Embedded newform 43.11.d.a.7.1

• Label: 43.11.d.a.7.1
• 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			7.1
Character	\(\chi\)	\(=\)	43.7
Dual form			43.11.d.a.37.36

$q$-expansion

\(f(q)\)	\(=\)	\(q-61.9282i q^{2} +(176.385 - 101.836i) q^{3} -2811.11 q^{4} +(-2896.62 + 1672.36i) q^{5} +(-6306.51 - 10923.2i) q^{6} +(14965.1 + 8640.13i) q^{7} +110672. i q^{8} +(-8783.43 + 15213.3i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 246 q^{3} - 38122 q^{4} - 3 q^{5} + 8511 q^{6} + 31377 q^{7} + 675876 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)		−	61.9282i		−	1.93526i	−0.252378	−	0.967629i	\(-0.581212\pi\)
							0.252378	−	0.967629i	\(-0.418788\pi\)
\(3\)	176.385	−	101.836i	0.725863	−	0.419077i	−0.0910435	−	0.995847i	\(-0.529020\pi\)
							0.816907	+	0.576769i	\(0.195687\pi\)
\(5\)	−2896.62	+	1672.36i	−0.926918	+	0.535156i	−0.885835	−	0.464000i	\(-0.846414\pi\)
							−0.0410823	+	0.999156i	\(0.513081\pi\)
\(7\)	14965.1	+	8640.13i	0.890412	+	0.514079i	0.874077	−	0.485787i	\(-0.161467\pi\)
							0.0163346	+	0.999867i	\(0.494800\pi\)
\(11\)	−79392.2			−0.492963			−0.246482	−	0.969147i	\(-0.579274\pi\)
							−0.246482	+	0.969147i	\(0.579274\pi\)
\(13\)	352040.	−	609751.i	0.948146	−	1.64224i	0.198818	−	0.980036i	\(-0.436290\pi\)
							0.749327	−	0.662200i	\(-0.230377\pi\)
\(17\)	−706396.	+	1.22351e6i	−0.497512	+	0.861717i	−0.999996	−	0.00287014i	\(-0.999086\pi\)
							0.502484	+	0.864587i	\(0.332420\pi\)
\(19\)	96399.9	−	55656.5i	0.0389322	−	0.0224775i	−0.480408	−	0.877045i	\(-0.659511\pi\)
							0.519340	+	0.854568i	\(0.326178\pi\)
\(23\)	−1.01478e6	−	1.75765e6i	−0.157664	−	0.273082i	0.776362	−	0.630288i	\(-0.217063\pi\)
							−0.934026	+	0.357205i	\(0.883730\pi\)
\(29\)	2.90999e7	+	1.68008e7i	1.41874	+	0.819107i	0.996188	−	0.0872334i	\(-0.0278026\pi\)
							0.422548	+	0.906341i	\(0.361136\pi\)
\(31\)	2.36169e7	+	4.09057e7i	0.824925	+	1.42881i	0.901977	+	0.431785i	\(0.142116\pi\)
							−0.0770516	+	0.997027i	\(0.524551\pi\)
\(37\)	9.18615e6	−	5.30363e6i	0.132472	−	0.0764829i	−0.432299	−	0.901730i	\(-0.642298\pi\)
							0.564772	+	0.825247i	\(0.308964\pi\)
\(41\)	1.42402e7			0.122912			0.0614562	−	0.998110i	\(-0.480426\pi\)
							0.0614562	+	0.998110i	\(0.480426\pi\)
\(43\)	−1.30563e8	+	6.75626e7i	−0.888135	+	0.459583i
							\(47\)	4.75916e7			0.207511			0.103755	−	0.994603i	\(-0.466914\pi\)
0.103755	+	0.994603i	\(0.466914\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.d.a.7.1	✓	72
43.37	odd	6	inner	43.11.d.a.37.36	yes	72

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.d.a.7.1	✓	72	1.1	even	1	trivial
43.11.d.a.37.36	yes	72	43.37	odd	6	inner