Embedded newform 43.11.d.a.7.15

• Label: 43.11.d.a.7.15
• 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			7.15
Character	\(\chi\)	\(=\)	43.7
Dual form			43.11.d.a.37.22

$q$-expansion

\(f(q)\)	\(=\)	\(q-19.4681i q^{2} +(-30.6608 + 17.7020i) q^{3} +644.993 q^{4} +(-4831.05 + 2789.21i) q^{5} +(344.625 + 596.908i) q^{6} +(9598.06 + 5541.44i) q^{7} -32492.1i q^{8} +(-28897.8 + 50052.4i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 246 q^{3} - 38122 q^{4} - 3 q^{5} + 8511 q^{6} + 31377 q^{7} + 675876 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)		−	19.4681i		−	0.608378i	−0.952612	−	0.304189i	\(-0.901615\pi\)
							0.952612	−	0.304189i	\(-0.0983854\pi\)
\(3\)	−30.6608	+	17.7020i	−0.126176	+	0.0728479i	−0.561760	−	0.827300i	\(-0.689875\pi\)
							0.435583	+	0.900148i	\(0.356542\pi\)
\(5\)	−4831.05	+	2789.21i	−1.54594	+	0.892546i	−0.547490	+	0.836812i	\(0.684416\pi\)
							−0.998446	+	0.0557337i	\(0.982250\pi\)
\(7\)	9598.06	+	5541.44i	0.571075	+	0.329710i	0.757579	−	0.652744i	\(-0.226382\pi\)
							−0.186503	+	0.982454i	\(0.559716\pi\)
\(11\)	−143396.			−0.890373			−0.445187	−	0.895438i	\(-0.646863\pi\)
							−0.445187	+	0.895438i	\(0.646863\pi\)
\(13\)	230213.	−	398741.i	0.620032	−	1.07393i	−0.369447	−	0.929252i	\(-0.620453\pi\)
							0.989479	−	0.144675i	\(-0.0462137\pi\)
\(17\)	1.10323e6	−	1.91085e6i	0.777001	−	1.34581i	−0.156662	−	0.987652i	\(-0.550073\pi\)
							0.933663	−	0.358153i	\(-0.116593\pi\)
\(19\)	−51825.6	+	29921.5i	−0.0209303	+	0.0120841i	−0.510429	−	0.859920i	\(-0.670513\pi\)
							0.489498	+	0.872004i	\(0.337180\pi\)
\(23\)	3.32423e6	+	5.75773e6i	0.516478	+	0.894565i	0.999817	+	0.0191323i	\(0.00609038\pi\)
							−0.483339	+	0.875433i	\(0.660576\pi\)
\(29\)	−9.46606e6	−	5.46523e6i	−0.461508	−	0.266452i	0.251170	−	0.967943i	\(-0.419185\pi\)
							−0.712678	+	0.701491i	\(0.752518\pi\)
\(31\)	−2.14827e7	−	3.72091e7i	−0.750377	−	1.29969i	−0.947640	−	0.319341i	\(-0.896538\pi\)
							0.197262	−	0.980351i	\(-0.436795\pi\)
\(37\)	9.85635e7	−	5.69057e7i	1.42137	−	0.820629i	0.424955	−	0.905214i	\(-0.360290\pi\)
							0.996416	+	0.0845851i	\(0.0269565\pi\)
\(41\)	−1.61920e8			−1.39760			−0.698799	−	0.715318i	\(-0.746282\pi\)
							−0.698799	+	0.715318i	\(0.746282\pi\)
\(43\)	−1.30451e8	−	6.77801e7i	−0.887367	−	0.461063i
							\(47\)	970817.			0.00423300			0.00211650	−	0.999998i	\(-0.499326\pi\)
0.00211650	+	0.999998i	\(0.499326\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.d.a.7.15	✓	72
43.37	odd	6	inner	43.11.d.a.37.22	yes	72

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.d.a.7.15	✓	72	1.1	even	1	trivial
43.11.d.a.37.22	yes	72	43.37	odd	6	inner