Embedded newform 105.4.q.b.4.14

• Label: 105.4.q.b.4.14
• Level: $105$
• Weight: $4$
• Character: 105.4
• Analytic conductor: $6.195$
• Analytic rank: $0$
• Dimension: $44$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.q (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.19520055060\)
Analytic rank:	\(0\)
Dimension:	\(44\)
Relative dimension:	\(22\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.14
Character	\(\chi\)	\(=\)	105.4
Dual form			105.4.q.b.79.14

$q$-expansion

\(f(q)\)	\(=\)	\(q+(1.50072 - 0.866440i) q^{2} +(2.59808 + 1.50000i) q^{3} +(-2.49856 + 4.32764i) q^{4} +(-8.24745 + 7.54848i) q^{5} +5.19864 q^{6} +(14.9159 - 10.9780i) q^{7} +22.5225i q^{8} +(4.50000 + 7.79423i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 62 q^{4} - 4 q^{5} + 108 q^{6} + 198 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\)	\(22\)	\(31\)	\(71\)
\(\chi(n)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	1.50072	−	0.866440i	0.530584	−	0.306333i	−0.210670	−	0.977557i	\(-0.567565\pi\)
							0.741254	+	0.671224i	\(0.234231\pi\)
\(3\)	2.59808	+	1.50000i	0.500000	+	0.288675i
							\(5\)	−8.24745	+	7.54848i	−0.737675	+	0.675156i
\(7\)	14.9159	−	10.9780i	0.805381	−	0.592758i
							\(11\)	−16.1754	+	28.0167i	−0.443370	+	0.767940i	−0.997937	−	0.0641992i	\(-0.979551\pi\)
0.554567	+	0.832139i	\(0.312884\pi\)
\(13\)			71.5312i			1.52609i	0.646345	+	0.763046i	\(0.276297\pi\)
							−0.646345	+	0.763046i	\(0.723703\pi\)
\(17\)	79.8568	+	46.1053i	1.13930	+	0.657776i	0.946257	−	0.323415i	\(-0.104831\pi\)
							0.193043	+	0.981190i	\(0.438164\pi\)
\(19\)	−69.3346	−	120.091i	−0.837182	−	1.45004i	−0.892241	−	0.451559i	\(-0.850868\pi\)
							0.0550595	−	0.998483i	\(-0.482465\pi\)
\(23\)	104.876	−	60.5505i	0.950794	−	0.548941i	0.0574664	−	0.998347i	\(-0.481698\pi\)
							0.893327	+	0.449406i	\(0.148364\pi\)
\(29\)	−4.48704			−0.0287318			−0.0143659	−	0.999897i	\(-0.504573\pi\)
							−0.0143659	+	0.999897i	\(0.504573\pi\)
\(31\)	9.30002	−	16.1081i	0.0538817	−	0.0933259i	−0.837826	−	0.545937i	\(-0.816174\pi\)
							0.891708	+	0.452611i	\(0.149507\pi\)
\(37\)	237.287	−	136.997i	1.05432	−	0.608709i	0.130461	−	0.991453i	\(-0.458354\pi\)
							0.923854	+	0.382744i	\(0.125021\pi\)
\(41\)	168.038			0.640077			0.320038	−	0.947405i	\(-0.396304\pi\)
							0.320038	+	0.947405i	\(0.396304\pi\)
\(43\)		−	176.871i		−	0.627269i	−0.949544	−	0.313635i	\(-0.898453\pi\)
							0.949544	−	0.313635i	\(-0.101547\pi\)
\(47\)	−151.771	+	87.6250i	−0.471023	+	0.271945i	−0.716668	−	0.697415i	\(-0.754334\pi\)
							0.245645	+	0.969360i	\(0.421000\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.q.b.4.14	yes	44
5.4	even	2	inner	105.4.q.b.4.9	✓	44
7.2	even	3	inner	105.4.q.b.79.9	yes	44
35.9	even	6	inner	105.4.q.b.79.14	yes	44

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.q.b.4.9	✓	44	5.4	even	2	inner
105.4.q.b.4.14	yes	44	1.1	even	1	trivial
105.4.q.b.79.9	yes	44	7.2	even	3	inner
105.4.q.b.79.14	yes	44	35.9	even	6	inner