Embedded newform 43.11.d.a.7.12

• Label: 43.11.d.a.7.12
• 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			7.12
Character	\(\chi\)	\(=\)	43.7
Dual form			43.11.d.a.37.25

$q$-expansion

\(f(q)\)	\(=\)	\(q-25.0169i q^{2} +(171.910 - 99.2521i) q^{3} +398.154 q^{4} +(3482.07 - 2010.37i) q^{5} +(-2482.98 - 4300.65i) q^{6} +(-9759.68 - 5634.76i) q^{7} -35577.9i q^{8} +(-9822.54 + 17013.1i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 246 q^{3} - 38122 q^{4} - 3 q^{5} + 8511 q^{6} + 31377 q^{7} + 675876 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)		−	25.0169i		−	0.781779i	−0.920438	−	0.390889i	\(-0.872167\pi\)
							0.920438	−	0.390889i	\(-0.127833\pi\)
\(3\)	171.910	−	99.2521i	0.707447	−	0.408445i	−0.102668	−	0.994716i	\(-0.532738\pi\)
							0.810115	+	0.586271i	\(0.199405\pi\)
\(5\)	3482.07	−	2010.37i	1.11426	−	0.643319i	0.174332	−	0.984687i	\(-0.444223\pi\)
							0.939930	+	0.341368i	\(0.110890\pi\)
\(7\)	−9759.68	−	5634.76i	−0.580692	−	0.335262i	0.180717	−	0.983535i	\(-0.442158\pi\)
							−0.761408	+	0.648273i	\(0.775492\pi\)
\(11\)	−142767.			−0.886468			−0.443234	−	0.896406i	\(-0.646169\pi\)
							−0.443234	+	0.896406i	\(0.646169\pi\)
\(13\)	126077.	−	218372.i	0.339562	−	0.588138i	−0.644789	−	0.764361i	\(-0.723055\pi\)
							0.984350	+	0.176223i	\(0.0563879\pi\)
\(17\)	86105.3	−	149139.i	0.0606436	−	0.105038i	−0.834110	−	0.551599i	\(-0.814018\pi\)
							0.894753	+	0.446561i	\(0.147351\pi\)
\(19\)	2.68849e6	−	1.55220e6i	1.08578	−	0.626874i	0.153329	−	0.988175i	\(-0.451001\pi\)
							0.932449	+	0.361301i	\(0.117667\pi\)
\(23\)	−3.89319e6	−	6.74320e6i	−0.604875	−	1.04767i	−0.992071	−	0.125677i	\(-0.959890\pi\)
							0.387196	−	0.921998i	\(-0.373444\pi\)
\(29\)	1.54996e7	+	8.94872e6i	0.755669	+	0.436286i	0.827739	−	0.561114i	\(-0.189627\pi\)
							−0.0720695	+	0.997400i	\(0.522960\pi\)
\(31\)	6.98509e6	+	1.20985e7i	0.243985	+	0.422595i	0.961846	−	0.273592i	\(-0.0882118\pi\)
							−0.717861	+	0.696187i	\(0.754878\pi\)
\(37\)	−5.98155e7	+	3.45345e7i	−0.862591	+	0.498017i	−0.864879	−	0.501980i	\(-0.832605\pi\)
							0.00228780	+	0.999997i	\(0.499272\pi\)
\(41\)	−3.51986e7			−0.303813			−0.151907	−	0.988395i	\(-0.548541\pi\)
							−0.151907	+	0.988395i	\(0.548541\pi\)
\(43\)	−6.89182e7	−	1.29853e8i	−0.468805	−	0.883302i
							\(47\)	2.13330e8			0.930171			0.465086	−	0.885266i	\(-0.346024\pi\)
0.465086	+	0.885266i	\(0.346024\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.d.a.7.12	✓	72
43.37	odd	6	inner	43.11.d.a.37.25	yes	72

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.d.a.7.12	✓	72	1.1	even	1	trivial
43.11.d.a.37.25	yes	72	43.37	odd	6	inner