Embedded newform 143.4.o.a.32.20

• Label: 143.4.o.a.32.20
• Level: $143$
• Weight: $4$
• Character: 143.32
• Analytic conductor: $8.437$
• Analytic rank: $0$
• Dimension: $160$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.o (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(8.43727313082\)
Analytic rank:	\(0\)
Dimension:	\(160\)
Relative dimension:	\(40\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			32.20
Character	\(\chi\)	\(=\)	143.32
Dual form			143.4.o.a.76.20

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-0.300514 + 0.0805224i) q^{2} +(-3.07985 + 5.33445i) q^{3} +(-6.84438 + 3.95160i) q^{4} +(-9.38759 + 9.38759i) q^{5} +(0.495993 - 1.85107i) q^{6} +(-9.89724 - 2.65196i) q^{7} +(3.49857 - 3.49857i) q^{8} +(-5.47090 - 9.47587i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 4 q^{3} - 12 q^{4} - 8 q^{5} - 652 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(67\)	\(79\)
\(\chi(n)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−0.300514	+	0.0805224i	−0.106248	+	0.0284690i	−0.311551	−	0.950229i	\(-0.600849\pi\)
							0.205303	+	0.978698i	\(0.434182\pi\)
\(3\)	−3.07985	+	5.33445i	−0.592717	+	1.02662i	0.401148	+	0.916013i	\(0.368611\pi\)
							−0.993865	+	0.110602i	\(0.964722\pi\)
\(5\)	−9.38759	+	9.38759i	−0.839651	+	0.839651i	−0.988813	−	0.149162i	\(-0.952343\pi\)
							0.149162	+	0.988813i	\(0.452343\pi\)
\(7\)	−9.89724	−	2.65196i	−0.534401	−	0.143192i	−0.0184811	−	0.999829i	\(-0.505883\pi\)
							−0.515920	+	0.856637i	\(0.672550\pi\)
\(11\)	16.3841	+	32.5969i	0.449091	+	0.893486i
							\(13\)	−2.18286	−	46.8213i	−0.0465704	−	0.998915i
\(17\)	41.6758	+	72.1847i	0.594581	+	1.02984i								0.993606	+	0.112904i	\(0.0360153\pi\)
							−0.399025	+	0.916940i	\(0.630651\pi\)
\(19\)	3.04683	−	11.3709i	0.0367890	−	0.137298i	−0.945089	−	0.326814i	\(-0.894025\pi\)
							0.981878	+	0.189515i	\(0.0606917\pi\)
\(23\)	9.46626	+	5.46535i	0.0858197	+	0.0495480i	0.542296	−	0.840188i	\(-0.317555\pi\)
							−0.456476	+	0.889736i	\(0.650889\pi\)
\(29\)	−167.275	−	96.5764i	−1.07111	−	0.618406i	−0.142626	−	0.989777i	\(-0.545555\pi\)
							−0.928485	+	0.371370i	\(0.878888\pi\)
\(31\)	−20.4836	+	20.4836i	−0.118676	+	0.118676i	−0.763951	−	0.645275i	\(-0.776743\pi\)
							0.645275	+	0.763951i	\(0.276743\pi\)
\(37\)	−105.759	+	28.3379i	−0.469908	+	0.125912i	−0.486000	−	0.873959i	\(-0.661544\pi\)
							0.0160914	+	0.999871i	\(0.494878\pi\)
\(41\)	161.832	−	43.3628i	0.616438	−	0.165174i	0.0629298	−	0.998018i	\(-0.479956\pi\)
							0.553508	+	0.832844i	\(0.313289\pi\)
\(43\)	46.7112	+	80.9061i	0.165660	+	0.286932i	0.936890	−	0.349626i	\(-0.113691\pi\)
							−0.771229	+	0.636557i	\(0.780358\pi\)
\(47\)	−229.166	−	229.166i	−0.711218	−	0.711218i	0.255572	−	0.966790i	\(-0.417736\pi\)
							−0.966790	+	0.255572i	\(0.917736\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.o.a.32.20	✓	160
11.10	odd	2	inner	143.4.o.a.32.21	yes	160
13.11	odd	12	inner	143.4.o.a.76.21	yes	160
143.76	even	12	inner	143.4.o.a.76.20	yes	160

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.o.a.32.20	✓	160	1.1	even	1	trivial
143.4.o.a.32.21	yes	160	11.10	odd	2	inner
143.4.o.a.76.20	yes	160	143.76	even	12	inner
143.4.o.a.76.21	yes	160	13.11	odd	12	inner