Embedded newform 43.10.c.a.6.2

• Label: 43.10.c.a.6.2
• Level: $43$
• Weight: $10$
• Character: 43.6
• 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			6.2
Character	\(\chi\)	\(=\)	43.6
Dual form			43.10.c.a.36.2

$q$-expansion

\(f(q)\)	\(=\)	\(q-42.7383 q^{2} +(18.2764 - 31.6557i) q^{3} +1314.56 q^{4} +(-1010.01 + 1749.40i) q^{5} +(-781.103 + 1352.91i) q^{6} +(-3156.96 - 5468.02i) q^{7} -34300.0 q^{8} +(9173.44 + 15888.9i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 70 q^{2} + 307 q^{3} + 16038 q^{4} + 681 q^{5} - 1281 q^{6} + 957 q^{7} - 10920 q^{8} - 255339 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{2}{3}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−42.7383			−1.88878			−0.944391	−	0.328824i	\(-0.893348\pi\)
							−0.944391	+	0.328824i	\(0.893348\pi\)
\(3\)	18.2764	−	31.6557i	0.130270	−	0.225635i	−0.793510	−	0.608557i	\(-0.791749\pi\)
							0.923781	+	0.382922i	\(0.125082\pi\)
\(5\)	−1010.01	+	1749.40i	−0.722708	+	1.25177i	0.237203	+	0.971460i	\(0.423769\pi\)
							−0.959911	+	0.280306i	\(0.909564\pi\)
\(7\)	−3156.96	−	5468.02i	−0.496968	−	0.860773i	0.503026	−	0.864271i	\(-0.332220\pi\)
							−0.999994	+	0.00349798i	\(0.998887\pi\)
\(11\)	−48546.9			−0.999758			−0.499879	−	0.866095i	\(-0.666622\pi\)
							−0.499879	+	0.866095i	\(0.666622\pi\)
\(13\)	66984.7	+	116021.i	0.650475	+	1.12666i	0.983008	+	0.183564i	\(0.0587633\pi\)
							−0.332533	+	0.943092i	\(0.607903\pi\)
\(17\)	235507.	+	407909.i	0.683885	+	1.18452i	0.973786	+	0.227466i	\(0.0730442\pi\)
							−0.289901	+	0.957057i	\(0.593622\pi\)
\(19\)	230593.	−	399399.i	0.405933	−	0.703097i	−0.588496	−	0.808500i	\(-0.700280\pi\)
							0.994430	+	0.105403i	\(0.0336132\pi\)
\(23\)	−260785.	+	451694.i	−0.194316	+	0.336565i	−0.946676	−	0.322187i	\(-0.895582\pi\)
							0.752360	+	0.658752i	\(0.228915\pi\)
\(29\)	−727214.	−	1.25957e6i	−0.190929	−	0.330698i	0.754630	−	0.656151i	\(-0.227817\pi\)
							−0.945558	+	0.325453i	\(0.894483\pi\)
\(31\)	784.333	−	1358.50i	0.000152536	−	0.000264200i	−0.865949	−	0.500132i	\(-0.833285\pi\)
							0.866102	+	0.499868i	\(0.166618\pi\)
\(37\)	−1.02987e7	+	1.78378e7i	−0.903384	+	1.56471i	−0.0803132	+	0.996770i	\(0.525592\pi\)
							−0.823071	+	0.567938i	\(0.807741\pi\)
\(41\)	−2.46712e7			−1.36353			−0.681763	−	0.731573i	\(-0.738787\pi\)
							−0.681763	+	0.731573i	\(0.738787\pi\)
\(43\)	3.46233e6	−	2.21496e7i	0.154440	−	0.988002i
							\(47\)	−1.76884e7			−0.528747			−0.264374	−	0.964420i	\(-0.585165\pi\)
−0.264374	+	0.964420i	\(0.585165\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.c.a.6.2	✓	64
43.36	even	3	inner	43.10.c.a.36.2	yes	64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.c.a.6.2	✓	64	1.1	even	1	trivial
43.10.c.a.36.2	yes	64	43.36	even	3	inner