Embedded newform 43.10.c.a.6.9

• Label: 43.10.c.a.6.9
• Level: $43$
• Weight: $10$
• Character: 43.6
• Analytic conductor: $22.147$
• Analytic rank: $0$
• Dimension: $64$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	43.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(22.1465409550\)
Analytic rank:	\(0\)
Dimension:	\(64\)
Relative dimension:	\(32\) over \(\Q(\zeta_{3})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			6.9
Character	\(\chi\)	\(=\)	43.6
Dual form			43.10.c.a.36.9

$q$-expansion

\(f(q)\)	\(=\)	\(q-25.7600 q^{2} +(66.1575 - 114.588i) q^{3} +151.580 q^{4} +(-107.144 + 185.579i) q^{5} +(-1704.22 + 2951.80i) q^{6} +(-2358.57 - 4085.17i) q^{7} +9284.43 q^{8} +(1087.86 + 1884.23i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 70 q^{2} + 307 q^{3} + 16038 q^{4} + 681 q^{5} - 1281 q^{6} + 957 q^{7} - 10920 q^{8} - 255339 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−25.7600			−1.13844			−0.569222	−	0.822184i	\(-0.692756\pi\)
							−0.569222	+	0.822184i	\(0.692756\pi\)
\(3\)	66.1575	−	114.588i	0.471556	−	0.816760i	−0.527914	−	0.849298i	\(-0.677026\pi\)
							0.999470	+	0.0325381i	\(0.0103590\pi\)
\(5\)	−107.144	+	185.579i	−0.0766659	+	0.132789i	−0.901809	−	0.432134i	\(-0.857761\pi\)
							0.825144	+	0.564923i	\(0.191094\pi\)
\(7\)	−2358.57	−	4085.17i	−0.371285	−	0.643085i	0.618478	−	0.785802i	\(-0.287750\pi\)
							−0.989764	+	0.142717i	\(0.954416\pi\)
\(11\)	40601.9			0.836141			0.418071	−	0.908415i	\(-0.362706\pi\)
							0.418071	+	0.908415i	\(0.362706\pi\)
\(13\)	22035.2	+	38166.0i	0.213979	+	0.370623i	0.952956	−	0.303108i	\(-0.0980242\pi\)
							−0.738977	+	0.673730i	\(0.764691\pi\)
\(17\)	142684.	+	247135.i	0.414337	+	0.717653i	0.995359	−	0.0962354i	\(-0.0306802\pi\)
							−0.581022	+	0.813888i	\(0.697347\pi\)
\(19\)	−290138.	+	502534.i	−0.510756	+	0.884656i	0.489166	+	0.872191i	\(0.337301\pi\)
							−0.999922	+	0.0124651i	\(0.996032\pi\)
\(23\)	1.10195e6	−	1.90863e6i	0.821083	−	1.42216i	−0.0837942	−	0.996483i	\(-0.526704\pi\)
							0.904877	−	0.425674i	\(-0.139963\pi\)
\(29\)	−2.97467e6	−	5.15228e6i	−0.780994	−	1.35272i	−0.931363	−	0.364091i	\(-0.881380\pi\)
							0.150370	−	0.988630i	\(-0.451954\pi\)
\(31\)	2.58112e6	−	4.47063e6i	0.501974	−	0.869444i	−0.498024	−	0.867163i	\(-0.665941\pi\)
							0.999997	−	0.00228038i	\(-0.000725869\pi\)
\(37\)	8.38706e6	−	1.45268e7i	0.735702	−	1.27427i	−0.218712	−	0.975789i	\(-0.570186\pi\)
							0.954414	−	0.298485i	\(-0.0964811\pi\)
\(41\)	−3.01904e6			−0.166856			−0.0834280	−	0.996514i	\(-0.526587\pi\)
							−0.0834280	+	0.996514i	\(0.526587\pi\)
\(43\)	−1.90060e7	−	1.18896e7i	−0.847780	−	0.530348i
							\(47\)	−1.15396e7			−0.344946			−0.172473	−	0.985014i	\(-0.555176\pi\)
−0.172473	+	0.985014i	\(0.555176\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.c.a.6.9	✓	64
43.36	even	3	inner	43.10.c.a.36.9	yes	64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.c.a.6.9	✓	64	1.1	even	1	trivial
43.10.c.a.36.9	yes	64	43.36	even	3	inner