Embedded newform 43.11.d.a.7.11

• Label: 43.11.d.a.7.11
• 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			7.11
Character	\(\chi\)	\(=\)	43.7
Dual form			43.11.d.a.37.26

$q$-expansion

\(f(q)\)	\(=\)	\(q-28.8579i q^{2} +(-341.461 + 197.142i) q^{3} +191.221 q^{4} +(-978.980 + 565.214i) q^{5} +(5689.12 + 9853.84i) q^{6} +(-26555.4 - 15331.8i) q^{7} -35068.7i q^{8} +(48205.7 - 83494.7i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 246 q^{3} - 38122 q^{4} - 3 q^{5} + 8511 q^{6} + 31377 q^{7} + 675876 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)		−	28.8579i		−	0.901810i	−0.892572	−	0.450905i	\(-0.851101\pi\)
							0.892572	−	0.450905i	\(-0.148899\pi\)
\(3\)	−341.461	+	197.142i	−1.40519	+	0.811285i	−0.994919	−	0.100679i	\(-0.967898\pi\)
							−0.410269	+	0.911965i	\(0.634565\pi\)
\(5\)	−978.980	+	565.214i	−0.313274	+	0.180869i	−0.648390	−	0.761308i	\(-0.724558\pi\)
							0.335117	+	0.942177i	\(0.391224\pi\)
\(7\)	−26555.4	−	15331.8i	−1.58002	−	0.912225i	−0.994855	−	0.101312i	\(-0.967696\pi\)
							−0.585166	−	0.810914i	\(-0.698971\pi\)
\(11\)	−168355.			−1.04535			−0.522675	−	0.852532i	\(-0.675066\pi\)
							−0.522675	+	0.852532i	\(0.675066\pi\)
\(13\)	13790.3	−	23885.4i	0.0371412	−	0.0643304i	−0.846857	−	0.531820i	\(-0.821508\pi\)
							0.883998	+	0.467490i	\(0.154842\pi\)
\(17\)	−135662.	+	234973.i	−0.0955462	+	0.165491i	−0.909836	−	0.414967i	\(-0.863793\pi\)
							0.814290	+	0.580458i	\(0.197126\pi\)
\(19\)	−440585.	+	254372.i	−0.177935	+	0.102731i	−0.586322	−	0.810078i	\(-0.699425\pi\)
							0.408387	+	0.912809i	\(0.366091\pi\)
\(23\)	−710071.	−	1.22988e6i	−0.110322	−	0.191084i	0.805578	−	0.592490i	\(-0.201855\pi\)
							−0.915900	+	0.401406i	\(0.868522\pi\)
\(29\)	3.31769e7	+	1.91547e7i	1.61751	+	0.933867i	0.987563	+	0.157226i	\(0.0502552\pi\)
							0.629943	+	0.776641i	\(0.283078\pi\)
\(31\)	−1.15422e7	−	1.99917e7i	−0.403163	−	0.698299i	0.590943	−	0.806713i	\(-0.298756\pi\)
							−0.994106	+	0.108415i	\(0.965423\pi\)
\(37\)	8.72706e7	−	5.03857e7i	1.25852	−	0.726605i	0.285731	−	0.958310i	\(-0.407764\pi\)
							0.972786	+	0.231705i	\(0.0744303\pi\)
\(41\)	−1.78315e8			−1.53911			−0.769555	−	0.638580i	\(-0.779522\pi\)
							−0.769555	+	0.638580i	\(0.779522\pi\)
\(43\)	2.30803e7	+	1.45185e8i	0.157000	+	0.987599i
							\(47\)	1.13171e8			0.493453			0.246727	−	0.969085i	\(-0.420645\pi\)
0.246727	+	0.969085i	\(0.420645\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.d.a.7.11	✓	72
43.37	odd	6	inner	43.11.d.a.37.26	yes	72

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.d.a.7.11	✓	72	1.1	even	1	trivial
43.11.d.a.37.26	yes	72	43.37	odd	6	inner