Embedded newform 43.6.c.a.6.3

• Label: 43.6.c.a.6.3
• Level: $43$
• Weight: $6$
• Character: 43.6
• Analytic conductor: $6.897$
• Analytic rank: $0$
• Dimension: $34$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	43.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.89650425196\)
Analytic rank:	\(0\)
Dimension:	\(34\)
Relative dimension:	\(17\) over \(\Q(\zeta_{3})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			6.3
Character	\(\chi\)	\(=\)	43.6
Dual form			43.6.c.a.36.3

$q$-expansion

\(f(q)\)	\(=\)	\(q-8.55067 q^{2} +(-3.32584 + 5.76053i) q^{3} +41.1139 q^{4} +(8.72223 - 15.1073i) q^{5} +(28.4382 - 49.2563i) q^{6} +(-112.908 - 195.562i) q^{7} -77.9301 q^{8} +(99.3776 + 172.127i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 14 q^{2} - 14 q^{3} + 454 q^{4} + 71 q^{5} + 15 q^{6} + 225 q^{7} - 936 q^{8} - 1011 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{2}{3}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−8.55067			−1.51156			−0.755779	−	0.654826i	\(-0.772742\pi\)
							−0.755779	+	0.654826i	\(0.772742\pi\)
\(3\)	−3.32584	+	5.76053i	−0.213353	+	0.369538i	−0.952762	−	0.303719i	\(-0.901772\pi\)
							0.739409	+	0.673257i	\(0.235105\pi\)
\(5\)	8.72223	−	15.1073i	0.156028	−	0.270248i	−0.777405	−	0.629000i	\(-0.783464\pi\)
							0.933433	+	0.358752i	\(0.116798\pi\)
\(7\)	−112.908	−	195.562i	−0.870922	−	1.50848i	−0.861044	−	0.508530i	\(-0.830189\pi\)
							−0.00987829	−	0.999951i	\(-0.503144\pi\)
\(11\)	−94.8489			−0.236347			−0.118174	−	0.992993i	\(-0.537704\pi\)
							−0.118174	+	0.992993i	\(0.537704\pi\)
\(13\)	387.984	+	672.008i	0.636731	+	1.10285i	0.986146	+	0.165882i	\(0.0530470\pi\)
							−0.349415	+	0.936968i	\(0.613620\pi\)
\(17\)	407.492	+	705.798i	0.341977	+	0.592322i	0.984800	−	0.173693i	\(-0.0555701\pi\)
							−0.642823	+	0.766015i	\(0.722237\pi\)
\(19\)	−1252.21	+	2168.89i	−0.795780	+	1.37833i	0.126562	+	0.991959i	\(0.459606\pi\)
							−0.922343	+	0.386373i	\(0.873728\pi\)
\(23\)	1284.33	−	2224.53i	0.506242	−	0.876837i	−0.493732	−	0.869614i	\(-0.664368\pi\)
							0.999974	−	0.00722288i	\(-0.00229913\pi\)
\(29\)	1154.17	+	1999.08i	0.254844	+	0.441403i	0.964853	−	0.262790i	\(-0.0846425\pi\)
							−0.710009	+	0.704193i	\(0.751309\pi\)
\(31\)	−550.205	+	952.983i	−0.102830	+	0.178107i	−0.912850	−	0.408296i	\(-0.866123\pi\)
							0.810019	+	0.586403i	\(0.199456\pi\)
\(37\)	−2898.78	+	5020.83i	−0.348105	+	0.602936i	−0.985913	−	0.167260i	\(-0.946508\pi\)
							0.637808	+	0.770196i	\(0.279841\pi\)
\(41\)	4811.95			0.447055			0.223528	−	0.974698i	\(-0.428243\pi\)
							0.223528	+	0.974698i	\(0.428243\pi\)
\(43\)	6825.71	+	10020.9i	0.562959	+	0.826485i
							\(47\)	28586.9			1.88766			0.943828	−	0.330437i	\(-0.107196\pi\)
0.943828	+	0.330437i	\(0.107196\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.c.a.6.3	✓	34
43.36	even	3	inner	43.6.c.a.36.3	yes	34

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.c.a.6.3	✓	34	1.1	even	1	trivial
43.6.c.a.36.3	yes	34	43.36	even	3	inner