Embedded newform 43.11.d.a.7.4

• Label: 43.11.d.a.7.4
• Level: $43$
• Weight: $11$
• Character: 43.7
• Analytic conductor: $27.320$
• Analytic rank: $0$
• Dimension: $72$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(27.3203618650\)
Analytic rank:	\(0\)
Dimension:	\(72\)
Relative dimension:	\(36\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			7.4
Character	\(\chi\)	\(=\)	43.7
Dual form			43.11.d.a.37.33

$q$-expansion

\(f(q)\)	\(=\)	\(q-55.4674i q^{2} +(-88.6325 + 51.1720i) q^{3} -2052.63 q^{4} +(-1275.79 + 736.579i) q^{5} +(2838.37 + 4916.21i) q^{6} +(-14307.5 - 8260.42i) q^{7} +57055.3i q^{8} +(-24287.4 + 42066.9i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 246 q^{3} - 38122 q^{4} - 3 q^{5} + 8511 q^{6} + 31377 q^{7} + 675876 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)		−	55.4674i		−	1.73336i	−0.498869	−	0.866678i	\(-0.666251\pi\)
							0.498869	−	0.866678i	\(-0.333749\pi\)
\(3\)	−88.6325	+	51.1720i	−0.364743	+	0.210584i	−0.671159	−	0.741313i	\(-0.734203\pi\)
							0.306417	+	0.951898i	\(0.400870\pi\)
\(5\)	−1275.79	+	736.579i	−0.408254	+	0.235705i	−0.690039	−	0.723772i	\(-0.742407\pi\)
							0.281785	+	0.959477i	\(0.409073\pi\)
\(7\)	−14307.5	−	8260.42i	−0.851280	−	0.491487i	0.00980243	−	0.999952i	\(-0.496880\pi\)
							−0.861083	+	0.508465i	\(0.830213\pi\)
\(11\)	24048.6			0.149323			0.0746614	−	0.997209i	\(-0.476212\pi\)
							0.0746614	+	0.997209i	\(0.476212\pi\)
\(13\)	−164284.	+	284549.i	−0.442466	+	0.766373i	−0.997872	−	0.0652061i	\(-0.979230\pi\)
							0.555406	+	0.831579i	\(0.312563\pi\)
\(17\)	1.06658e6	−	1.84737e6i	0.751186	−	1.30109i	−0.196062	−	0.980592i	\(-0.562815\pi\)
							0.947248	−	0.320501i	\(-0.103851\pi\)
\(19\)	2.62539e6	−	1.51577e6i	1.06029	−	0.612159i	0.134778	−	0.990876i	\(-0.456968\pi\)
							0.925513	+	0.378716i	\(0.123634\pi\)
\(23\)	212189.	+	367523.i	0.0329674	+	0.0571012i	0.882038	−	0.471178i	\(-0.156171\pi\)
							−0.849071	+	0.528279i	\(0.822838\pi\)
\(29\)	−1.41543e7	−	8.17197e6i	−0.690077	−	0.398416i	0.113564	−	0.993531i	\(-0.463773\pi\)
							−0.803641	+	0.595115i	\(0.797107\pi\)
\(31\)	4.52927e6	+	7.84492e6i	0.158205	+	0.274019i	0.934221	−	0.356694i	\(-0.116096\pi\)
							−0.776017	+	0.630712i	\(0.782763\pi\)
\(37\)	1.34275e6	−	775235.i	0.0193636	−	0.0111796i	−0.490287	−	0.871561i	\(-0.663108\pi\)
							0.509651	+	0.860382i	\(0.329775\pi\)
\(41\)	5.83940e7			0.504021			0.252011	−	0.967724i	\(-0.418908\pi\)
							0.252011	+	0.967724i	\(0.418908\pi\)
\(43\)	−1.41175e8	+	4.10027e7i	−0.960316	+	0.278914i
							\(47\)	3.25900e8			1.42100			0.710501	−	0.703696i	\(-0.248468\pi\)
0.710501	+	0.703696i	\(0.248468\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.d.a.7.4	✓	72
43.37	odd	6	inner	43.11.d.a.37.33	yes	72

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.d.a.7.4	✓	72	1.1	even	1	trivial
43.11.d.a.37.33	yes	72	43.37	odd	6	inner