Embedded newform 105.4.q.b.4.3

• Label: 105.4.q.b.4.3
• 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			4.3
Character	\(\chi\)	\(=\)	105.4
Dual form			105.4.q.b.79.3

$q$-expansion

\(f(q)\)	\(=\)	\(q+(-3.89316 + 2.24772i) q^{2} +(2.59808 + 1.50000i) q^{3} +(6.10447 - 10.5732i) q^{4} +(-0.533135 - 11.1676i) q^{5} -13.4863 q^{6} +(-3.71892 + 18.1430i) q^{7} +18.9210i q^{8} +(4.50000 + 7.79423i) q^{9} +O(q^{10})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 62 q^{4} - 4 q^{5} + 108 q^{6} + 198 q^{9}+O(q^{10}) \)

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)

\(p\)	\(a_p\)			\(a_p / p^{(k-1)/2}\)			\( \alpha_p\)			\( \theta_p \)
\(2\)	−3.89316	+	2.24772i	−1.37644	+	0.794688i	−0.991729	−	0.128349i	\(-0.959032\pi\)
							−0.384711	+	0.923037i	\(0.625699\pi\)
\(3\)	2.59808	+	1.50000i	0.500000	+	0.288675i
							\(5\)	−0.533135	−	11.1676i	−0.0476851	−	0.998862i
\(7\)	−3.71892	+	18.1430i	−0.200803	+	0.979632i
							\(11\)	−11.2260	+	19.4440i	−0.307707	+	0.532963i	−0.977860	−	0.209259i	\(-0.932895\pi\)
0.670154	+	0.742222i	\(0.266228\pi\)
\(13\)			70.4777i			1.50361i	0.659383	+	0.751807i	\(0.270818\pi\)
							−0.659383	+	0.751807i	\(0.729182\pi\)
\(17\)	−52.3790	−	30.2411i	−0.747281	−	0.431443i	0.0774294	−	0.996998i	\(-0.475329\pi\)
							−0.824711	+	0.565555i	\(0.808662\pi\)
\(19\)	−18.2123	−	31.5446i	−0.219904	−	0.380886i	0.734874	−	0.678204i	\(-0.237241\pi\)
							−0.954779	+	0.297318i	\(0.903908\pi\)
\(23\)	−169.882	+	98.0815i	−1.54013	+	0.889192i	−0.541296	+	0.840832i	\(0.682066\pi\)
							−0.998830	+	0.0483598i	\(0.984601\pi\)
\(29\)	144.503			0.925293			0.462647	−	0.886543i	\(-0.346900\pi\)
							0.462647	+	0.886543i	\(0.346900\pi\)
\(31\)	−88.3619	+	153.047i	−0.511944	+	0.886713i	0.487960	+	0.872866i	\(0.337741\pi\)
							−0.999904	+	0.0138468i	\(0.995592\pi\)
\(37\)	190.243	−	109.837i	0.845290	−	0.488029i	−0.0137686	−	0.999905i	\(-0.504383\pi\)
							0.859059	+	0.511877i	\(0.171050\pi\)
\(41\)	157.341			0.599332			0.299666	−	0.954044i	\(-0.403125\pi\)
							0.299666	+	0.954044i	\(0.403125\pi\)
\(43\)			99.6949i			0.353566i	0.984250	+	0.176783i	\(0.0565690\pi\)
							−0.984250	+	0.176783i	\(0.943431\pi\)
\(47\)	−372.040	+	214.798i	−1.15463	+	0.666626i	−0.950011	−	0.312215i	\(-0.898929\pi\)
							−0.204619	+	0.978842i	\(0.565596\pi\)

(See \(a_n\) instead)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.q.b.4.3	✓	44
5.4	even	2	inner	105.4.q.b.4.20	yes	44
7.2	even	3	inner	105.4.q.b.79.20	yes	44
35.9	even	6	inner	105.4.q.b.79.3	yes	44

    

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.q.b.4.3	✓	44	1.1	even	1	trivial
105.4.q.b.4.20	yes	44	5.4	even	2	inner
105.4.q.b.79.3	yes	44	35.9	even	6	inner
105.4.q.b.79.20	yes	44	7.2	even	3	inner