Embedded newform 105.4.q.b.4.6

• Label: 105.4.q.b.4.6
• 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			4.6
Character	\(\chi\)	\(=\)	105.4
Dual form			105.4.q.b.79.6

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-2.21373 + 1.27810i) q^{2} +(2.59808 + 1.50000i) q^{3} +(-0.732945 + 1.26950i) q^{4} +(5.74885 - 9.58910i) q^{5} -7.66857 q^{6} +(-2.98784 - 18.2777i) q^{7} -24.1966i q^{8} +(4.50000 + 7.79423i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 62 q^{4} - 4 q^{5} + 108 q^{6} + 198 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−2.21373	+	1.27810i	−0.782670	+	0.451875i	−0.837376	−	0.546628i	\(-0.815911\pi\)
							0.0547055	+	0.998503i	\(0.482578\pi\)
\(3\)	2.59808	+	1.50000i	0.500000	+	0.288675i
							\(5\)	5.74885	−	9.58910i	0.514192	−	0.857675i
\(7\)	−2.98784	−	18.2777i	−0.161328	−	0.986901i
							\(11\)	0.664331	−	1.15066i	0.0182094	−	0.0315396i	−0.856777	−	0.515687i	\(-0.827537\pi\)
0.874987	+	0.484147i	\(0.160870\pi\)
\(13\)		−	46.0431i		−	0.982313i	−0.871071	−	0.491156i	\(-0.836574\pi\)
							0.871071	−	0.491156i	\(-0.163426\pi\)
\(17\)	77.3228	+	44.6423i	1.10315	+	0.636903i	0.937046	−	0.349205i	\(-0.113548\pi\)
							0.166102	+	0.986109i	\(0.446882\pi\)
\(19\)	−27.1979	−	47.1082i	−0.328402	−	0.568809i	0.653793	−	0.756673i	\(-0.273177\pi\)
							−0.982195	+	0.187865i	\(0.939843\pi\)
\(23\)	132.406	−	76.4445i	1.20037	−	0.693034i	0.239732	−	0.970839i	\(-0.422940\pi\)
							0.960637	+	0.277806i	\(0.0896071\pi\)
\(29\)	154.664			0.990359			0.495180	−	0.868791i	\(-0.335102\pi\)
							0.495180	+	0.868791i	\(0.335102\pi\)
\(31\)	−57.7388	+	100.007i	−0.334523	+	0.579410i	−0.983393	−	0.181489i	\(-0.941908\pi\)
							0.648870	+	0.760899i	\(0.275242\pi\)
\(37\)	−112.360	+	64.8710i	−0.499239	+	0.288236i	−0.728399	−	0.685153i	\(-0.759735\pi\)
							0.229160	+	0.973389i	\(0.426402\pi\)
\(41\)	−128.188			−0.488283			−0.244141	−	0.969740i	\(-0.578506\pi\)
							−0.244141	+	0.969740i	\(0.578506\pi\)
\(43\)		−	428.881i		−	1.52102i	−0.649328	−	0.760508i	\(-0.724950\pi\)
							0.649328	−	0.760508i	\(-0.275050\pi\)
\(47\)	−487.253	+	281.316i	−1.51220	+	0.873067i	−0.512298	+	0.858808i	\(0.671206\pi\)
							−0.999898	+	0.0142588i	\(0.995461\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.q.b.4.6	✓	44
5.4	even	2	inner	105.4.q.b.4.17	yes	44
7.2	even	3	inner	105.4.q.b.79.17	yes	44
35.9	even	6	inner	105.4.q.b.79.6	yes	44

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.q.b.4.6	✓	44	1.1	even	1	trivial
105.4.q.b.4.17	yes	44	5.4	even	2	inner
105.4.q.b.79.6	yes	44	35.9	even	6	inner
105.4.q.b.79.17	yes	44	7.2	even	3	inner