Embedded newform 43.6.e.a.4.18

• Label: 43.6.e.a.4.18
• Level: $43$
• Weight: $6$
• Character: 43.4
• 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			4.18
Character	\(\chi\)	\(=\)	43.4
Dual form			43.6.e.a.11.18

$q$-expansion

\(f(q)\)	\(=\)	\(q+(6.45965 - 8.10014i) q^{2} +(-16.9351 - 21.2360i) q^{3} +(-16.7646 - 73.4505i) q^{4} +(36.1651 + 17.4162i) q^{5} -281.410 q^{6} +237.288 q^{7} +(-404.550 - 194.821i) q^{8} +(-110.096 + 482.362i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 3 q^{2} - 9 q^{3} - 331 q^{4} + 67 q^{5} - 20 q^{6} - 624 q^{7} + 589 q^{8} - 579 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{2}{7}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	6.45965	−	8.10014i	1.14192	−	1.43192i	0.256849	−	0.966452i	\(-0.417316\pi\)
							0.885066	−	0.465465i	\(-0.154113\pi\)
\(3\)	−16.9351	−	21.2360i	−1.08639	−	1.36229i	−0.926994	−	0.375075i	\(-0.877617\pi\)
							−0.159396	−	0.987215i	\(-0.550955\pi\)
\(5\)	36.1651	+	17.4162i	0.646941	+	0.311550i	0.728426	−	0.685124i	\(-0.240252\pi\)
							−0.0814855	+	0.996675i	\(0.525966\pi\)
\(7\)	237.288			1.83033			0.915167	−	0.403074i	\(-0.132058\pi\)
							0.915167	+	0.403074i	\(0.132058\pi\)
\(11\)	−32.8986	+	144.138i	−0.0819776	+	0.359167i	−0.999234	−	0.0391295i	\(-0.987542\pi\)
							0.917257	+	0.398297i	\(0.130399\pi\)
\(13\)	−470.081	−	226.379i	−0.771461	−	0.371516i	0.00637794	−	0.999980i	\(-0.497970\pi\)
							−0.777839	+	0.628464i	\(0.783684\pi\)
\(17\)	1136.18	−	547.155i	0.953509	−	0.459186i	0.108594	−	0.994086i	\(-0.465365\pi\)
							0.844915	+	0.534900i	\(0.179651\pi\)
\(19\)	347.967	+	1524.54i	0.221133	+	0.968848i	0.956627	+	0.291316i	\(0.0940932\pi\)
							−0.735494	+	0.677532i	\(0.763050\pi\)
\(23\)	280.952	−	1230.93i	0.110742	−	0.485192i	−0.888891	−	0.458118i	\(-0.848524\pi\)
							0.999633	−	0.0270743i	\(-0.00861907\pi\)
\(29\)	−2611.20	+	3274.34i	−0.576560	+	0.722983i	−0.981522	−	0.191350i	\(-0.938713\pi\)
							0.404962	+	0.914334i	\(0.367285\pi\)
\(31\)	−2747.79	+	3445.62i	−0.513546	+	0.643966i	−0.969225	−	0.246178i	\(-0.920825\pi\)
							0.455679	+	0.890144i	\(0.349397\pi\)
\(37\)	4495.14			0.539807			0.269903	−	0.962887i	\(-0.413008\pi\)
							0.269903	+	0.962887i	\(0.413008\pi\)
\(41\)	−122.765	+	153.943i	−0.0114055	+	0.0143021i	−0.787502	−	0.616313i	\(-0.788626\pi\)
							0.776096	+	0.630615i	\(0.217197\pi\)
\(43\)	11145.6	+	4773.28i	0.919246	+	0.393683i
							\(47\)	−652.238	−	2857.64i	−0.0430687	−	0.188696i	0.948818	−	0.315825i	\(-0.102281\pi\)
−0.991886	+	0.127128i	\(0.959424\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.e.a.4.18	✓	108
43.11	even	7	inner	43.6.e.a.11.18	yes	108

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.e.a.4.18	✓	108	1.1	even	1	trivial
43.6.e.a.11.18	yes	108	43.11	even	7	inner