Embedded newform 43.9.d.a.7.18

• Label: 43.9.d.a.7.18
• Level: $43$
• Weight: $9$
• Character: 43.7
• Analytic conductor: $17.517$
• Analytic rank: $0$
• Dimension: $56$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(17.5172802326\)
Analytic rank:	\(0\)
Dimension:	\(56\)
Relative dimension:	\(28\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			7.18
Character	\(\chi\)	\(=\)	43.7
Dual form			43.9.d.a.37.11

$q$-expansion

\(f(q)\)	\(=\)	\(q+9.49614i q^{2} +(-65.9694 + 38.0875i) q^{3} +165.823 q^{4} +(-622.087 + 359.162i) q^{5} +(-361.684 - 626.455i) q^{6} +(2996.66 + 1730.12i) q^{7} +4005.69i q^{8} +(-379.191 + 656.777i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 84 q^{3} - 6474 q^{4} - 3 q^{5} + 1791 q^{6} - 5031 q^{7} + 57858 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{5}{6}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)			9.49614i			0.593509i	0.954954	+	0.296754i	\(0.0959042\pi\)
							−0.954954	+	0.296754i	\(0.904096\pi\)
\(3\)	−65.9694	+	38.0875i	−0.814437	+	0.470216i	−0.848494	−	0.529204i	\(-0.822491\pi\)
							0.0340572	+	0.999420i	\(0.489157\pi\)
\(5\)	−622.087	+	359.162i	−0.995339	+	0.574659i	−0.906866	−	0.421420i	\(-0.861532\pi\)
							−0.0884728	+	0.996079i	\(0.528199\pi\)
\(7\)	2996.66	+	1730.12i	1.24809	+	0.720584i	0.970728	−	0.240182i	\(-0.0772070\pi\)
							0.277360	+	0.960766i	\(0.410540\pi\)
\(11\)	−7733.05			−0.528178			−0.264089	−	0.964498i	\(-0.585071\pi\)
							−0.264089	+	0.964498i	\(0.585071\pi\)
\(13\)	−9719.12	+	16834.0i	−0.340294	+	0.589406i	−0.984487	−	0.175457i	\(-0.943860\pi\)
							0.644194	+	0.764862i	\(0.277193\pi\)
\(17\)	34393.9	−	59572.0i	0.411799	−	0.713257i	−0.583287	−	0.812266i	\(-0.698234\pi\)
							0.995087	+	0.0990085i	\(0.0315671\pi\)
\(19\)	−29752.6	+	17177.7i	−0.228302	+	0.131810i	−0.609789	−	0.792564i	\(-0.708746\pi\)
							0.381486	+	0.924375i	\(0.375412\pi\)
\(23\)	−192071.	−	332677.i	−0.686359	−	1.18881i	−0.973008	−	0.230773i	\(-0.925875\pi\)
							0.286649	−	0.958036i	\(-0.407459\pi\)
\(29\)	−353027.	−	203820.i	−0.499133	−	0.288175i	0.229222	−	0.973374i	\(-0.426382\pi\)
							−0.728355	+	0.685199i	\(0.759715\pi\)
\(31\)	−145825.	−	252577.i	−0.157901	−	0.273493i	0.776210	−	0.630474i	\(-0.217139\pi\)
							−0.934112	+	0.356981i	\(0.883806\pi\)
\(37\)	−161053.	+	92984.2i	−0.0859336	+	0.0496138i	−0.542351	−	0.840152i	\(-0.682466\pi\)
							0.456417	+	0.889766i	\(0.349132\pi\)
\(41\)	−2.57119e6			−0.909911			−0.454955	−	0.890514i	\(-0.650345\pi\)
							−0.454955	+	0.890514i	\(0.650345\pi\)
\(43\)	1.97616e6	+	2.78980e6i	0.578026	+	0.816018i
							\(47\)	−706924.			−0.144871			−0.0724354	−	0.997373i	\(-0.523077\pi\)
−0.0724354	+	0.997373i	\(0.523077\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.9.d.a.7.18	✓	56
43.37	odd	6	inner	43.9.d.a.37.11	yes	56

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.9.d.a.7.18	✓	56	1.1	even	1	trivial
43.9.d.a.37.11	yes	56	43.37	odd	6	inner