Embedded newform 43.10.c.a.6.20

• Label: 43.10.c.a.6.20
• Level: $43$
• Weight: $10$
• Character: 43.6
• Analytic conductor: $22.147$
• Analytic rank: $0$
• Dimension: $64$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	43.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(22.1465409550\)
Analytic rank:	\(0\)
Dimension:	\(64\)
Relative dimension:	\(32\) over \(\Q(\zeta_{3})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			6.20
Character	\(\chi\)	\(=\)	43.6
Dual form			43.10.c.a.36.20

$q$-expansion

\(f(q)\)	\(=\)	\(q+4.33792 q^{2} +(-9.83652 + 17.0374i) q^{3} -493.182 q^{4} +(215.967 - 374.066i) q^{5} +(-42.6701 + 73.9068i) q^{6} +(2230.56 + 3863.44i) q^{7} -4360.41 q^{8} +(9647.99 + 16710.8i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 70 q^{2} + 307 q^{3} + 16038 q^{4} + 681 q^{5} - 1281 q^{6} + 957 q^{7} - 10920 q^{8} - 255339 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{2}{3}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	4.33792			0.191711			0.0958555	−	0.995395i	\(-0.469441\pi\)
							0.0958555	+	0.995395i	\(0.469441\pi\)
\(3\)	−9.83652	+	17.0374i	−0.0701126	+	0.121439i	−0.898950	−	0.438050i	\(-0.855669\pi\)
							0.828838	+	0.559489i	\(0.189003\pi\)
\(5\)	215.967	−	374.066i	0.154533	−	0.267660i	−0.778356	−	0.627824i	\(-0.783946\pi\)
							0.932889	+	0.360164i	\(0.117279\pi\)
\(7\)	2230.56	+	3863.44i	0.351134	+	0.608181i	0.986448	−	0.164072i	\(-0.0524629\pi\)
							−0.635315	+	0.772253i	\(0.719130\pi\)
\(11\)	−27416.0			−0.564595			−0.282297	−	0.959327i	\(-0.591097\pi\)
							−0.282297	+	0.959327i	\(0.591097\pi\)
\(13\)	−46001.4	−	79676.7i	−0.446710	−	0.773724i	0.551460	−	0.834202i	\(-0.314071\pi\)
							−0.998170	+	0.0604772i	\(0.980738\pi\)
\(17\)	−200882.	−	347939.i	−0.583340	−	1.01037i	−0.995080	−	0.0990735i	\(-0.968412\pi\)
							0.411740	−	0.911301i	\(-0.364921\pi\)
\(19\)	390211.	−	675865.i	0.686923	−	1.18978i	−0.285906	−	0.958258i	\(-0.592294\pi\)
							0.972828	−	0.231527i	\(-0.0743722\pi\)
\(23\)	576163.	−	997943.i	0.429309	−	0.743585i	−0.567503	−	0.823371i	\(-0.692090\pi\)
							0.996812	+	0.0797864i	\(0.0254238\pi\)
\(29\)	−1.36339e6	−	2.36146e6i	−0.357955	−	0.619997i	0.629664	−	0.776868i	\(-0.283193\pi\)
							−0.987619	+	0.156871i	\(0.949859\pi\)
\(31\)	2.80533e6	−	4.85898e6i	0.545578	−	0.944969i	−0.452992	−	0.891514i	\(-0.649643\pi\)
							0.998570	−	0.0534545i	\(-0.0170232\pi\)
\(37\)	5.55400e6	−	9.61980e6i	0.487189	−	0.843837i	−0.512702	−	0.858567i	\(-0.671355\pi\)
							0.999892	+	0.0147298i	\(0.00468881\pi\)
\(41\)	8.96775e6			0.495628			0.247814	−	0.968808i	\(-0.420288\pi\)
							0.247814	+	0.968808i	\(0.420288\pi\)
\(43\)	−1.88438e7	−	1.21451e7i	−0.840543	−	0.541744i
							\(47\)	−3.27725e7			−0.979646			−0.489823	−	0.871822i	\(-0.662939\pi\)
−0.489823	+	0.871822i	\(0.662939\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.c.a.6.20	✓	64
43.36	even	3	inner	43.10.c.a.36.20	yes	64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.c.a.6.20	✓	64	1.1	even	1	trivial
43.10.c.a.36.20	yes	64	43.36	even	3	inner