Embedded newform 43.11.d.a.7.2

• Label: 43.11.d.a.7.2
• 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			7.2
Character	\(\chi\)	\(=\)	43.7
Dual form			43.11.d.a.37.35

$q$-expansion

\(f(q)\)	\(=\)	\(q-60.2423i q^{2} +(-388.590 + 224.353i) q^{3} -2605.13 q^{4} +(3532.79 - 2039.66i) q^{5} +(13515.5 + 23409.6i) q^{6} +(1359.86 + 785.115i) q^{7} +95251.0i q^{8} +(71143.8 - 123225. i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 246 q^{3} - 38122 q^{4} - 3 q^{5} + 8511 q^{6} + 31377 q^{7} + 675876 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)		−	60.2423i		−	1.88257i	−0.337612	−	0.941286i	\(-0.609619\pi\)
							0.337612	−	0.941286i	\(-0.390381\pi\)
\(3\)	−388.590	+	224.353i	−1.59914	+	0.923263i	−0.607484	+	0.794332i	\(0.707821\pi\)
							−0.991654	+	0.128931i	\(0.958846\pi\)
\(5\)	3532.79	−	2039.66i	1.13049	−	0.652690i	0.186434	−	0.982468i	\(-0.440307\pi\)
							0.944059	+	0.329777i	\(0.106974\pi\)
\(7\)	1359.86	+	785.115i	0.0809103	+	0.0467136i	0.539909	−	0.841723i	\(-0.318459\pi\)
							−0.458999	+	0.888437i	\(0.651792\pi\)
\(11\)	30292.3			0.188091			0.0940456	−	0.995568i	\(-0.470020\pi\)
							0.0940456	+	0.995568i	\(0.470020\pi\)
\(13\)	236798.	−	410146.i	0.637766	−	1.10464i	−0.348156	−	0.937437i	\(-0.613192\pi\)
							0.985922	−	0.167206i	\(-0.0534746\pi\)
\(17\)	−575773.	+	997268.i	−0.405515	+	0.702372i	−0.994381	−	0.105858i	\(-0.966241\pi\)
							0.588866	+	0.808230i	\(0.299574\pi\)
\(19\)	3.61873e6	−	2.08927e6i	1.46146	−	0.843777i	0.462385	−	0.886679i	\(-0.346994\pi\)
							0.999079	+	0.0429025i	\(0.0136605\pi\)
\(23\)	4.02466e6	+	6.97091e6i	0.625302	+	1.08305i	0.988482	+	0.151335i	\(0.0483574\pi\)
							−0.363181	+	0.931719i	\(0.618309\pi\)
\(29\)	1.14375e6	+	660347.i	0.0557626	+	0.0321945i	0.527622	−	0.849479i	\(-0.323084\pi\)
							−0.471860	+	0.881674i	\(0.656417\pi\)
\(31\)	−2.17463e7	−	3.76657e7i	−0.759587	−	1.31564i	−0.943062	−	0.332618i	\(-0.892068\pi\)
							0.183475	−	0.983024i	\(-0.441265\pi\)
\(37\)	−5.29076e7	+	3.05462e7i	−0.762974	+	0.440503i	−0.830363	−	0.557223i	\(-0.811867\pi\)
							0.0673884	+	0.997727i	\(0.478533\pi\)
\(41\)	−1.75251e7			−0.151266			−0.0756329	−	0.997136i	\(-0.524098\pi\)
							−0.0756329	+	0.997136i	\(0.524098\pi\)
\(43\)	6.67129e7	−	1.31000e8i	0.453803	−	0.891102i
							\(47\)	1.91389e8			0.834501			0.417251	−	0.908792i	\(-0.362994\pi\)
0.417251	+	0.908792i	\(0.362994\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.d.a.7.2	✓	72
43.37	odd	6	inner	43.11.d.a.37.35	yes	72

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.d.a.7.2	✓	72	1.1	even	1	trivial
43.11.d.a.37.35	yes	72	43.37	odd	6	inner