Embedded newform 43.6.e.a.11.14

• Label: 43.6.e.a.11.14
• Level: $43$
• Weight: $6$
• Character: 43.11
• Analytic conductor: $6.897$
• Analytic rank: $0$
• Dimension: $108$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	43.e (of order \(7\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.89650425196\)
Analytic rank:	\(0\)
Dimension:	\(108\)
Relative dimension:	\(18\) over \(\Q(\zeta_{7})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			11.14
Character	\(\chi\)	\(=\)	43.11
Dual form			43.6.e.a.4.14

$q$-expansion

\(f(q)\)	\(=\)	\(q+(3.56453 + 4.46978i) q^{2} +(18.2022 - 22.8249i) q^{3} +(-0.152384 + 0.667640i) q^{4} +(-27.3877 + 13.1892i) q^{5} +166.905 q^{6} -9.91522 q^{7} +(161.301 - 77.6786i) q^{8} +(-135.581 - 594.021i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 3 q^{2} - 9 q^{3} - 331 q^{4} + 67 q^{5} - 20 q^{6} - 624 q^{7} + 589 q^{8} - 579 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{5}{7}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	3.56453	+	4.46978i	0.630126	+	0.790153i	0.989730	−	0.142952i	\(-0.0456595\pi\)
							−0.359604	+	0.933105i	\(0.617088\pi\)
\(3\)	18.2022	−	22.8249i	1.16767	−	1.46422i	0.309470	−	0.950909i	\(-0.399848\pi\)
							0.858204	−	0.513308i	\(-0.171580\pi\)
\(5\)	−27.3877	+	13.1892i	−0.489925	+	0.235936i	−0.662502	−	0.749061i	\(-0.730505\pi\)
							0.172576	+	0.984996i	\(0.444791\pi\)
\(7\)	−9.91522			−0.0764817			−0.0382408	−	0.999269i	\(-0.512175\pi\)
							−0.0382408	+	0.999269i	\(0.512175\pi\)
\(11\)	51.8515	+	227.176i	0.129205	+	0.566084i	0.997540	+	0.0701055i	\(0.0223336\pi\)
							−0.868334	+	0.495979i	\(0.834809\pi\)
\(13\)	41.6628	−	20.0638i	0.0683739	−	0.0329271i	−0.399384	−	0.916784i	\(-0.630776\pi\)
							0.467758	+	0.883856i	\(0.345062\pi\)
\(17\)	869.335	+	418.650i	0.729566	+	0.351341i	0.761514	−	0.648149i	\(-0.224457\pi\)
							−0.0319474	+	0.999490i	\(0.510171\pi\)
\(19\)	−164.861	+	722.304i	−0.104769	+	0.459024i	0.895143	+	0.445779i	\(0.147073\pi\)
							−0.999912	+	0.0132452i	\(0.995784\pi\)
\(23\)	1072.95	+	4700.88i	0.422920	+	1.85293i	0.515012	+	0.857183i	\(0.327788\pi\)
							−0.0920914	+	0.995751i	\(0.529355\pi\)
\(29\)	−4815.59	−	6038.56i	−1.06330	−	1.33333i	−0.940080	−	0.340953i	\(-0.889250\pi\)
							−0.123217	−	0.992380i	\(-0.539321\pi\)
\(31\)	1279.45	+	1604.37i	0.239121	+	0.299848i	0.886883	−	0.461995i	\(-0.152866\pi\)
							−0.647762	+	0.761843i	\(0.724295\pi\)
\(37\)	5451.72			0.654681			0.327340	−	0.944907i	\(-0.393848\pi\)
							0.327340	+	0.944907i	\(0.393848\pi\)
\(41\)	7081.69	+	8880.16i	0.657927	+	0.825014i	0.993116	−	0.117137i	\(-0.0373716\pi\)
							−0.335189	+	0.942151i	\(0.608800\pi\)
\(43\)	−11140.0	−	4786.26i	−0.918787	−	0.394753i
							\(47\)	2875.24	−	12597.2i	0.189858	−	0.831823i	−0.786832	−	0.617168i	\(-0.788280\pi\)
0.976690	−	0.214655i	\(-0.0688629\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.e.a.11.14	yes	108
43.4	even	7	inner	43.6.e.a.4.14	✓	108

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.e.a.4.14	✓	108	43.4	even	7	inner
43.6.e.a.11.14	yes	108	1.1	even	1	trivial