Embedded newform 43.10.c.a.36.12

• Label: 43.10.c.a.36.12
• Level: $43$
• Weight: $10$
• Character: 43.36
• 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			36.12
Character	\(\chi\)	\(=\)	43.36
Dual form			43.10.c.a.6.12

$q$-expansion

\(f(q)\)	\(=\)	\(q-12.6048 q^{2} +(108.034 + 187.120i) q^{3} -353.118 q^{4} +(242.203 + 419.508i) q^{5} +(-1361.75 - 2358.62i) q^{6} +(-2218.86 + 3843.18i) q^{7} +10904.7 q^{8} +(-13501.1 + 23384.6i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 70 q^{2} + 307 q^{3} + 16038 q^{4} + 681 q^{5} - 1281 q^{6} + 957 q^{7} - 10920 q^{8} - 255339 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{1}{3}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−12.6048			−0.557060			−0.278530	−	0.960428i	\(-0.589847\pi\)
							−0.278530	+	0.960428i	\(0.589847\pi\)
\(3\)	108.034	+	187.120i	0.770042	+	1.33375i	0.937540	+	0.347879i	\(0.113098\pi\)
							−0.167498	+	0.985872i	\(0.553569\pi\)
\(5\)	242.203	+	419.508i	0.173306	+	0.300175i	0.939574	−	0.342346i	\(-0.111222\pi\)
							−0.766268	+	0.642522i	\(0.777888\pi\)
\(7\)	−2218.86	+	3843.18i	−0.349292	+	0.604992i	−0.986124	−	0.166011i	\(-0.946911\pi\)
							0.636832	+	0.771003i	\(0.280245\pi\)
\(11\)	−46033.7			−0.948000			−0.474000	−	0.880525i	\(-0.657190\pi\)
							−0.474000	+	0.880525i	\(0.657190\pi\)
\(13\)	−85447.2	+	147999.i	−0.829761	+	1.43719i	0.0684648	+	0.997654i	\(0.478190\pi\)
							−0.898226	+	0.439534i	\(0.855143\pi\)
\(17\)	229801.	−	398026.i	0.667315	−	1.15582i	−0.311337	−	0.950300i	\(-0.600777\pi\)
							0.978652	−	0.205524i	\(-0.0658900\pi\)
\(19\)	470311.	+	814602.i	0.827930	+	1.43402i	0.899659	+	0.436593i	\(0.143815\pi\)
							−0.0717285	+	0.997424i	\(0.522852\pi\)
\(23\)	−1.06052e6	−	1.83688e6i	−0.790214	−	1.36869i	−0.925834	−	0.377929i	\(-0.876636\pi\)
							0.135621	−	0.990761i	\(-0.456697\pi\)
\(29\)	−2.59539e6	+	4.49535e6i	−0.681416	+	1.18025i	0.293133	+	0.956072i	\(0.405302\pi\)
							−0.974549	+	0.224175i	\(0.928031\pi\)
\(31\)	−3.99146e6	−	6.91341e6i	−0.776254	−	1.34451i	−0.934087	−	0.357046i	\(-0.883784\pi\)
							0.157833	−	0.987466i	\(-0.449549\pi\)
\(37\)	−6.10681e6	−	1.05773e7i	−0.535681	−	0.927827i	−0.999130	−	0.0417033i	\(-0.986722\pi\)
							0.463449	−	0.886124i	\(-0.346612\pi\)
\(41\)	2.75796e6			0.152426			0.0762132	−	0.997092i	\(-0.475717\pi\)
							0.0762132	+	0.997092i	\(0.475717\pi\)
\(43\)	2.20309e7	−	4.15126e6i	0.982706	−	0.185171i
							\(47\)	1.31583e7			0.393331			0.196666	−	0.980471i	\(-0.436989\pi\)
0.196666	+	0.980471i	\(0.436989\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.c.a.36.12	yes	64
43.6	even	3	inner	43.10.c.a.6.12	✓	64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.c.a.6.12	✓	64	43.6	even	3	inner
43.10.c.a.36.12	yes	64	1.1	even	1	trivial