Embedded newform 43.11.d.a.7.10

• Label: 43.11.d.a.7.10
• Level: $43$
• Weight: $11$
• Character: 43.7
• Analytic conductor: $27.320$
• Analytic rank: $0$
• Dimension: $72$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(27.3203618650\)
Analytic rank:	\(0\)
Dimension:	\(72\)
Relative dimension:	\(36\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			7.10
Character	\(\chi\)	\(=\)	43.7
Dual form			43.11.d.a.37.27

$q$-expansion

\(f(q)\)	\(=\)	\(q-35.7982i q^{2} +(113.973 - 65.8024i) q^{3} -257.513 q^{4} +(-2374.16 + 1370.72i) q^{5} +(-2355.61 - 4080.03i) q^{6} +(-18980.1 - 10958.2i) q^{7} -27438.9i q^{8} +(-20864.6 + 36138.5i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 246 q^{3} - 38122 q^{4} - 3 q^{5} + 8511 q^{6} + 31377 q^{7} + 675876 q^{9}+O(q^{10}) \)

Character values

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

\(n\)	\(3\)
\(\chi(n)\)	\(e\left(\frac{5}{6}\right)\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)		−	35.7982i		−	1.11869i	−0.828933	−	0.559347i	\(-0.811052\pi\)
							0.828933	−	0.559347i	\(-0.188948\pi\)
\(3\)	113.973	−	65.8024i	0.469025	−	0.270792i	−0.246807	−	0.969065i	\(-0.579381\pi\)
							0.715831	+	0.698273i	\(0.246048\pi\)
\(5\)	−2374.16	+	1370.72i	−0.759732	+	0.438631i	−0.829199	−	0.558953i	\(-0.811203\pi\)
							0.0694676	+	0.997584i	\(0.477870\pi\)
\(7\)	−18980.1	−	10958.2i	−1.12930	−	0.652001i	−0.185541	−	0.982637i	\(-0.559404\pi\)
							−0.943759	+	0.330635i	\(0.892737\pi\)
\(11\)	133645.			0.829832			0.414916	−	0.909860i	\(-0.363811\pi\)
							0.414916	+	0.909860i	\(0.363811\pi\)
\(13\)	149767.	−	259404.i	0.403366	−	0.698650i	−0.590764	−	0.806844i	\(-0.701174\pi\)
							0.994130	+	0.108194i	\(0.0345069\pi\)
\(17\)	−1.16735e6	+	2.02190e6i	−0.822158	+	1.42402i	0.0819148	+	0.996639i	\(0.473896\pi\)
							−0.904072	+	0.427379i	\(0.859437\pi\)
\(19\)	−242035.	+	139739.i	−0.0977486	+	0.0564352i	−0.548077	−	0.836428i	\(-0.684640\pi\)
							0.450329	+	0.892863i	\(0.351307\pi\)
\(23\)	5.37401e6	+	9.30806e6i	0.834948	+	1.44617i	0.894073	+	0.447921i	\(0.147835\pi\)
							−0.0591254	+	0.998251i	\(0.518831\pi\)
\(29\)	−6.12050e6	−	3.53367e6i	−0.298399	−	0.172280i	0.343325	−	0.939217i	\(-0.388447\pi\)
							−0.641723	+	0.766936i	\(0.721780\pi\)
\(31\)	−2.33045e6	−	4.03647e6i	−0.0814015	−	0.140991i	0.822451	−	0.568836i	\(-0.192606\pi\)
							−0.903852	+	0.427845i	\(0.859273\pi\)
\(37\)	−7.61741e7	+	4.39792e7i	−1.09850	+	0.634218i	−0.935826	−	0.352463i	\(-0.885344\pi\)
							−0.162671	+	0.986680i	\(0.552011\pi\)
\(41\)	2.11016e8			1.82136			0.910681	−	0.413111i	\(-0.135558\pi\)
							0.910681	+	0.413111i	\(0.135558\pi\)
\(43\)	1.11445e8	+	9.58721e7i	0.758087	+	0.652154i
							\(47\)	−3.99136e8			−1.74033			−0.870166	−	0.492759i	\(-0.835988\pi\)
−0.870166	+	0.492759i	\(0.835988\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.d.a.7.10	✓	72
43.37	odd	6	inner	43.11.d.a.37.27	yes	72

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.d.a.7.10	✓	72	1.1	even	1	trivial
43.11.d.a.37.27	yes	72	43.37	odd	6	inner