Embedded newform 43.6.e.a.4.8

• Label: 43.6.e.a.4.8
• Level: $43$
• Weight: $6$
• Character: 43.4
• Analytic conductor: $6.897$
• Analytic rank: $0$
• Dimension: $108$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	43.e (of order \(7\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.89650425196\)
Analytic rank:	\(0\)
Dimension:	\(108\)
Relative dimension:	\(18\) over \(\Q(\zeta_{7})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			4.8
Character	\(\chi\)	\(=\)	43.4
Dual form			43.6.e.a.11.8

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-1.82630 + 2.29011i) q^{2} +(-7.90210 - 9.90892i) q^{3} +(5.21144 + 22.8328i) q^{4} +(-7.91873 - 3.81346i) q^{5} +37.1242 q^{6} +25.4167 q^{7} +(-146.258 - 70.4342i) q^{8} +(18.3291 - 80.3048i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 3 q^{2} - 9 q^{3} - 331 q^{4} + 67 q^{5} - 20 q^{6} - 624 q^{7} + 589 q^{8} - 579 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{2}{7}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−1.82630	+	2.29011i	−0.322848	+	0.404839i	−0.916597	−	0.399811i	\(-0.869076\pi\)
							0.593749	+	0.804650i	\(0.297647\pi\)
\(3\)	−7.90210	−	9.90892i	−0.506920	−	0.635658i	0.460855	−	0.887476i	\(-0.347543\pi\)
							−0.967775	+	0.251818i	\(0.918972\pi\)
\(5\)	−7.91873	−	3.81346i	−0.141655	−	0.0682172i	0.361714	−	0.932289i	\(-0.382192\pi\)
							−0.503368	+	0.864072i	\(0.667906\pi\)
\(7\)	25.4167			0.196053			0.0980266	−	0.995184i	\(-0.468747\pi\)
							0.0980266	+	0.995184i	\(0.468747\pi\)
\(11\)	132.390	−	580.039i	0.329893	−	1.44536i	−0.489438	−	0.872038i	\(-0.662798\pi\)
							0.819332	−	0.573320i	\(-0.194345\pi\)
\(13\)	−615.567	−	296.441i	−1.01022	−	0.486497i	−0.145827	−	0.989310i	\(-0.546584\pi\)
							−0.864395	+	0.502813i	\(0.832298\pi\)
\(17\)	2062.99	−	993.486i	1.73131	−	0.833757i	0.745375	−	0.666645i	\(-0.232270\pi\)
							0.985938	−	0.167112i	\(-0.0534441\pi\)
\(19\)	−310.472	−	1360.27i	−0.197305	−	0.864451i	−0.972532	−	0.232768i	\(-0.925222\pi\)
							0.775227	−	0.631683i	\(-0.217636\pi\)
\(23\)	−586.870	+	2571.24i	−0.231325	+	1.01350i	0.717218	+	0.696849i	\(0.245415\pi\)
							−0.948542	+	0.316651i	\(0.897442\pi\)
\(29\)	−2299.64	+	2883.66i	−0.507768	+	0.636721i	−0.967962	−	0.251098i	\(-0.919208\pi\)
							0.460194	+	0.887818i	\(0.347780\pi\)
\(31\)	−1052.61	+	1319.93i	−0.196726	+	0.246687i	−0.870404	−	0.492339i	\(-0.836142\pi\)
							0.673678	+	0.739025i	\(0.264714\pi\)
\(37\)	13410.6			1.61043			0.805216	−	0.592981i	\(-0.202049\pi\)
							0.805216	+	0.592981i	\(0.202049\pi\)
\(41\)	−6778.62	+	8500.12i	−0.629770	+	0.789706i	−0.989682	−	0.143280i	\(-0.954235\pi\)
							0.359913	+	0.932986i	\(0.382806\pi\)
\(43\)	391.502	−	12118.4i	0.0322896	−	0.999479i
							\(47\)	−2416.80	−	10588.7i	−0.159587	−	0.699195i	−0.989885	−	0.141875i	\(-0.954687\pi\)
0.830298	−	0.557320i	\(-0.188170\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.e.a.4.8	✓	108
43.11	even	7	inner	43.6.e.a.11.8	yes	108

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.e.a.4.8	✓	108	1.1	even	1	trivial
43.6.e.a.11.8	yes	108	43.11	even	7	inner