Embedded newform 43.10.c.a.36.19

• Label: 43.10.c.a.36.19
• 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			36.19
Character	\(\chi\)	\(=\)	43.36
Dual form			43.10.c.a.6.19

$q$-expansion

\(f(q)\)	\(=\)	\(q+3.31091 q^{2} +(64.4391 + 111.612i) q^{3} -501.038 q^{4} +(-994.242 - 1722.08i) q^{5} +(213.352 + 369.536i) q^{6} +(-3834.95 + 6642.33i) q^{7} -3354.07 q^{8} +(1536.70 - 2661.64i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 70 q^{2} + 307 q^{3} + 16038 q^{4} + 681 q^{5} - 1281 q^{6} + 957 q^{7} - 10920 q^{8} - 255339 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	3.31091			0.146323			0.0731614	−	0.997320i	\(-0.476691\pi\)
							0.0731614	+	0.997320i	\(0.476691\pi\)
\(3\)	64.4391	+	111.612i	0.459308	+	0.795545i	0.998925	−	0.0463661i	\(-0.0147641\pi\)
							−0.539617	+	0.841911i	\(0.681431\pi\)
\(5\)	−994.242	−	1722.08i	−0.711421	−	1.23222i	−0.964324	−	0.264726i	\(-0.914718\pi\)
							0.252902	−	0.967492i	\(-0.418615\pi\)
\(7\)	−3834.95	+	6642.33i	−0.603697	+	1.04563i	0.388559	+	0.921424i	\(0.372973\pi\)
							−0.992256	+	0.124210i	\(0.960360\pi\)
\(11\)	56849.2			1.17073			0.585366	−	0.810769i	\(-0.300951\pi\)
							0.585366	+	0.810769i	\(0.300951\pi\)
\(13\)	31462.4	−	54494.4i	0.305525	−	0.529184i	−0.671853	−	0.740684i	\(-0.734502\pi\)
							0.977378	+	0.211500i	\(0.0678349\pi\)
\(17\)	−33278.7	+	57640.4i	−0.0966376	+	0.167381i	−0.910291	−	0.413969i	\(-0.864142\pi\)
							0.813653	+	0.581350i	\(0.197475\pi\)
\(19\)	343804.	+	595487.i	0.605230	+	1.04829i	0.992015	+	0.126119i	\(0.0402521\pi\)
							−0.386785	+	0.922170i	\(0.626415\pi\)
\(23\)	−93712.2	−	162314.i	−0.0698266	−	0.120943i	0.828998	−	0.559251i	\(-0.188911\pi\)
							−0.898825	+	0.438308i	\(0.855578\pi\)
\(29\)	2.36009e6	−	4.08780e6i	0.619638	−	1.07325i	−0.369913	−	0.929066i	\(-0.620613\pi\)
							0.989552	−	0.144179i	\(-0.0460540\pi\)
\(31\)	419930.	+	727340.i	0.0816675	+	0.141452i	0.903966	−	0.427604i	\(-0.140642\pi\)
							−0.822299	+	0.569056i	\(0.807309\pi\)
\(37\)	−1.90633e6	−	3.30187e6i	−0.167221	−	0.289635i	0.770221	−	0.637777i	\(-0.220146\pi\)
							−0.937442	+	0.348142i	\(0.886813\pi\)
\(41\)	1.88228e7			1.04030			0.520149	−	0.854076i	\(-0.325876\pi\)
							0.520149	+	0.854076i	\(0.325876\pi\)
\(43\)	−1.72113e7	−	1.43654e7i	−0.767725	−	0.640780i
							\(47\)	4.22243e7			1.26218			0.631091	−	0.775709i	\(-0.282607\pi\)
0.631091	+	0.775709i	\(0.282607\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.c.a.36.19	yes	64
43.6	even	3	inner	43.10.c.a.6.19	✓	64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.c.a.6.19	✓	64	43.6	even	3	inner
43.10.c.a.36.19	yes	64	1.1	even	1	trivial