36178i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{2} + 12 q^{3} - 16 q^{4} + 24 q^{5} + 7 q^{6} + 8 q^{7} - 34 q^{8} - 55 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.0253892	+	0.0184463i	−0.00897643	+	0.00652176i	−0.592264	−	0.805744i	\(-0.701766\pi\)
							0.583288	+	0.812265i	\(0.301766\pi\)
\(3\)	1.76760	+	5.44013i	0.340176	+	1.04695i	0.964116	+	0.265481i	\(0.0855308\pi\)
							−0.623940	+	0.781472i	\(0.714469\pi\)
\(5\)	−6.11234	−	4.44088i	−0.546705	−	0.397204i	0.279864	−	0.960040i	\(-0.409710\pi\)
							−0.826569	+	0.562835i	\(0.809710\pi\)
\(7\)	−1.91554	+	5.89541i	−0.103429	+	0.318322i	−0.989359	−	0.145498i	\(-0.953522\pi\)
							0.885929	+	0.463820i	\(0.153522\pi\)
\(11\)	−9.37562	+	35.2576i	−0.256987	+	0.966415i
							\(13\)	−10.5172	+	7.64121i	−0.224381	+	0.163022i
\(17\)	−53.6013	−	38.9436i	−0.764719	−	0.555601i								0.135635	−	0.990759i	\(-0.456693\pi\)
							−0.900354	+	0.435158i	\(0.856693\pi\)
\(19\)	−12.9976	−	40.0024i	−0.156939	−	0.483009i	0.841413	−	0.540392i	\(-0.181724\pi\)
							−0.998352	+	0.0573835i	\(0.981724\pi\)
\(23\)	−43.6708			−0.395912			−0.197956	−	0.980211i	\(-0.563430\pi\)
							−0.197956	+	0.980211i	\(0.563430\pi\)
\(29\)	−58.9332	+	181.378i	−0.377366	+	1.16141i	0.564502	+	0.825431i	\(0.309068\pi\)
							−0.941868	+	0.335982i	\(0.890932\pi\)
\(31\)	41.1986	−	29.9325i	0.238693	−	0.173421i	−0.462008	−	0.886876i	\(-0.652871\pi\)
							0.700701	+	0.713455i	\(0.252871\pi\)
\(37\)	−31.8570	+	98.0456i	−0.141547	+	0.435638i	−0.996551	−	0.0829842i	\(-0.973555\pi\)
							0.855003	+	0.518622i	\(0.173555\pi\)
\(41\)	152.313	+	468.770i	0.580176	+	1.78560i	0.617834	+	0.786309i	\(0.288010\pi\)
							−0.0376572	+	0.999291i	\(0.511990\pi\)
\(43\)	−178.619			−0.633468			−0.316734	−	0.948514i	\(-0.602586\pi\)
							−0.316734	+	0.948514i	\(0.602586\pi\)
\(47\)	158.028	+	486.359i	0.490440	+	1.50942i	0.823944	+	0.566671i	\(0.191769\pi\)
							−0.333504	+	0.942749i	\(0.608231\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.h.a.14.9	✓	68
11.2	odd	10		1573.4.a.p.1.18		34
11.4	even	5	inner	143.4.h.a.92.9	yes	68
11.9	even	5		1573.4.a.o.1.17		34

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.14.9	✓	68	1.1	even	1	trivial
143.4.h.a.92.9	yes	68	11.4	even	5	inner
1573.4.a.o.1.17		34	11.9	even	5
1573.4.a.p.1.18		34	11.2	odd	10