Embedded newform 43.6.e.a.11.10

• Label: 43.6.e.a.11.10
• Level: $43$
• Weight: $6$
• Character: 43.11
• 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			11.10
Character	\(\chi\)	\(=\)	43.11
Dual form			43.6.e.a.4.10

$q$-expansion

\(f(q)\)	\(=\)	\(q+(0.186655 + 0.234058i) q^{2} +(-17.0687 + 21.4035i) q^{3} +(7.10073 - 31.1103i) q^{4} +(-36.3074 + 17.4847i) q^{5} -8.19562 q^{6} +50.2807 q^{7} +(17.2382 - 8.30146i) q^{8} +(-112.696 - 493.753i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 3 q^{2} - 9 q^{3} - 331 q^{4} + 67 q^{5} - 20 q^{6} - 624 q^{7} + 589 q^{8} - 579 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{5}{7}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	0.186655	+	0.234058i	0.0329962	+	0.0413760i	0.798056	−	0.602584i	\(-0.205862\pi\)
							−0.765060	+	0.643959i	\(0.777291\pi\)
\(3\)	−17.0687	+	21.4035i	−1.09496	+	1.37304i	−0.173375	+	0.984856i	\(0.555467\pi\)
							−0.921584	+	0.388179i	\(0.873104\pi\)
\(5\)	−36.3074	+	17.4847i	−0.649486	+	0.312776i	−0.729463	−	0.684021i	\(-0.760230\pi\)
							0.0799764	+	0.996797i	\(0.474516\pi\)
\(7\)	50.2807			0.387843			0.193922	−	0.981017i	\(-0.437879\pi\)
							0.193922	+	0.981017i	\(0.437879\pi\)
\(11\)	−100.713	−	441.253i	−0.250960	−	1.09953i	−0.930616	−	0.365997i	\(-0.880728\pi\)
							0.679656	−	0.733531i	\(-0.262129\pi\)
\(13\)	894.852	−	430.938i	1.46856	−	0.707223i	0.482858	−	0.875699i	\(-0.339599\pi\)
							0.985706	+	0.168476i	\(0.0538844\pi\)
\(17\)	−1430.54	−	688.910i	−1.20054	−	0.578150i	−0.276711	−	0.960953i	\(-0.589244\pi\)
							−0.923830	+	0.382804i	\(0.874959\pi\)
\(19\)	−308.765	+	1352.79i	−0.196221	+	0.859698i	0.776941	+	0.629574i	\(0.216771\pi\)
							−0.973161	+	0.230125i	\(0.926087\pi\)
\(23\)	−512.109	−	2243.70i	−0.201857	−	0.884392i	−0.969805	−	0.243880i	\(-0.921580\pi\)
							0.767949	−	0.640511i	\(-0.221278\pi\)
\(29\)	−3699.43	−	4638.94i	−0.816846	−	1.02429i	−0.999157	−	0.0410519i	\(-0.986929\pi\)
							0.182311	−	0.983241i	\(-0.441642\pi\)
\(31\)	3757.82	+	4712.16i	0.702314	+	0.880674i	0.997194	−	0.0748599i	\(-0.0238510\pi\)
							−0.294880	+	0.955534i	\(0.595280\pi\)
\(37\)	−729.331			−0.0875831			−0.0437916	−	0.999041i	\(-0.513944\pi\)
							−0.0437916	+	0.999041i	\(0.513944\pi\)
\(41\)	−6481.09	−	8127.03i	−0.602127	−	0.755044i	0.383580	−	0.923507i	\(-0.374691\pi\)
							−0.985708	+	0.168464i	\(0.946119\pi\)
\(43\)	−2894.51	−	11774.1i	−0.238728	−	0.971086i
							\(47\)	2619.36	−	11476.2i	0.172962	−	0.757797i	−0.811806	−	0.583927i	\(-0.801516\pi\)
0.984769	−	0.173870i	\(-0.0556273\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.e.a.11.10	yes	108
43.4	even	7	inner	43.6.e.a.4.10	✓	108

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.e.a.4.10	✓	108	43.4	even	7	inner
43.6.e.a.11.10	yes	108	1.1	even	1	trivial