Embedded newform 43.5.h.a.26.5

• Label: 43.5.h.a.26.5
• Level: $43$
• Weight: $5$
• Character: 43.26
• Analytic conductor: $4.445$
• Analytic rank: $0$
• Dimension: $168$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	43.h (of order \(42\), degree \(12\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.44490841261\)
Analytic rank:	\(0\)
Dimension:	\(168\)
Relative dimension:	\(14\) over \(\Q(\zeta_{42})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			26.5
Character	\(\chi\)	\(=\)	43.26
Dual form			43.5.h.a.5.5

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-3.69887 + 0.844242i) q^{2} +(-0.654121 - 2.12061i) q^{3} +(-1.44664 + 0.696665i) q^{4} +(5.40819 + 2.12256i) q^{5} +(4.20981 + 7.29161i) q^{6} +(-10.8272 - 6.25106i) q^{7} +(52.2229 - 41.6464i) q^{8} +(62.8562 - 42.8547i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 14 q^{2} - 20 q^{3} + 220 q^{4} - 11 q^{5} - 22 q^{6} - 150 q^{7} + 322 q^{8} - 660 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{17}{42}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−3.69887	+	0.844242i	−0.924716	+	0.211060i	−0.658264	−	0.752788i	\(-0.728709\pi\)
							−0.266453	+	0.963848i	\(0.585852\pi\)
\(3\)	−0.654121	−	2.12061i	−0.0726801	−	0.235623i	0.911942	−	0.410318i	\(-0.134582\pi\)
							−0.984623	+	0.174695i	\(0.944106\pi\)
\(5\)	5.40819	+	2.12256i	0.216327	+	0.0849023i	0.471030	−	0.882117i	\(-0.343882\pi\)
							−0.254703	+	0.967019i	\(0.581978\pi\)
\(7\)	−10.8272	−	6.25106i	−0.220962	−	0.127573i	0.385433	−	0.922736i	\(-0.374052\pi\)
							−0.606396	+	0.795163i	\(0.707385\pi\)
\(11\)	63.6004	+	30.6284i	0.525623	+	0.253127i	0.677826	−	0.735222i	\(-0.262922\pi\)
							−0.152202	+	0.988349i	\(0.548637\pi\)
\(13\)	299.518	−	45.1450i	1.77229	−	0.267130i	0.820011	−	0.572348i	\(-0.193967\pi\)
							0.952282	+	0.305218i	\(0.0987294\pi\)
\(17\)	−118.216	−	301.209i	−0.409052	−	1.04225i	−0.975860	−	0.218397i	\(-0.929917\pi\)
							0.566809	−	0.823850i	\(-0.308178\pi\)
\(19\)	36.3637	−	53.3357i	0.100730	−	0.147744i	−0.772565	−	0.634936i	\(-0.781026\pi\)
							0.873295	+	0.487192i	\(0.161979\pi\)
\(23\)	40.3512	+	538.450i	0.0762783	+	1.01786i	0.895696	+	0.444667i	\(0.146678\pi\)
							−0.819418	+	0.573197i	\(0.805703\pi\)
\(29\)	−203.122	+	658.505i	−0.241524	+	0.783003i	0.750929	+	0.660383i	\(0.229606\pi\)
							−0.992454	+	0.122620i	\(0.960870\pi\)
\(31\)	954.166	−	885.337i	0.992889	−	0.921266i	−0.00400756	−	0.999992i	\(-0.501276\pi\)
							0.996896	+	0.0787258i	\(0.0250852\pi\)
\(37\)	1674.41	−	966.721i	1.22309	−	0.706152i	0.257515	−	0.966274i	\(-0.417096\pi\)
							0.965576	+	0.260123i	\(0.0837631\pi\)
\(41\)	21.8858	+	95.8880i	0.0130195	+	0.0570422i	0.981020	−	0.193905i	\(-0.0621152\pi\)
							−0.968001	+	0.250947i	\(0.919258\pi\)
\(43\)	1550.66	+	1007.10i	0.838650	+	0.544670i
							\(47\)	330.926	−	159.365i	0.149808	−	0.0721437i	−0.357478	−	0.933922i	\(-0.616363\pi\)
0.507286	+	0.861778i	\(0.330649\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.5.h.a.26.5	yes	168
43.5	odd	42	inner	43.5.h.a.5.5	✓	168

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.5.h.a.5.5	✓	168	43.5	odd	42	inner
43.5.h.a.26.5	yes	168	1.1	even	1	trivial