Embedded newform 43.6.e.a.11.16

• Label: 43.6.e.a.11.16
• 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			11.16
Character	\(\chi\)	\(=\)	43.11
Dual form			43.6.e.a.4.16

$q$-expansion

\(f(q)\)	\(=\)	\(q+(5.75093 + 7.21143i) q^{2} +(8.62525 - 10.8157i) q^{3} +(-11.8110 + 51.7472i) q^{4} +(90.5645 - 43.6136i) q^{5} +127.600 q^{6} -71.2640 q^{7} +(-175.165 + 84.3549i) q^{8} +(11.4876 + 50.3307i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 3 q^{2} - 9 q^{3} - 331 q^{4} + 67 q^{5} - 20 q^{6} - 624 q^{7} + 589 q^{8} - 579 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	5.75093	+	7.21143i	1.01663	+	1.27481i	0.961054	+	0.276359i	\(0.0891279\pi\)
							0.0555755	+	0.998454i	\(0.482301\pi\)
\(3\)	8.62525	−	10.8157i	0.553310	−	0.693829i	−0.423995	−	0.905665i	\(-0.639373\pi\)
							0.977305	+	0.211835i	\(0.0679440\pi\)
\(5\)	90.5645	−	43.6136i	1.62007	−	0.780183i	0.620077	−	0.784541i	\(-0.287102\pi\)
							0.999991	+	0.00435811i	\(0.00138723\pi\)
\(7\)	−71.2640			−0.549699			−0.274850	−	0.961487i	\(-0.588628\pi\)
							−0.274850	+	0.961487i	\(0.588628\pi\)
\(11\)	−24.3267	−	106.582i	−0.0606181	−	0.265585i	0.935533	−	0.353240i	\(-0.114920\pi\)
							−0.996151	+	0.0876545i	\(0.972063\pi\)
\(13\)	−693.245	+	333.849i	−1.13770	+	0.547888i	−0.905317	−	0.424736i	\(-0.860367\pi\)
							−0.232385	+	0.972624i	\(0.574653\pi\)
\(17\)	−1309.02	−	630.389i	−1.09856	−	0.529037i	−0.205353	−	0.978688i	\(-0.565834\pi\)
							−0.893204	+	0.449651i	\(0.851548\pi\)
\(19\)	−314.177	+	1376.50i	−0.199660	+	0.874768i	0.771479	+	0.636254i	\(0.219517\pi\)
							−0.971139	+	0.238513i	\(0.923340\pi\)
\(23\)	−236.868	−	1037.79i	−0.0933656	−	0.409062i	0.906549	−	0.422100i	\(-0.138707\pi\)
							−0.999915	+	0.0130382i	\(0.995850\pi\)
\(29\)	−2658.34	−	3333.45i	−0.586969	−	0.736036i	0.396315	−	0.918115i	\(-0.370289\pi\)
							−0.983284	+	0.182079i	\(0.941717\pi\)
\(31\)	−7.83439	−	9.82402i	−0.00146420	−	0.00183605i	0.781099	−	0.624407i	\(-0.214659\pi\)
							−0.782563	+	0.622571i	\(0.786088\pi\)
\(37\)	11255.0			1.35157			0.675787	−	0.737097i	\(-0.263804\pi\)
							0.675787	+	0.737097i	\(0.263804\pi\)
\(41\)	−12554.0	−	15742.2i	−1.16633	−	1.46253i	−0.859769	−	0.510683i	\(-0.829392\pi\)
							−0.306563	−	0.951850i	\(-0.599179\pi\)
\(43\)	−5506.17	+	10802.3i	−0.454128	+	0.890936i
							\(47\)	2118.49	−	9281.71i	0.139888	−	0.612891i	−0.855569	−	0.517688i	\(-0.826793\pi\)
0.995458	−	0.0952032i	\(-0.0303501\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.e.a.11.16	yes	108
43.4	even	7	inner	43.6.e.a.4.16	✓	108

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.e.a.4.16	✓	108	43.4	even	7	inner
43.6.e.a.11.16	yes	108	1.1	even	1	trivial