Embedded newform 43.6.e.a.11.11

• Label: 43.6.e.a.11.11
• 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			11.11
Character	\(\chi\)	\(=\)	43.11
Dual form			43.6.e.a.4.11

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.240368 + 0.301412i) q^{2} +(8.08269 - 10.1354i) q^{3} +(7.08760 - 31.0528i) q^{4} +(33.3160 - 16.0441i) q^{5} +4.99775 q^{6} -195.731 q^{7} +(22.1783 - 10.6805i) q^{8} +(16.6767 + 73.0652i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 3 q^{2} - 9 q^{3} - 331 q^{4} + 67 q^{5} - 20 q^{6} - 624 q^{7} + 589 q^{8} - 579 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.240368	+	0.301412i	0.0424915	+	0.0532826i	0.802623	−	0.596486i	\(-0.203437\pi\)
							−0.760132	+	0.649769i	\(0.774866\pi\)
\(3\)	8.08269	−	10.1354i	0.518505	−	0.650185i	−0.451786	−	0.892126i	\(-0.649213\pi\)
							0.970291	+	0.241942i	\(0.0777843\pi\)
\(5\)	33.3160	−	16.0441i	0.595975	−	0.287006i	−0.111478	−	0.993767i	\(-0.535558\pi\)
							0.707453	+	0.706760i	\(0.249844\pi\)
\(7\)	−195.731			−1.50978			−0.754890	−	0.655852i	\(-0.772310\pi\)
							−0.754890	+	0.655852i	\(0.772310\pi\)
\(11\)	−118.569	−	519.484i	−0.295453	−	1.29446i	−0.876818	−	0.480822i	\(-0.840338\pi\)
							0.581365	−	0.813643i	\(-0.302519\pi\)
\(13\)	330.557	−	159.188i	0.542486	−	0.261247i	−0.142511	−	0.989793i	\(-0.545518\pi\)
							0.684997	+	0.728546i	\(0.259803\pi\)
\(17\)	1704.28	+	820.737i	1.43027	+	0.688782i	0.979048	−	0.203630i	\(-0.0652739\pi\)
							0.451222	+	0.892412i	\(0.350988\pi\)
\(19\)	168.830	−	739.694i	0.107292	−	0.470076i	−0.892526	−	0.450996i	\(-0.851069\pi\)
							0.999818	−	0.0190803i	\(-0.00607383\pi\)
\(23\)	−707.903	−	3101.53i	−0.279032	−	1.22252i	−0.899020	−	0.437908i	\(-0.855720\pi\)
							0.619988	−	0.784612i	\(-0.287138\pi\)
\(29\)	1603.49	+	2010.72i	0.354056	+	0.443973i	0.926683	−	0.375844i	\(-0.122647\pi\)
							−0.572627	+	0.819816i	\(0.694076\pi\)
\(31\)	4485.88	+	5625.12i	0.838385	+	1.05130i	0.997943	+	0.0641130i	\(0.0204218\pi\)
							−0.159558	+	0.987189i	\(0.551007\pi\)
\(37\)	7266.79			0.872646			0.436323	−	0.899790i	\(-0.356280\pi\)
							0.436323	+	0.899790i	\(0.356280\pi\)
\(41\)	7512.66	+	9420.58i	0.697966	+	0.875222i	0.996870	−	0.0790616i	\(-0.0251924\pi\)
							−0.298904	+	0.954283i	\(0.596621\pi\)
\(43\)	653.714	−	12107.1i	0.0539159	−	0.998545i
							\(47\)	−1117.67	+	4896.84i	−0.0738022	+	0.323349i	−0.998330	−	0.0577656i	\(-0.981602\pi\)
0.924528	+	0.381114i	\(0.124460\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.e.a.11.11	yes	108
43.4	even	7	inner	43.6.e.a.4.11	✓	108

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.e.a.4.11	✓	108	43.4	even	7	inner
43.6.e.a.11.11	yes	108	1.1	even	1	trivial