Embedded newform 43.10.g.a.24.18

• Label: 43.10.g.a.24.18
• 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			24.18
Character	\(\chi\)	\(=\)	43.24
Dual form			43.10.g.a.9.18

$q$-expansion

\(f(q)\)	\(=\)	\(q+(3.74995 - 4.70229i) q^{2} +(29.2285 - 4.40549i) q^{3} +(105.881 + 463.896i) q^{4} +(328.917 - 224.252i) q^{5} +(88.8898 - 153.962i) q^{6} +(2917.98 + 5054.09i) q^{7} +(5352.87 + 2577.81i) q^{8} +(-17973.6 + 5544.13i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + 56 q^{2} - 321 q^{3} - 16052 q^{4} - 695 q^{5} + 1274 q^{6} + 32650 q^{7} - 50022 q^{8} + 373611 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	3.74995	−	4.70229i	0.165726	−	0.207814i	−0.692033	−	0.721866i	\(-0.743285\pi\)
							0.857759	+	0.514052i	\(0.171856\pi\)
\(3\)	29.2285	−	4.40549i	0.208335	−	0.0314014i	−0.0440457	−	0.999030i	\(-0.514025\pi\)
							0.252380	+	0.967628i	\(0.418787\pi\)
\(5\)	328.917	−	224.252i	0.235354	−	0.160462i	−0.439900	−	0.898047i	\(-0.644986\pi\)
							0.675254	+	0.737585i	\(0.264034\pi\)
\(7\)	2917.98	+	5054.09i	0.459347	+	0.795612i	0.998927	−	0.0463224i	\(-0.0147501\pi\)
							−0.539580	+	0.841935i	\(0.681417\pi\)
\(11\)	11485.7	−	50322.0i	0.236531	−	1.03631i	−0.707566	−	0.706647i	\(-0.750207\pi\)
							0.944098	−	0.329665i	\(-0.106936\pi\)
\(13\)	10237.6	+	136611.i	0.0994149	+	1.32660i	0.794321	+	0.607499i	\(0.207827\pi\)
							−0.694906	+	0.719101i	\(0.744554\pi\)
\(17\)	−245586.	−	167437.i	−0.713153	−	0.486219i	0.151584	−	0.988444i	\(-0.451563\pi\)
							−0.864737	+	0.502225i	\(0.832515\pi\)
\(19\)	−476246.	−	146903.i	−0.838379	−	0.258606i	−0.154310	−	0.988023i	\(-0.549315\pi\)
							−0.684070	+	0.729417i	\(0.739792\pi\)
\(23\)	1.37504e6	+	1.27585e6i	1.02457	+	0.950658i	0.998798	−	0.0490105i	\(-0.0156068\pi\)
							0.0257669	+	0.999668i	\(0.491797\pi\)
\(29\)	2.86487e6	+	431810.i	0.752167	+	0.113371i	0.513925	−	0.857835i	\(-0.328191\pi\)
							0.238242	+	0.971206i	\(0.423429\pi\)
\(31\)	397917.	+	1.01388e6i	0.0773865	+	0.197178i	0.964332	−	0.264697i	\(-0.0852721\pi\)
							−0.886945	+	0.461875i	\(0.847177\pi\)
\(37\)	−1.11916e7	+	1.93844e7i	−0.981712	+	1.70038i	−0.325989	+	0.945374i	\(0.605697\pi\)
							−0.655723	+	0.755002i	\(0.727636\pi\)
\(41\)	−1.69923e7	+	2.13076e7i	−0.939127	+	1.17763i	0.0447889	+	0.998996i	\(0.485738\pi\)
							−0.983916	+	0.178632i	\(0.942833\pi\)
\(43\)	2.20579e7	−	4.00520e6i	0.983912	−	0.178655i
							\(47\)	−3.75046e6	−	1.64318e7i	−0.112110	−	0.491185i	−0.999542	−	0.0302479i	\(-0.990370\pi\)
0.887433	−	0.460938i	\(-0.152487\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.g.a.24.18	yes	384
43.9	even	21	inner	43.10.g.a.9.18	✓	384

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.g.a.9.18	✓	384	43.9	even	21	inner
43.10.g.a.24.18	yes	384	1.1	even	1	trivial