Embedded newform 43.6.c.a.6.11

• Label: 43.6.c.a.6.11
• 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			6.11
Character	\(\chi\)	\(=\)	43.6
Dual form			43.6.c.a.36.11

$q$-expansion

\(f(q)\)	\(=\)	\(q+3.69441 q^{2} +(-11.8232 + 20.4784i) q^{3} -18.3513 q^{4} +(21.7696 - 37.7061i) q^{5} +(-43.6798 + 75.6556i) q^{6} +(-19.0405 - 32.9792i) q^{7} -186.018 q^{8} +(-158.077 - 273.797i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 14 q^{2} - 14 q^{3} + 454 q^{4} + 71 q^{5} + 15 q^{6} + 225 q^{7} - 936 q^{8} - 1011 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	3.69441			0.653085			0.326543	−	0.945182i	\(-0.394116\pi\)
							0.326543	+	0.945182i	\(0.394116\pi\)
\(3\)	−11.8232	+	20.4784i	−0.758460	+	1.31369i	0.185176	+	0.982705i	\(0.440714\pi\)
							−0.943636	+	0.330985i	\(0.892619\pi\)
\(5\)	21.7696	−	37.7061i	0.389427	−	0.674507i	−0.602946	−	0.797782i	\(-0.706006\pi\)
							0.992373	+	0.123275i	\(0.0393398\pi\)
\(7\)	−19.0405	−	32.9792i	−0.146870	−	0.254387i	0.783199	−	0.621771i	\(-0.213587\pi\)
							−0.930069	+	0.367384i	\(0.880253\pi\)
\(11\)	−444.024			−1.10643			−0.553216	−	0.833038i	\(-0.686599\pi\)
							−0.553216	+	0.833038i	\(0.686599\pi\)
\(13\)	−340.030	−	588.949i	−0.558032	−	0.966539i	−0.997661	−	0.0683599i	\(-0.978223\pi\)
							0.439629	−	0.898179i	\(-0.355110\pi\)
\(17\)	541.066	+	937.154i	0.454075	+	0.786482i	0.998635	−	0.0522407i	\(-0.0166363\pi\)
							−0.544559	+	0.838722i	\(0.683303\pi\)
\(19\)	−1273.64	+	2206.01i	−0.809400	+	1.40192i	0.103880	+	0.994590i	\(0.466874\pi\)
							−0.913280	+	0.407332i	\(0.866459\pi\)
\(23\)	498.242	−	862.980i	0.196391	−	0.340158i	−0.750965	−	0.660342i	\(-0.770411\pi\)
							0.947355	+	0.320184i	\(0.103745\pi\)
\(29\)	−2082.57	−	3607.12i	−0.459838	−	0.796464i	0.539114	−	0.842233i	\(-0.318759\pi\)
							−0.998952	+	0.0457695i	\(0.985426\pi\)
\(31\)	−3780.97	+	6548.83i	−0.706641	+	1.22394i	0.259455	+	0.965755i	\(0.416457\pi\)
							−0.966096	+	0.258183i	\(0.916876\pi\)
\(37\)	−2346.41	+	4064.10i	−0.281773	+	0.488045i	−0.971822	−	0.235718i	\(-0.924256\pi\)
							0.690048	+	0.723763i	\(0.257589\pi\)
\(41\)	−6616.86			−0.614741			−0.307370	−	0.951590i	\(-0.599449\pi\)
							−0.307370	+	0.951590i	\(0.599449\pi\)
\(43\)	4133.94	−	11398.2i	0.340952	−	0.940081i
							\(47\)	−7398.21			−0.488520			−0.244260	−	0.969710i	\(-0.578545\pi\)
−0.244260	+	0.969710i	\(0.578545\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.c.a.6.11	✓	34
43.36	even	3	inner	43.6.c.a.36.11	yes	34

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.c.a.6.11	✓	34	1.1	even	1	trivial
43.6.c.a.36.11	yes	34	43.36	even	3	inner