Embedded newform 43.11.d.a.7.7

• Label: 43.11.d.a.7.7
• 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			7.7
Character	\(\chi\)	\(=\)	43.7
Dual form			43.11.d.a.37.30

$q$-expansion

\(f(q)\)	\(=\)	\(q-42.2308i q^{2} +(235.040 - 135.700i) q^{3} -759.441 q^{4} +(1173.21 - 677.354i) q^{5} +(-5730.73 - 9925.91i) q^{6} +(26152.5 + 15099.1i) q^{7} -11172.5i q^{8} +(7304.58 - 12651.9i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 246 q^{3} - 38122 q^{4} - 3 q^{5} + 8511 q^{6} + 31377 q^{7} + 675876 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)		−	42.2308i		−	1.31971i	−0.751392	−	0.659856i	\(-0.770617\pi\)
							0.751392	−	0.659856i	\(-0.229383\pi\)
\(3\)	235.040	−	135.700i	0.967241	−	0.558437i	0.0688471	−	0.997627i	\(-0.478068\pi\)
							0.898394	+	0.439190i	\(0.144735\pi\)
\(5\)	1173.21	−	677.354i	0.375428	−	0.216753i	−0.300399	−	0.953814i	\(-0.597120\pi\)
							0.675827	+	0.737060i	\(0.263787\pi\)
\(7\)	26152.5	+	15099.1i	1.55605	+	0.898385i	0.997629	+	0.0688255i	\(0.0219252\pi\)
							0.558419	+	0.829559i	\(0.311408\pi\)
\(11\)	229830.			1.42706			0.713530	−	0.700624i	\(-0.247095\pi\)
							0.713530	+	0.700624i	\(0.247095\pi\)
\(13\)	−65962.9	+	114251.i	−0.177657	+	0.307711i	−0.941078	−	0.338191i	\(-0.890185\pi\)
							0.763420	+	0.645902i	\(0.223519\pi\)
\(17\)	529741.	−	917539.i	0.373095	−	0.646219i	−0.616945	−	0.787006i	\(-0.711630\pi\)
							0.990040	+	0.140787i	\(0.0449633\pi\)
\(19\)	2.71587e6	−	1.56801e6i	1.09684	−	0.633259i	0.161448	−	0.986881i	\(-0.448384\pi\)
							0.935388	+	0.353623i	\(0.115050\pi\)
\(23\)	2.85398e6	+	4.94324e6i	0.443416	+	0.768020i	0.997940	−	0.0641480i	\(-0.0204330\pi\)
							−0.554524	+	0.832168i	\(0.687100\pi\)
\(29\)	−3.41762e6	−	1.97317e6i	−0.166623	−	0.0961997i	0.414370	−	0.910109i	\(-0.364002\pi\)
							−0.580992	+	0.813909i	\(0.697335\pi\)
\(31\)	−1.98658e7	−	3.44087e7i	−0.693903	−	1.20187i	−0.970549	−	0.240903i	\(-0.922556\pi\)
							0.276646	−	0.960972i	\(-0.410777\pi\)
\(37\)	−7.59479e7	+	4.38485e7i	−1.09523	+	0.632334i	−0.934965	−	0.354740i	\(-0.884570\pi\)
							−0.160269	+	0.987073i	\(0.551236\pi\)
\(41\)	−1.46737e8			−1.26655			−0.633273	−	0.773928i	\(-0.718289\pi\)
							−0.633273	+	0.773928i	\(0.718289\pi\)
\(43\)	−1.18843e8	−	8.65327e7i	−0.808407	−	0.588624i
							\(47\)	−3.17908e8			−1.38616			−0.693078	−	0.720863i	\(-0.743746\pi\)
−0.693078	+	0.720863i	\(0.743746\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.d.a.7.7	✓	72
43.37	odd	6	inner	43.11.d.a.37.30	yes	72

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.d.a.7.7	✓	72	1.1	even	1	trivial
43.11.d.a.37.30	yes	72	43.37	odd	6	inner