Embedded newform 43.10.g.a.24.15

• Label: 43.10.g.a.24.15
• Level: $43$
• Weight: $10$
• Character: 43.24
• Analytic conductor: $22.147$
• Analytic rank: $0$
• Dimension: $384$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	43.g (of order \(21\), degree \(12\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(22.1465409550\)
Analytic rank:	\(0\)
Dimension:	\(384\)
Relative dimension:	\(32\) over \(\Q(\zeta_{21})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			24.15
Character	\(\chi\)	\(=\)	43.24
Dual form			43.10.g.a.9.15

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-4.32399 + 5.42212i) q^{2} +(83.5118 - 12.5874i) q^{3} +(103.228 + 452.273i) q^{4} +(-697.274 + 475.394i) q^{5} +(-292.854 + 507.238i) q^{6} +(3015.21 + 5222.49i) q^{7} +(-6097.79 - 2936.54i) q^{8} +(-11992.8 + 3699.28i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + 56 q^{2} - 321 q^{3} - 16052 q^{4} - 695 q^{5} + 1274 q^{6} + 32650 q^{7} - 50022 q^{8} + 373611 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{20}{21}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−4.32399	+	5.42212i	−0.191095	+	0.239626i	−0.868144	−	0.496312i	\(-0.834687\pi\)
							0.677049	+	0.735938i	\(0.263259\pi\)
\(3\)	83.5118	−	12.5874i	0.595253	−	0.0897200i	0.155496	−	0.987837i	\(-0.450302\pi\)
							0.439758	+	0.898117i	\(0.355064\pi\)
\(5\)	−697.274	+	475.394i	−0.498929	+	0.340164i	−0.786495	−	0.617597i	\(-0.788106\pi\)
							0.287566	+	0.957761i	\(0.407154\pi\)
\(7\)	3015.21	+	5222.49i	0.474653	+	0.822123i	0.999579	−	0.0290251i	\(-0.00924028\pi\)
							−0.524926	+	0.851148i	\(0.675907\pi\)
\(11\)	−6452.18	+	28268.9i	−0.132874	+	0.582159i	0.864024	+	0.503451i	\(0.167937\pi\)
							−0.996898	+	0.0787077i	\(0.974921\pi\)
\(13\)	−10990.0	−	146652.i	−0.106722	−	1.42411i	−0.751498	−	0.659735i	\(-0.770669\pi\)
							0.644776	−	0.764371i	\(-0.276951\pi\)
\(17\)	−58486.9	−	39875.7i	−0.169839	−	0.115794i	0.475417	−	0.879760i	\(-0.342297\pi\)
							−0.645257	+	0.763966i	\(0.723250\pi\)
\(19\)	797406.	+	245967.i	1.40374	+	0.432998i	0.901894	−	0.431956i	\(-0.142177\pi\)
							0.501850	+	0.864954i	\(0.332653\pi\)
\(23\)	−644771.	−	598260.i	−0.480430	−	0.445774i	0.402402	−	0.915463i	\(-0.368176\pi\)
							−0.882832	+	0.469689i	\(0.844366\pi\)
\(29\)	−5.34099e6	−	805025.i	−1.40227	−	0.211358i	−0.596036	−	0.802958i	\(-0.703258\pi\)
							−0.806232	+	0.591600i	\(0.798497\pi\)
\(31\)	−3.04664e6	−	7.76271e6i	−0.592507	−	1.50968i	−0.840992	−	0.541047i	\(-0.818028\pi\)
							0.248485	−	0.968636i	\(-0.420067\pi\)
\(37\)	−3.49242e6	+	6.04905e6i	−0.306350	+	0.530615i	−0.977561	−	0.210652i	\(-0.932441\pi\)
							0.671211	+	0.741267i	\(0.265775\pi\)
\(41\)	−1.74301e7	+	2.18567e7i	−0.963324	+	1.20797i	0.0147877	+	0.999891i	\(0.495293\pi\)
							−0.978112	+	0.208080i	\(0.933279\pi\)
\(43\)	−1.64853e6	−	2.23579e7i	−0.0735341	−	0.997293i
							\(47\)	1.37646e7	+	6.03068e7i	0.411457	+	1.80271i	0.577271	+	0.816553i	\(0.304118\pi\)
−0.165814	+	0.986157i	\(0.553025\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.g.a.24.15	yes	384
43.9	even	21	inner	43.10.g.a.9.15	✓	384

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.g.a.9.15	✓	384	43.9	even	21	inner
43.10.g.a.24.15	yes	384	1.1	even	1	trivial