Embedded newform 43.4.g.a.10.6

• Label: 43.4.g.a.10.6
• Level: $43$
• Weight: $4$
• Character: 43.10
• Analytic conductor: $2.537$
• Analytic rank: $0$
• Dimension: $120$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	43.g (of order \(21\), degree \(12\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.53708213025\)
Analytic rank:	\(0\)
Dimension:	\(120\)
Relative dimension:	\(10\) over \(\Q(\zeta_{21})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			10.6
Character	\(\chi\)	\(=\)	43.10
Dual form			43.4.g.a.13.6

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.113555 + 0.497516i) q^{2} +(4.85972 + 4.50917i) q^{3} +(6.97312 - 3.35808i) q^{4} +(-8.91725 + 1.34406i) q^{5} +(-1.69154 + 2.92983i) q^{6} +(2.21697 + 3.83991i) q^{7} +(5.00791 + 6.27973i) q^{8} +(1.26664 + 16.9021i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 12 q^{2} - 9 q^{3} - 92 q^{4} + 5 q^{5} - 22 q^{6} - 54 q^{7} + 2 q^{8} + 201 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{5}{21}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.113555	+	0.497516i	0.0401477	+	0.175898i	0.991027	−	0.133664i	\(-0.0426744\pi\)
							−0.950879	+	0.309563i	\(0.899817\pi\)
\(3\)	4.85972	+	4.50917i	0.935254	+	0.867789i	0.991431	−	0.130632i	\(-0.0417005\pi\)
							−0.0561765	+	0.998421i	\(0.517891\pi\)
\(5\)	−8.91725	+	1.34406i	−0.797584	+	0.120216i	−0.535176	−	0.844741i	\(-0.679755\pi\)
							−0.262408	+	0.964957i	\(0.584517\pi\)
\(7\)	2.21697	+	3.83991i	0.119705	+	0.207335i	0.919651	−	0.392737i	\(-0.128472\pi\)
							−0.799946	+	0.600072i	\(0.795138\pi\)
\(11\)	5.96279	+	2.87153i	0.163441	+	0.0787089i	0.513816	−	0.857901i	\(-0.328232\pi\)
							−0.350375	+	0.936610i	\(0.613946\pi\)
\(13\)	4.94815	−	12.6077i	0.105567	−	0.268980i	−0.868324	−	0.495998i	\(-0.834802\pi\)
							0.973891	+	0.227018i	\(0.0728975\pi\)
\(17\)	−125.638	−	18.9368i	−1.79245	−	0.270168i	−0.833248	−	0.552900i	\(-0.813521\pi\)
							−0.959199	+	0.282732i	\(0.908759\pi\)
\(19\)	6.32317	−	84.3768i	0.0763492	−	1.01881i	−0.819102	−	0.573648i	\(-0.805528\pi\)
							0.895451	−	0.445161i	\(-0.146853\pi\)
\(23\)	10.5279	−	7.17783i	0.0954446	−	0.0650731i	−0.514657	−	0.857396i	\(-0.672081\pi\)
							0.610102	+	0.792323i	\(0.291128\pi\)
\(29\)	60.8880	−	56.4958i	0.389884	−	0.361759i	−0.460739	−	0.887536i	\(-0.652416\pi\)
							0.850623	+	0.525777i	\(0.176225\pi\)
\(31\)	62.7379	+	19.3521i	0.363486	+	0.112121i	0.471118	−	0.882070i	\(-0.343851\pi\)
							−0.107632	+	0.994191i	\(0.534327\pi\)
\(37\)	−130.912	+	226.746i	−0.581669	+	1.00748i	0.413613	+	0.910453i	\(0.364267\pi\)
							−0.995282	+	0.0970272i	\(0.969067\pi\)
\(41\)	54.5075	+	238.813i	0.207625	+	0.909666i	0.966142	+	0.258012i	\(0.0830674\pi\)
							−0.758516	+	0.651654i	\(0.774075\pi\)
\(43\)	211.051	+	186.988i	0.748486	+	0.663150i
							\(47\)	−513.729	+	247.399i	−1.59436	+	0.767805i	−0.999355	−	0.0359132i	\(-0.988566\pi\)
−0.595009	+	0.803719i	\(0.702852\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.4.g.a.10.6	✓	120
43.13	even	21	inner	43.4.g.a.13.6	yes	120
43.20	odd	42		1849.4.a.k.1.34		60
43.23	even	21		1849.4.a.l.1.27		60

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.g.a.10.6	✓	120	1.1	even	1	trivial
43.4.g.a.13.6	yes	120	43.13	even	21	inner
1849.4.a.k.1.34		60	43.20	odd	42
1849.4.a.l.1.27		60	43.23	even	21