Embedded newform 43.6.c.a.6.4

• Label: 43.6.c.a.6.4
• Level: $43$
• Weight: $6$
• Character: 43.6
• Analytic conductor: $6.897$
• Analytic rank: $0$
• Dimension: $34$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	43.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.89650425196\)
Analytic rank:	\(0\)
Dimension:	\(34\)
Relative dimension:	\(17\) over \(\Q(\zeta_{3})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			6.4
Character	\(\chi\)	\(=\)	43.6
Dual form			43.6.c.a.36.4

$q$-expansion

\(f(q)\)	\(=\)	\(q-8.35737 q^{2} +(-3.42253 + 5.92800i) q^{3} +37.8456 q^{4} +(-28.3920 + 49.1763i) q^{5} +(28.6033 - 49.5425i) q^{6} +(46.8510 + 81.1483i) q^{7} -48.8539 q^{8} +(98.0726 + 169.867i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 14 q^{2} - 14 q^{3} + 454 q^{4} + 71 q^{5} + 15 q^{6} + 225 q^{7} - 936 q^{8} - 1011 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−8.35737			−1.47739			−0.738694	−	0.674041i	\(-0.764557\pi\)
							−0.738694	+	0.674041i	\(0.764557\pi\)
\(3\)	−3.42253	+	5.92800i	−0.219555	+	0.380281i	−0.954672	−	0.297659i	\(-0.903794\pi\)
							0.735117	+	0.677941i	\(0.237127\pi\)
\(5\)	−28.3920	+	49.1763i	−0.507891	+	0.879693i	0.492067	+	0.870557i	\(0.336241\pi\)
							−0.999958	+	0.00913576i	\(0.997092\pi\)
\(7\)	46.8510	+	81.1483i	0.361388	+	0.625943i	0.988190	−	0.153236i	\(-0.0489696\pi\)
							−0.626801	+	0.779179i	\(0.715636\pi\)
\(11\)	−458.660			−1.14290			−0.571451	−	0.820636i	\(-0.693619\pi\)
							−0.571451	+	0.820636i	\(0.693619\pi\)
\(13\)	−575.015	−	995.955i	−0.943671	−	1.63449i	−0.758390	−	0.651801i	\(-0.774014\pi\)
							−0.185281	−	0.982686i	\(-0.559320\pi\)
\(17\)	130.007	+	225.178i	0.109105	+	0.188975i	0.915408	−	0.402528i	\(-0.131868\pi\)
							−0.806303	+	0.591503i	\(0.798535\pi\)
\(19\)	788.988	−	1366.57i	0.501403	−	0.868455i	−0.498596	−	0.866834i	\(-0.666151\pi\)
							0.999999	−	0.00162026i	\(-0.000515744\pi\)
\(23\)	−825.957	+	1430.60i	−0.325565	+	0.563895i	−0.981627	−	0.190812i	\(-0.938888\pi\)
							0.656062	+	0.754707i	\(0.272221\pi\)
\(29\)	−2565.15	−	4442.97i	−0.566393	−	0.981021i	−0.996919	−	0.0784425i	\(-0.975005\pi\)
							0.430526	−	0.902578i	\(-0.358328\pi\)
\(31\)	2875.50	−	4980.52i	0.537415	−	0.930829i	−0.461628	−	0.887074i	\(-0.652734\pi\)
							0.999042	−	0.0437555i	\(-0.0139323\pi\)
\(37\)	−4113.59	+	7124.94i	−0.493988	+	0.855613i	−0.999976	−	0.00692807i	\(-0.997795\pi\)
							0.505988	+	0.862541i	\(0.331128\pi\)
\(41\)	2696.36			0.250506			0.125253	−	0.992125i	\(-0.460026\pi\)
							0.125253	+	0.992125i	\(0.460026\pi\)
\(43\)	−359.727	−	12119.4i	−0.0296689	−	0.999560i
							\(47\)	−18376.8			−1.21346			−0.606729	−	0.794909i	\(-0.707518\pi\)
−0.606729	+	0.794909i	\(0.707518\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.c.a.6.4	✓	34
43.36	even	3	inner	43.6.c.a.36.4	yes	34

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.c.a.6.4	✓	34	1.1	even	1	trivial
43.6.c.a.36.4	yes	34	43.36	even	3	inner