Embedded newform 43.10.c.a.36.13

• Label: 43.10.c.a.36.13
• 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			36.13
Character	\(\chi\)	\(=\)	43.36
Dual form			43.10.c.a.6.13

$q$-expansion

\(f(q)\)	\(=\)	\(q-11.0082 q^{2} +(-0.196357 - 0.340100i) q^{3} -390.819 q^{4} +(-1072.23 - 1857.16i) q^{5} +(2.16154 + 3.74389i) q^{6} +(3698.39 - 6405.81i) q^{7} +9938.43 q^{8} +(9841.42 - 17045.8i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 70 q^{2} + 307 q^{3} + 16038 q^{4} + 681 q^{5} - 1281 q^{6} + 957 q^{7} - 10920 q^{8} - 255339 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−11.0082			−0.486499			−0.243250	−	0.969964i	\(-0.578213\pi\)
							−0.243250	+	0.969964i	\(0.578213\pi\)
\(3\)	−0.196357	−	0.340100i	−0.00139959	−	0.00242416i	0.865325	−	0.501212i	\(-0.167112\pi\)
							−0.866724	+	0.498787i	\(0.833779\pi\)
\(5\)	−1072.23	−	1857.16i	−0.767227	−	1.32888i	−0.939061	−	0.343750i	\(-0.888303\pi\)
							0.171835	−	0.985126i	\(-0.445031\pi\)
\(7\)	3698.39	−	6405.81i	0.582200	−	1.00840i	−0.413018	−	0.910723i	\(-0.635525\pi\)
							0.995218	−	0.0976769i	\(-0.0311412\pi\)
\(11\)	−22256.9			−0.458351			−0.229176	−	0.973385i	\(-0.573603\pi\)
							−0.229176	+	0.973385i	\(0.573603\pi\)
\(13\)	−26087.3	+	45184.5i	−0.253329	+	0.438778i	−0.964440	−	0.264301i	\(-0.914859\pi\)
							0.711112	+	0.703079i	\(0.248192\pi\)
\(17\)	78745.5	−	136391.i	0.228668	−	0.396065i	−0.728745	−	0.684785i	\(-0.759896\pi\)
							0.957414	+	0.288720i	\(0.0932296\pi\)
\(19\)	−411179.	−	712183.i	−0.723835	−	1.25372i	−0.959452	−	0.281873i	\(-0.909044\pi\)
							0.235617	−	0.971846i	\(-0.424289\pi\)
\(23\)	−838605.	−	1.45251e6i	−0.624859	−	1.08229i	−0.988568	−	0.150775i	\(-0.951823\pi\)
							0.363709	−	0.931513i	\(-0.381510\pi\)
\(29\)	−1.78342e6	+	3.08897e6i	−0.468233	+	0.811004i	−0.999341	−	0.0363007i	\(-0.988443\pi\)
							0.531108	+	0.847304i	\(0.321776\pi\)
\(31\)	1.79439e6	+	3.10797e6i	0.348971	+	0.604435i	0.986067	−	0.166349i	\(-0.0531979\pi\)
							−0.637096	+	0.770784i	\(0.719865\pi\)
\(37\)	−1.48951e6	−	2.57991e6i	−0.130658	−	0.226306i	0.793272	−	0.608867i	\(-0.208376\pi\)
							−0.923930	+	0.382561i	\(0.875042\pi\)
\(41\)	−3.19453e6			−0.176555			−0.0882774	−	0.996096i	\(-0.528136\pi\)
							−0.0882774	+	0.996096i	\(0.528136\pi\)
\(43\)	5.15455e6	+	2.18180e7i	0.229923	+	0.973209i
							\(47\)	4.11426e7			1.22985			0.614924	−	0.788587i	\(-0.289187\pi\)
0.614924	+	0.788587i	\(0.289187\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.c.a.36.13	yes	64
43.6	even	3	inner	43.10.c.a.6.13	✓	64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.c.a.6.13	✓	64	43.6	even	3	inner
43.10.c.a.36.13	yes	64	1.1	even	1	trivial