Embedded newform 43.10.c.a.6.11

• Label: 43.10.c.a.6.11
• Level: $43$
• Weight: $10$
• Character: 43.6
• Analytic conductor: $22.147$
• Analytic rank: $0$
• Dimension: $64$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	43.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(22.1465409550\)
Analytic rank:	\(0\)
Dimension:	\(64\)
Relative dimension:	\(32\) over \(\Q(\zeta_{3})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			6.11
Character	\(\chi\)	\(=\)	43.6
Dual form			43.10.c.a.36.11

$q$-expansion

\(f(q)\)	\(=\)	\(q-17.1502 q^{2} +(-66.7974 + 115.697i) q^{3} -217.870 q^{4} +(-131.077 + 227.033i) q^{5} +(1145.59 - 1984.22i) q^{6} +(1324.62 + 2294.32i) q^{7} +12517.4 q^{8} +(917.711 + 1589.52i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 70 q^{2} + 307 q^{3} + 16038 q^{4} + 681 q^{5} - 1281 q^{6} + 957 q^{7} - 10920 q^{8} - 255339 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{2}{3}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−17.1502			−0.757939			−0.378970	−	0.925409i	\(-0.623722\pi\)
							−0.378970	+	0.925409i	\(0.623722\pi\)
\(3\)	−66.7974	+	115.697i	−0.476117	+	0.824659i	−0.999626	−	0.0273612i	\(-0.991290\pi\)
							0.523508	+	0.852021i	\(0.324623\pi\)
\(5\)	−131.077	+	227.033i	−0.0937914	+	0.162451i	−0.909104	−	0.416570i	\(-0.863232\pi\)
							0.815312	+	0.579022i	\(0.196565\pi\)
\(7\)	1324.62	+	2294.32i	0.208522	+	0.361170i	0.951249	−	0.308424i	\(-0.0998015\pi\)
							−0.742727	+	0.669594i	\(0.766468\pi\)
\(11\)	44267.8			0.911634			0.455817	−	0.890074i	\(-0.349347\pi\)
							0.455817	+	0.890074i	\(0.349347\pi\)
\(13\)	75299.8	+	130423.i	0.731221	+	1.26651i	0.956361	+	0.292186i	\(0.0943827\pi\)
							−0.225140	+	0.974326i	\(0.572284\pi\)
\(17\)	2936.61	+	5086.36i	0.00852759	+	0.0147702i	0.870258	−	0.492597i	\(-0.163952\pi\)
							−0.861730	+	0.507367i	\(0.830619\pi\)
\(19\)	262927.	−	455403.i	0.462854	−	0.801686i	−0.536248	−	0.844060i	\(-0.680159\pi\)
							0.999102	+	0.0423743i	\(0.0134922\pi\)
\(23\)	38900.5	−	67377.7i	0.0289855	−	0.0502043i	−0.851169	−	0.524892i	\(-0.824106\pi\)
							0.880154	+	0.474688i	\(0.157439\pi\)
\(29\)	448696.	+	777164.i	0.117804	+	0.204043i	0.918897	−	0.394497i	\(-0.129081\pi\)
							−0.801093	+	0.598540i	\(0.795748\pi\)
\(31\)	−2.80274e6	+	4.85450e6i	−0.545075	+	0.944097i	0.453528	+	0.891242i	\(0.350165\pi\)
							−0.998602	+	0.0528547i	\(0.983168\pi\)
\(37\)	−5.36678e6	+	9.29553e6i	−0.470767	+	0.815392i	−0.999441	−	0.0334327i	\(-0.989356\pi\)
							0.528674	+	0.848825i	\(0.322689\pi\)
\(41\)	4.03062e6			0.222764			0.111382	−	0.993778i	\(-0.464472\pi\)
							0.111382	+	0.993778i	\(0.464472\pi\)
\(43\)	2.17421e7	−	5.46573e6i	0.969825	−	0.243804i
							\(47\)	−3.12891e7			−0.935303			−0.467651	−	0.883913i	\(-0.654900\pi\)
−0.467651	+	0.883913i	\(0.654900\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.c.a.6.11	✓	64
43.36	even	3	inner	43.10.c.a.36.11	yes	64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.c.a.6.11	✓	64	1.1	even	1	trivial
43.10.c.a.36.11	yes	64	43.36	even	3	inner