Embedded newform 43.10.c.a.6.8

• Label: 43.10.c.a.6.8
• 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			6.8
Character	\(\chi\)	\(=\)	43.6
Dual form			43.10.c.a.36.8

$q$-expansion

\(f(q)\)	\(=\)	\(q-26.2732 q^{2} +(-64.5490 + 111.802i) q^{3} +178.282 q^{4} +(-856.618 + 1483.71i) q^{5} +(1695.91 - 2937.40i) q^{6} +(-4325.00 - 7491.12i) q^{7} +8767.84 q^{8} +(1508.35 + 2612.53i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 70 q^{2} + 307 q^{3} + 16038 q^{4} + 681 q^{5} - 1281 q^{6} + 957 q^{7} - 10920 q^{8} - 255339 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−26.2732			−1.16112			−0.580562	−	0.814216i	\(-0.697167\pi\)
							−0.580562	+	0.814216i	\(0.697167\pi\)
\(3\)	−64.5490	+	111.802i	−0.460091	+	0.796902i	−0.998965	−	0.0454850i	\(-0.985517\pi\)
							0.538874	+	0.842387i	\(0.318850\pi\)
\(5\)	−856.618	+	1483.71i	−0.612946	+	1.06165i	0.377795	+	0.925889i	\(0.376682\pi\)
							−0.990741	+	0.135765i	\(0.956651\pi\)
\(7\)	−4325.00	−	7491.12i	−0.680840	−	1.17925i	−0.974725	−	0.223408i	\(-0.928282\pi\)
							0.293885	−	0.955841i	\(-0.405052\pi\)
\(11\)	4663.85			0.0960456			0.0480228	−	0.998846i	\(-0.484708\pi\)
							0.0480228	+	0.998846i	\(0.484708\pi\)
\(13\)	−98804.7	−	171135.i	−0.959472	−	1.66185i	−0.723785	−	0.690026i	\(-0.757599\pi\)
							−0.235687	−	0.971829i	\(-0.575734\pi\)
\(17\)	−34947.9	−	60531.6i	−0.101485	−	0.175777i	0.810812	−	0.585307i	\(-0.199026\pi\)
							−0.912297	+	0.409530i	\(0.865693\pi\)
\(19\)	70887.4	−	122781.i	0.124789	−	0.216142i	−0.796861	−	0.604162i	\(-0.793508\pi\)
							0.921651	+	0.388021i	\(0.126841\pi\)
\(23\)	383607.	−	664427.i	0.285832	−	0.495076i	−0.686978	−	0.726678i	\(-0.741063\pi\)
							0.972811	+	0.231602i	\(0.0743967\pi\)
\(29\)	3.46117e6	+	5.99493e6i	0.908725	+	1.57396i	0.815837	+	0.578281i	\(0.196276\pi\)
							0.0928877	+	0.995677i	\(0.470390\pi\)
\(31\)	−1.22088e6	+	2.11462e6i	−0.237435	+	0.411249i	−0.959977	−	0.280077i	\(-0.909640\pi\)
							0.722543	+	0.691326i	\(0.242973\pi\)
\(37\)	6.26387e6	−	1.08493e7i	0.549458	−	0.951689i	−0.448854	−	0.893605i	\(-0.648168\pi\)
							0.998312	−	0.0580841i	\(-0.0184992\pi\)
\(41\)	1.39602e6			0.0771548			0.0385774	−	0.999256i	\(-0.487717\pi\)
							0.0385774	+	0.999256i	\(0.487717\pi\)
\(43\)	2.58527e6	+	2.22690e7i	0.115318	+	0.993329i
							\(47\)	−2.95069e7			−0.882029			−0.441015	−	0.897500i	\(-0.645381\pi\)
−0.441015	+	0.897500i	\(0.645381\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.c.a.6.8	✓	64
43.36	even	3	inner	43.10.c.a.36.8	yes	64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.c.a.6.8	✓	64	1.1	even	1	trivial
43.10.c.a.36.8	yes	64	43.36	even	3	inner