Embedded newform 43.5.h.a.18.3

• Label: 43.5.h.a.18.3
• Level: $43$
• Weight: $5$
• Character: 43.18
• 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			18.3
Character	\(\chi\)	\(=\)	43.18
Dual form			43.5.h.a.12.3

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-2.38753 + 4.95776i) q^{2} +(-4.88264 + 7.16152i) q^{3} +(-8.90321 - 11.1643i) q^{4} +(-29.1574 - 31.4242i) q^{5} +(-23.8476 - 41.3053i) q^{6} +(51.1675 + 29.5416i) q^{7} +(-9.22928 + 2.10652i) q^{8} +(2.14548 + 5.46659i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 14 q^{2} - 20 q^{3} + 220 q^{4} - 11 q^{5} - 22 q^{6} - 150 q^{7} + 322 q^{8} - 660 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{29}{42}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−2.38753	+	4.95776i	−0.596882	+	1.23944i	0.355541	+	0.934661i	\(0.384297\pi\)
							−0.952423	+	0.304778i	\(0.901418\pi\)
\(3\)	−4.88264	+	7.16152i	−0.542515	+	0.795724i	−0.995396	−	0.0958472i	\(-0.969444\pi\)
							0.452881	+	0.891571i	\(0.350396\pi\)
\(5\)	−29.1574	−	31.4242i	−1.16629	−	1.25697i	−0.960472	−	0.278378i	\(-0.910203\pi\)
							−0.205823	−	0.978589i	\(-0.565987\pi\)
\(7\)	51.1675	+	29.5416i	1.04424	+	0.602890i	0.921030	−	0.389492i	\(-0.127349\pi\)
							0.123205	+	0.992381i	\(0.460683\pi\)
\(11\)	69.0352	−	86.5674i	0.570539	−	0.715433i	−0.409928	−	0.912118i	\(-0.634446\pi\)
							0.980467	+	0.196685i	\(0.0630175\pi\)
\(13\)	−319.902	−	98.6768i	−1.89291	−	0.583887i	−0.987074	−	0.160268i	\(-0.948764\pi\)
							−0.905841	−	0.423619i	\(-0.860760\pi\)
\(17\)	−89.1035	−	82.6759i	−0.308317	−	0.286076i	0.510804	−	0.859697i	\(-0.329348\pi\)
							−0.819121	+	0.573621i	\(0.805538\pi\)
\(19\)	125.206	+	49.1396i	0.346830	+	0.136121i	0.532360	−	0.846518i	\(-0.321305\pi\)
							−0.185530	+	0.982639i	\(0.559400\pi\)
\(23\)	−770.262	−	116.098i	−1.45607	−	0.219468i	−0.627179	−	0.778875i	\(-0.715791\pi\)
							−0.828893	+	0.559407i	\(0.811029\pi\)
\(29\)	−352.302	−	516.732i	−0.418908	−	0.614425i	0.557547	−	0.830145i	\(-0.311743\pi\)
							−0.976455	+	0.215720i	\(0.930790\pi\)
\(31\)	52.0504	+	694.564i	0.0541627	+	0.722751i	0.956502	+	0.291725i	\(0.0942293\pi\)
							−0.902339	+	0.431026i	\(0.858152\pi\)
\(37\)	−574.411	+	331.636i	−0.419584	+	0.242247i	−0.694899	−	0.719107i	\(-0.744551\pi\)
							0.275315	+	0.961354i	\(0.411218\pi\)
\(41\)	0.785587	+	0.378319i	0.000467333	+	0.000225056i	0.434117	−	0.900856i	\(-0.357060\pi\)
							−0.433650	+	0.901081i	\(0.642775\pi\)
\(43\)	154.967	+	1842.49i	0.0838113	+	0.996482i
							\(47\)	253.845	+	318.312i	0.114914	+	0.144098i	0.835962	−	0.548788i	\(-0.184911\pi\)
−0.721048	+	0.692886i	\(0.756339\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.5.h.a.18.3	yes	168
43.12	odd	42	inner	43.5.h.a.12.3	✓	168

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.5.h.a.12.3	✓	168	43.12	odd	42	inner
43.5.h.a.18.3	yes	168	1.1	even	1	trivial