Embedded newform 43.11.d.a.37.29

• Label: 43.11.d.a.37.29
• 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			37.29
Character	\(\chi\)	\(=\)	43.37
Dual form			43.11.d.a.7.8

$q$-expansion

\(f(q)\)	\(=\)	\(q+41.6701i q^{2} +(347.294 + 200.510i) q^{3} -712.398 q^{4} +(-2813.29 - 1624.26i) q^{5} +(-8355.28 + 14471.8i) q^{6} +(-3430.02 + 1980.32i) q^{7} +12984.5i q^{8} +(50884.2 + 88134.0i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 246 q^{3} - 38122 q^{4} - 3 q^{5} + 8511 q^{6} + 31377 q^{7} + 675876 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)			41.6701i			1.30219i	0.758996	+	0.651095i	\(0.225690\pi\)
							−0.758996	+	0.651095i	\(0.774310\pi\)
\(3\)	347.294	+	200.510i	1.42919	+	0.825145i	0.997057	−	0.0766639i	\(-0.0244268\pi\)
							0.432136	+	0.901809i	\(0.357760\pi\)
\(5\)	−2813.29	−	1624.26i	−0.900254	−	0.519762i	−0.0229712	−	0.999736i	\(-0.507313\pi\)
							−0.877282	+	0.479974i	\(0.840646\pi\)
\(7\)	−3430.02	+	1980.32i	−0.204083	+	0.117827i	−0.598558	−	0.801079i	\(-0.704260\pi\)
							0.394476	+	0.918906i	\(0.370926\pi\)
\(11\)	−194386.			−1.20698			−0.603491	−	0.797370i	\(-0.706224\pi\)
							−0.603491	+	0.797370i	\(0.706224\pi\)
\(13\)	−162297.	−	281107.i	−0.437113	−	0.757103i	0.560352	−	0.828255i	\(-0.310666\pi\)
							−0.997465	+	0.0711518i	\(0.977333\pi\)
\(17\)	506714.	+	877654.i	0.356877	+	0.618129i	0.987437	−	0.158011i	\(-0.0505083\pi\)
							−0.630561	+	0.776140i	\(0.717175\pi\)
\(19\)	−944110.	−	545082.i	−0.381289	−	0.220137i	0.297090	−	0.954850i	\(-0.403984\pi\)
							−0.678379	+	0.734712i	\(0.737317\pi\)
\(23\)	−3.26678e6	+	5.65823e6i	−0.507552	+	0.879106i	0.492410	+	0.870364i	\(0.336116\pi\)
							−0.999962	+	0.00874261i	\(0.997217\pi\)
\(29\)	−5.32700e6	+	3.07555e6i	−0.259713	+	0.149945i	−0.624203	−	0.781262i	\(-0.714576\pi\)
							0.364491	+	0.931207i	\(0.381243\pi\)
\(31\)	−8.01681e6	+	1.38855e7i	−0.280023	+	0.485014i	−0.971390	−	0.237490i	\(-0.923675\pi\)
							0.691367	+	0.722503i	\(0.257009\pi\)
\(37\)	−1.45120e7	−	8.37854e6i	−0.209276	−	0.120826i	0.391699	−	0.920094i	\(-0.371888\pi\)
							−0.600975	+	0.799268i	\(0.705221\pi\)
\(41\)	4.23364e7			0.365422			0.182711	−	0.983167i	\(-0.441513\pi\)
							0.182711	+	0.983167i	\(0.441513\pi\)
\(43\)	1.42570e8	+	3.58496e7i	0.969810	+	0.243861i
							\(47\)	4.42952e8			1.93138			0.965690	−	0.259698i	\(-0.0836231\pi\)
0.965690	+	0.259698i	\(0.0836231\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.d.a.37.29	yes	72
43.7	odd	6	inner	43.11.d.a.7.8	✓	72

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.d.a.7.8	✓	72	43.7	odd	6	inner
43.11.d.a.37.29	yes	72	1.1	even	1	trivial