Embedded newform 43.6.g.a.24.5

• Label: 43.6.g.a.24.5
• Level: $43$
• Weight: $6$
• Character: 43.24
• Analytic conductor: $6.897$
• Analytic rank: $0$
• Dimension: $204$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	43.g (of order \(21\), degree \(12\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.89650425196\)
Analytic rank:	\(0\)
Dimension:	\(204\)
Relative dimension:	\(17\) over \(\Q(\zeta_{21})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			24.5
Character	\(\chi\)	\(=\)	43.24
Dual form			43.6.g.a.9.5

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-3.60873 + 4.52520i) q^{2} +(-0.0525050 + 0.00791386i) q^{3} +(-0.333852 - 1.46270i) q^{4} +(-19.3143 + 13.1682i) q^{5} +(0.153664 - 0.266155i) q^{6} +(53.2202 + 92.1801i) q^{7} +(-159.048 - 76.5937i) q^{8} +(-232.201 + 71.6247i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 468 q^{4} - 85 q^{5} - 22 q^{6} + 454 q^{7} + 698 q^{8} - 333 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{20}{21}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−3.60873	+	4.52520i	−0.637939	+	0.799950i	−0.990743	−	0.135747i	\(-0.956656\pi\)
							0.352805	+	0.935697i	\(0.385228\pi\)
\(3\)	−0.0525050	+	0.00791386i	−0.00336820	+	0.000507674i	−0.150726	−	0.988576i	\(-0.548161\pi\)
							0.147358	+	0.989083i	\(0.452923\pi\)
\(5\)	−19.3143	+	13.1682i	−0.345504	+	0.235561i	−0.723622	−	0.690197i	\(-0.757524\pi\)
							0.378117	+	0.925758i	\(0.376572\pi\)
\(7\)	53.2202	+	92.1801i	0.410517	+	0.711037i	0.994946	−	0.100408i	\(-0.0320148\pi\)
							−0.584429	+	0.811445i	\(0.698681\pi\)
\(11\)	72.6939	−	318.493i	0.181141	−	0.793629i	−0.799948	−	0.600070i	\(-0.795140\pi\)
							0.981089	−	0.193560i	\(-0.0620033\pi\)
\(13\)	−28.9290	−	386.031i	−0.0474762	−	0.633525i	−0.969294	−	0.245903i	\(-0.920916\pi\)
							0.921818	−	0.387622i	\(-0.126704\pi\)
\(17\)	−1252.61	−	854.014i	−1.05122	−	0.716709i	−0.0909700	−	0.995854i	\(-0.528997\pi\)
							−0.960249	+	0.279145i	\(0.909949\pi\)
\(19\)	−1795.13	−	553.723i	−1.14080	−	0.351891i	−0.333920	−	0.942601i	\(-0.608372\pi\)
							−0.806884	+	0.590710i	\(0.798848\pi\)
\(23\)	1876.56	+	1741.19i	0.739676	+	0.686319i	0.957100	−	0.289758i	\(-0.0935748\pi\)
							−0.217424	+	0.976077i	\(0.569765\pi\)
\(29\)	−3584.75	−	540.314i	−0.791524	−	0.119303i	−0.259178	−	0.965830i	\(-0.583452\pi\)
							−0.532346	+	0.846527i	\(0.678690\pi\)
\(31\)	3638.18	+	9269.93i	0.679954	+	1.73250i	0.680772	+	0.732496i	\(0.261645\pi\)
							−0.000817346		1.00000i	\(0.500260\pi\)
\(37\)	−5995.89	+	10385.2i	−0.720028	+	1.24713i	0.240960	+	0.970535i	\(0.422538\pi\)
							−0.960988	+	0.276590i	\(0.910796\pi\)
\(41\)	3849.10	−	4826.61i	0.357601	−	0.448418i	−0.570193	−	0.821511i	\(-0.693131\pi\)
							0.927794	+	0.373093i	\(0.121703\pi\)
\(43\)	−8519.04	−	8627.54i	−0.702618	−	0.711567i
							\(47\)	−232.404	−	1018.23i	−0.0153461	−	0.0672359i	0.966675	−	0.256007i	\(-0.0824069\pi\)
−0.982021	+	0.188771i	\(0.939550\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.g.a.24.5	yes	204
43.9	even	21	inner	43.6.g.a.9.5	✓	204

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.g.a.9.5	✓	204	43.9	even	21	inner
43.6.g.a.24.5	yes	204	1.1	even	1	trivial