Embedded newform 43.11.d.a.37.24

• Label: 43.11.d.a.37.24
• Level: $43$
• Weight: $11$
• Character: 43.37
• 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			37.24
Character	\(\chi\)	\(=\)	43.37
Dual form			43.11.d.a.7.13

$q$-expansion

\(f(q)\)	\(=\)	\(q+24.2487i q^{2} +(-256.468 - 148.072i) q^{3} +436.000 q^{4} +(1350.56 + 779.746i) q^{5} +(3590.55 - 6219.01i) q^{6} +(21767.9 - 12567.7i) q^{7} +35403.1i q^{8} +(14325.9 + 24813.2i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 246 q^{3} - 38122 q^{4} - 3 q^{5} + 8511 q^{6} + 31377 q^{7} + 675876 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{1}{6}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)			24.2487i			0.757772i	0.925443	+	0.378886i	\(0.123693\pi\)
							−0.925443	+	0.378886i	\(0.876307\pi\)
\(3\)	−256.468	−	148.072i	−1.05542	−	0.609348i	−0.131260	−	0.991348i	\(-0.541902\pi\)
							−0.924162	+	0.382000i	\(0.875235\pi\)
\(5\)	1350.56	+	779.746i	0.432179	+	0.249519i	0.700275	−	0.713874i	\(-0.253061\pi\)
							−0.268095	+	0.963392i	\(0.586394\pi\)
\(7\)	21767.9	−	12567.7i	1.29517	−	0.747765i	0.315602	−	0.948892i	\(-0.397794\pi\)
							0.979565	+	0.201126i	\(0.0644602\pi\)
\(11\)	−240072.			−1.49066			−0.745328	−	0.666698i	\(-0.767707\pi\)
							−0.745328	+	0.666698i	\(0.767707\pi\)
\(13\)	−104286.	−	180628.i	−0.280872	−	0.486484i	0.690728	−	0.723115i	\(-0.257290\pi\)
							−0.971600	+	0.236631i	\(0.923957\pi\)
\(17\)	10923.1	+	18919.4i	0.00769313	+	0.0133249i	0.869846	−	0.493323i	\(-0.164218\pi\)
							−0.862153	+	0.506648i	\(0.830885\pi\)
\(19\)	2.97684e6	+	1.71868e6i	1.20223	+	0.694108i	0.961051	−	0.276373i	\(-0.0891325\pi\)
							0.241179	+	0.970481i	\(0.422466\pi\)
\(23\)	4.72971e6	−	8.19210e6i	0.734844	−	1.27279i	−0.219947	−	0.975512i	\(-0.570588\pi\)
							0.954792	−	0.297276i	\(-0.0960782\pi\)
\(29\)	−9.90965e6	+	5.72134e6i	−0.483135	+	0.278938i	−0.721722	−	0.692183i	\(-0.756649\pi\)
							0.238587	+	0.971121i	\(0.423316\pi\)
\(31\)	2.64824e7	−	4.58689e7i	0.925017	−	1.60218i	0.133483	−	0.991051i	\(-0.457384\pi\)
							0.791534	−	0.611125i	\(-0.209283\pi\)
\(37\)	−7.02328e7	−	4.05489e7i	−1.01282	−	0.584750i	−0.100802	−	0.994906i	\(-0.532141\pi\)
							−0.912015	+	0.410156i	\(0.865474\pi\)
\(41\)	1.98050e8			1.70945			0.854724	−	0.519083i	\(-0.173726\pi\)
							0.854724	+	0.519083i	\(0.173726\pi\)
\(43\)	6.67374e7	−	1.30987e8i	0.453970	−	0.891017i
							\(47\)	1.22485e8			0.534065			0.267032	−	0.963688i	\(-0.413957\pi\)
0.267032	+	0.963688i	\(0.413957\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.d.a.37.24	yes	72
43.7	odd	6	inner	43.11.d.a.7.13	✓	72

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.d.a.7.13	✓	72	43.7	odd	6	inner
43.11.d.a.37.24	yes	72	1.1	even	1	trivial