Embedded newform 43.6.c.a.36.11

• Label: 43.6.c.a.36.11
• Level: $43$
• Weight: $6$
• Character: 43.36
• 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			36.11
Character	\(\chi\)	\(=\)	43.36
Dual form			43.6.c.a.6.11

$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

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

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	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	−0.943636	−	0.330985i	\(-0.892619\pi\)
							0.185176	−	0.982705i	\(-0.440714\pi\)
\(5\)	21.7696	+	37.7061i	0.389427	+	0.674507i	0.992373	−	0.123275i	\(-0.0393398\pi\)
							−0.602946	+	0.797782i	\(0.706006\pi\)
\(7\)	−19.0405	+	32.9792i	−0.146870	+	0.254387i	−0.930069	−	0.367384i	\(-0.880253\pi\)
							0.783199	+	0.621771i	\(0.213587\pi\)
\(11\)	−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	0.439629	+	0.898179i	\(0.355110\pi\)
							−0.997661	+	0.0683599i	\(0.978223\pi\)
\(17\)	541.066	−	937.154i	0.454075	−	0.786482i	−0.544559	−	0.838722i	\(-0.683303\pi\)
							0.998635	+	0.0522407i	\(0.0166363\pi\)
\(19\)	−1273.64	−	2206.01i	−0.809400	−	1.40192i	−0.913280	−	0.407332i	\(-0.866459\pi\)
							0.103880	−	0.994590i	\(-0.466874\pi\)
\(23\)	498.242	+	862.980i	0.196391	+	0.340158i	0.947355	−	0.320184i	\(-0.103745\pi\)
							−0.750965	+	0.660342i	\(0.770411\pi\)
\(29\)	−2082.57	+	3607.12i	−0.459838	+	0.796464i	−0.998952	−	0.0457695i	\(-0.985426\pi\)
							0.539114	+	0.842233i	\(0.318759\pi\)
\(31\)	−3780.97	−	6548.83i	−0.706641	−	1.22394i	−0.966096	−	0.258183i	\(-0.916876\pi\)
							0.259455	−	0.965755i	\(-0.416457\pi\)
\(37\)	−2346.41	−	4064.10i	−0.281773	−	0.488045i	0.690048	−	0.723763i	\(-0.257589\pi\)
							−0.971822	+	0.235718i	\(0.924256\pi\)
\(41\)	−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.36.11	yes	34
43.6	even	3	inner	43.6.c.a.6.11	✓	34

    

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