Embedded newform 43.6.c.a.6.7

• Label: 43.6.c.a.6.7
• 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			6.7
Character	\(\chi\)	\(=\)	43.6
Dual form			43.6.c.a.36.7

$q$-expansion

\(f(q)\)	\(=\)	\(q-3.30883 q^{2} +(-12.3585 + 21.4055i) q^{3} -21.0516 q^{4} +(-32.1287 + 55.6486i) q^{5} +(40.8922 - 70.8273i) q^{6} +(-2.83477 - 4.90997i) q^{7} +175.539 q^{8} +(-183.964 - 318.635i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 14 q^{2} - 14 q^{3} + 454 q^{4} + 71 q^{5} + 15 q^{6} + 225 q^{7} - 936 q^{8} - 1011 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−3.30883			−0.584925			−0.292462	−	0.956277i	\(-0.594475\pi\)
							−0.292462	+	0.956277i	\(0.594475\pi\)
\(3\)	−12.3585	+	21.4055i	−0.792797	+	1.37316i	0.131431	+	0.991325i	\(0.458043\pi\)
							−0.924229	+	0.381840i	\(0.875291\pi\)
\(5\)	−32.1287	+	55.6486i	−0.574736	+	0.995472i	0.421334	+	0.906905i	\(0.361562\pi\)
							−0.996070	+	0.0885663i	\(0.971771\pi\)
\(7\)	−2.83477	−	4.90997i	−0.0218662	−	0.0378734i	0.854885	−	0.518817i	\(-0.173627\pi\)
							−0.876751	+	0.480944i	\(0.840294\pi\)
\(11\)	−20.0109			−0.0498638			−0.0249319	−	0.999689i	\(-0.507937\pi\)
							−0.0249319	+	0.999689i	\(0.507937\pi\)
\(13\)	308.316	+	534.019i	0.505985	+	0.876392i	0.999976	+	0.00692491i	\(0.00220428\pi\)
							−0.493991	+	0.869467i	\(0.664462\pi\)
\(17\)	−987.938	−	1711.16i	−0.829101	−	1.43605i	−0.898744	−	0.438473i	\(-0.855519\pi\)
							0.0696433	−	0.997572i	\(-0.477814\pi\)
\(19\)	−488.757	+	846.552i	−0.310605	+	0.537984i	−0.978494	−	0.206277i	\(-0.933865\pi\)
							0.667888	+	0.744262i	\(0.267198\pi\)
\(23\)	−165.175	+	286.091i	−0.0651065	+	0.112768i	−0.896741	−	0.442555i	\(-0.854072\pi\)
							0.831635	+	0.555323i	\(0.187405\pi\)
\(29\)	4087.98	+	7080.58i	0.902638	+	1.56341i	0.824057	+	0.566507i	\(0.191705\pi\)
							0.0785806	+	0.996908i	\(0.474961\pi\)
\(31\)	2161.10	−	3743.14i	0.403897	−	0.699571i	−0.590295	−	0.807188i	\(-0.700989\pi\)
							0.994192	+	0.107617i	\(0.0343219\pi\)
\(37\)	3707.25	−	6421.15i	0.445193	−	0.771096i	−0.552873	−	0.833265i	\(-0.686469\pi\)
							0.998066	+	0.0621694i	\(0.0198019\pi\)
\(41\)	−18961.8			−1.76165			−0.880826	−	0.473440i	\(-0.843012\pi\)
							−0.880826	+	0.473440i	\(0.843012\pi\)
\(43\)	−8008.53	−	9103.40i	−0.660513	−	0.750814i
							\(47\)	−7983.99			−0.527200			−0.263600	−	0.964632i	\(-0.584910\pi\)
−0.263600	+	0.964632i	\(0.584910\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.c.a.6.7	✓	34
43.36	even	3	inner	43.6.c.a.36.7	yes	34

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.c.a.6.7	✓	34	1.1	even	1	trivial
43.6.c.a.36.7	yes	34	43.36	even	3	inner