Embedded newform 43.5.d.a.7.7

• Label: 43.5.d.a.7.7
• Level: $43$
• Weight: $5$
• Character: 43.7
• Analytic conductor: $4.445$
• Analytic rank: $0$
• Dimension: $28$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.44490841261\)
Analytic rank:	\(0\)
Dimension:	\(28\)
Relative dimension:	\(14\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			7.7
Character	\(\chi\)	\(=\)	43.7
Dual form			43.5.d.a.37.8

$q$-expansion

\(f(q)\)	\(=\)	\(q-2.45393i q^{2} +(-7.53154 + 4.34833i) q^{3} +9.97824 q^{4} +(-12.0383 + 6.95034i) q^{5} +(10.6705 + 18.4818i) q^{6} +(83.6059 + 48.2699i) q^{7} -63.7487i q^{8} +(-2.68397 + 4.64877i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 6 q^{3} - 234 q^{4} - 3 q^{5} + 15 q^{6} + 129 q^{7} + 534 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{5}{6}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)		−	2.45393i		−	0.613482i	−0.951793	−	0.306741i	\(-0.900761\pi\)
							0.951793	−	0.306741i	\(-0.0992385\pi\)
\(3\)	−7.53154	+	4.34833i	−0.836837	+	0.483148i	−0.856188	−	0.516664i	\(-0.827173\pi\)
							0.0193505	+	0.999813i	\(0.493840\pi\)
\(5\)	−12.0383	+	6.95034i	−0.481534	+	0.278014i	−0.721055	−	0.692877i	\(-0.756343\pi\)
							0.239522	+	0.970891i	\(0.423009\pi\)
\(7\)	83.6059	+	48.2699i	1.70624	+	0.985100i	0.939112	+	0.343610i	\(0.111650\pi\)
							0.767131	+	0.641490i	\(0.221683\pi\)
\(11\)	176.930			1.46224			0.731118	−	0.682251i	\(-0.238999\pi\)
							0.731118	+	0.682251i	\(0.238999\pi\)
\(13\)	−73.8797	+	127.963i	−0.437158	+	0.757180i	−0.997469	−	0.0711026i	\(-0.977348\pi\)
							0.560311	+	0.828282i	\(0.310682\pi\)
\(17\)	127.354	−	220.584i	0.440671	−	0.763265i	−0.557068	−	0.830467i	\(-0.688074\pi\)
							0.997739	+	0.0672018i	\(0.0214071\pi\)
\(19\)	−409.242	+	236.276i	−1.13364	+	0.654505i	−0.944847	−	0.327513i	\(-0.893789\pi\)
							−0.188789	+	0.982018i	\(0.560456\pi\)
\(23\)	193.866	+	335.786i	0.366476	+	0.634755i	0.989012	−	0.147836i	\(-0.0472308\pi\)
							−0.622536	+	0.782591i	\(0.713897\pi\)
\(29\)	−576.867	−	333.055i	−0.685930	−	0.396022i	0.116155	−	0.993231i	\(-0.462943\pi\)
							−0.802086	+	0.597209i	\(0.796276\pi\)
\(31\)	−270.354	−	468.266i	−0.281325	−	0.487270i	0.690386	−	0.723441i	\(-0.257441\pi\)
							−0.971711	+	0.236171i	\(0.924107\pi\)
\(37\)	1901.73	−	1097.97i	1.38914	−	0.802020i	0.395921	−	0.918284i	\(-0.370425\pi\)
							0.993218	+	0.116264i	\(0.0370920\pi\)
\(41\)	2056.02			1.22310			0.611548	−	0.791207i	\(-0.290547\pi\)
							0.611548	+	0.791207i	\(0.290547\pi\)
\(43\)	−407.975	−	1803.43i	−0.220646	−	0.975354i
							\(47\)	−825.383			−0.373646			−0.186823	−	0.982394i	\(-0.559819\pi\)
−0.186823	+	0.982394i	\(0.559819\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.5.d.a.7.7	✓	28
43.37	odd	6	inner	43.5.d.a.37.8	yes	28

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.5.d.a.7.7	✓	28	1.1	even	1	trivial
43.5.d.a.37.8	yes	28	43.37	odd	6	inner