Embedded newform 43.10.c.a.6.18

• Label: 43.10.c.a.6.18
• 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			6.18
Character	\(\chi\)	\(=\)	43.6
Dual form			43.10.c.a.36.18

$q$-expansion

\(f(q)\)	\(=\)	\(q+2.09785 q^{2} +(102.202 - 177.020i) q^{3} -507.599 q^{4} +(-192.277 + 333.034i) q^{5} +(214.405 - 371.361i) q^{6} +(2053.75 + 3557.19i) q^{7} -2138.97 q^{8} +(-11049.2 - 19137.7i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 70 q^{2} + 307 q^{3} + 16038 q^{4} + 681 q^{5} - 1281 q^{6} + 957 q^{7} - 10920 q^{8} - 255339 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	2.09785			0.0927128			0.0463564	−	0.998925i	\(-0.485239\pi\)
							0.0463564	+	0.998925i	\(0.485239\pi\)
\(3\)	102.202	−	177.020i	0.728476	−	1.26176i	−0.229051	−	0.973414i	\(-0.573562\pi\)
							0.957527	−	0.288343i	\(-0.0931045\pi\)
\(5\)	−192.277	+	333.034i	−0.137582	+	0.238300i	−0.926581	−	0.376095i	\(-0.877267\pi\)
							0.788999	+	0.614395i	\(0.210600\pi\)
\(7\)	2053.75	+	3557.19i	0.323300	+	0.559972i	0.981167	−	0.193162i	\(-0.0618744\pi\)
							−0.657867	+	0.753134i	\(0.728541\pi\)
\(11\)	−71976.0			−1.48225			−0.741124	−	0.671368i	\(-0.765707\pi\)
							−0.741124	+	0.671368i	\(0.765707\pi\)
\(13\)	58452.9	+	101243.i	0.567624	+	0.983154i	0.996800	+	0.0799334i	\(0.0254708\pi\)
							−0.429176	+	0.903221i	\(0.641196\pi\)
\(17\)	−50468.0	−	87413.1i	−0.146553	−	0.253838i	0.783398	−	0.621520i	\(-0.213485\pi\)
							−0.929951	+	0.367683i	\(0.880151\pi\)
\(19\)	−478542.	+	828858.i	−0.842420	+	1.45911i	0.0454235	+	0.998968i	\(0.485536\pi\)
							−0.887843	+	0.460146i	\(0.847797\pi\)
\(23\)	1.31140e6	−	2.27141e6i	0.977148	−	1.69247i	0.304492	−	0.952515i	\(-0.401513\pi\)
							0.672656	−	0.739955i	\(-0.265153\pi\)
\(29\)	2.71377e6	+	4.70039e6i	0.712495	+	1.23408i	0.963918	+	0.266200i	\(0.0857683\pi\)
							−0.251422	+	0.967877i	\(0.580898\pi\)
\(31\)	−3.22702e6	+	5.58936e6i	−0.627587	+	1.08701i	0.360447	+	0.932780i	\(0.382624\pi\)
							−0.988034	+	0.154233i	\(0.950709\pi\)
\(37\)	−1.12717e6	+	1.95231e6i	−0.0988738	+	0.171254i	−0.911219	−	0.411923i	\(-0.864857\pi\)
							0.812345	+	0.583177i	\(0.198191\pi\)
\(41\)	−3.25017e7			−1.79630			−0.898149	−	0.439692i	\(-0.855088\pi\)
							−0.898149	+	0.439692i	\(0.855088\pi\)
\(43\)	1.00494e7	+	2.00400e7i	0.448261	+	0.893903i
							\(47\)	−4.35786e7			−1.30267			−0.651333	−	0.758792i	\(-0.725790\pi\)
−0.651333	+	0.758792i	\(0.725790\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.c.a.6.18	✓	64
43.36	even	3	inner	43.10.c.a.36.18	yes	64

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.c.a.6.18	✓	64	1.1	even	1	trivial
43.10.c.a.36.18	yes	64	43.36	even	3	inner